\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\@writefile{toc}{\contentsline {paragraph}{Statement of scope:}{1}{section*.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF}{1}{section*.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Executive Summary}{1}{section*.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{UTFANSWF v21 --- Cosmology Update and Row 20 Resolution}{2}{section*.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Versioning Rationale (v22).}{2}{section*.5}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Motivation.}{2}{section*.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Diagnosis.}{2}{section*.7}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{v21 Correction (Structural, Constraint-Preserving).}{2}{section*.8}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Validation Outcome.}{3}{section*.9}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{v22 Interpretation.}{3}{section*.10}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Derivation of Distributed Hubble Parameter}{3}{section*.11}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{4}{section*.12}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Continuity.}{4}{section*.13}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{ }{5}{section*.18}\protected@file@percent }
\newlabel{sec:math_innovations}{{}{6}{Mathematical Innovations within UTFANSWF}{section*.20}{}}
\@writefile{toc}{\contentsline {paragraph}{Conic Neutral Zone (NZ) Geometry with Dual Certificates.}{6}{section*.23}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Fisher--Rao Information Geometry on the Repair Manifold.}{7}{section*.25}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Entropy--Fisher Cross--Metric.}{7}{section*.26}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate Tensor Composition (CFGL Monoidal Closure).}{7}{section*.28}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Category--Functor Gate Logic (CFGL) as a Monoidal Enriched Category.}{8}{section*.29}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Refractal Operator and Energy Law.}{8}{section*.31}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Tight--Frame Stability (HB Parseval).}{9}{section*.32}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{QND--in--NZ Read (Mode Matching).}{9}{section*.33}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Refractal Robustness Inequality.}{9}{section*.34}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Reaction--Path (Sensitivity) Matrix.}{9}{section*.36}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Regularized NZ--Constrained Update.}{9}{section*.37}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate Decision (Pass / Repair / Fail).}{10}{section*.38}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Entropy--Geometry Alignment (Ellipsoid Check).}{10}{section*.39}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Identifiability Condition.}{10}{section*.40}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Pass/Fail Tiering Framework.}{10}{section*.41}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces UTFANSWF v22 Pass/Fail Tiering. \textbf  {Critical} gates must pass; \textbf  {Diagnostic} gates log and revisit; \textbf  {Informational} gates are non-blocking.}}{11}{table.caption.43}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Dynamic Repair Flow (Refractal ODE).}{12}{section*.44}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces v22 Predictions — The Reactivation Phase}}{12}{table.caption.45}\protected@file@percent }
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{tab:v19_predictions_boxed}{{2}{12}{v22 Predictions — The Reactivation Phase}{table.caption.45}{}}
\newlabel{sec:v19_key_predictions_gates}{{}{13}{Key Falsifiable Predictions and Consistency Gates (v22)}{section*.46}{}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces v22 Key Falsifiable Predictions \& Consistency Gates (boxed).}}{13}{table.caption.47}\protected@file@percent }
\newlabel{tab:v19_key_pf_gates}{{3}{13}{v22 Key Falsifiable Predictions \& Consistency Gates (boxed)}{table.caption.47}{}}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{31}{section.1}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {2}Acronyms}{31}{section.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {3}Zero State (ZS)}{31}{section.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Absence to Structure.}{31}{section*.48}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Axiomatic Definition}{32}{subsection.3.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Immediate Consequences}{32}{subsection.3.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Constraint-Induced Structure}{32}{subsection.3.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Kernel Construction}{33}{subsection.3.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Entropy Maximization}{33}{subsection.3.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Wavefunctional Construction}{34}{subsection.3.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretive Note.}{34}{section*.49}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {4}SWF--ISM Workup: Foundations, Symmetry Adaptation, and EFT Embedding}{34}{section.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Zero State to Information Structure.}{34}{section*.50}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Acronyms (fixed).}{34}{section*.51}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Neutral solution: ANSWF.}{35}{section*.53}\protected@file@percent }
\newlabel{eq:expfamily}{{39}{35}{Neutral solution: ANSWF}{equation.39}{}}
\@writefile{toc}{\contentsline {paragraph}{(i) ANSWF by maximum entropy.}{37}{section*.59}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(ii) SANSWF with axial symmetry and fixed quadrupole.}{37}{section*.60}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(iii) Positivity sign test (toy).}{37}{section*.61}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{38}{section*.63}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {5}SWF-ISM: Information-Theoretic Foundations}{38}{section.5}\protected@file@percent }
\newlabel{sec:swfism}{{5}{38}{SWF-ISM: Information-Theoretic Foundations}{section.5}{}}
\newlabel{eq:gaussian}{{49}{38}{SWF-ISM: Information-Theoretic Foundations}{equation.49}{}}
\newlabel{eq:S0}{{50}{38}{SWF-ISM: Information-Theoretic Foundations}{equation.50}{}}
\newlabel{eq:spectral}{{51}{38}{SWF-ISM: Information-Theoretic Foundations}{equation.51}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6}ANSWF: EFT Positivity and Constraints}{38}{section.6}\protected@file@percent }
\newlabel{sec:eft-gates}{{6}{38}{ANSWF: EFT Positivity and Constraints}{section.6}{}}
\@writefile{toc}{\contentsline {paragraph}{From Information Structure to Physical Constraints.}{38}{section*.64}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Scattering amplitudes and analyticity.}{39}{section*.65}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Positivity from the optical theorem.}{39}{section*.66}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Implications for the effective field theory.}{39}{section*.67}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation within UTFANSWF.}{39}{section*.68}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {7}SANSWF: Symmetry-Augmented Layer}{40}{section.7}\protected@file@percent }
\newlabel{sec:sanswf}{{7}{40}{SANSWF: Symmetry-Augmented Layer}{section.7}{}}
\@writefile{toc}{\contentsline {paragraph}{From Consistency to Symmetry Enforcement.}{40}{section*.69}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gauge covariance.}{40}{section*.70}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Mass generation and symmetry breaking.}{40}{section*.71}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Scalar sector and bounded-from-below stability.}{40}{section*.72}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Perturbative unitarity.}{41}{section*.73}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation within UTFANSWF.}{41}{section*.74}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {8}UTFANSWF Proper: SU(5) and Seesaw Embedding}{41}{section.8}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Symmetry Enforcement to Unification.}{41}{section*.75}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Field content and representation structure.}{41}{section*.76}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Neutrino masses via Type-I seesaw.}{42}{section*.77}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Renormalization group evolution and unification.}{42}{section*.78}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Schematic gauge coupling running indicating approximate unification near $\mu \!\sim \!10^{16}$ GeV.}}{42}{figure.caption.79}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Threshold corrections and heavy scales.}{43}{section*.80}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Proton decay constraints.}{43}{section*.81}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Median proton lifetime $\tau _p$ vs heavy Higgs triplet mass $M_{HC}$ (scaled).}}{43}{figure.caption.82}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Seesaw Yukawa constraints.}{44}{section*.83}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Seesaw Yukawa upper bound $\|Y_\nu \|_{\max }$ vs right-handed neutrino mass $M_R$.}}{44}{figure.caption.84}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation within UTFANSWF.}{44}{section*.85}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {9}Predictions and SMEFT Matching}{45}{section.9}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Unified Embedding to Observable Predictions.}{45}{section*.86}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Heavy field integration and operator matching.}{45}{section*.87}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation of Wilson coefficients.}{45}{section*.88}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Radiative corrections and vacuum structure.}{45}{section*.89}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Coleman--Weinberg effective potential (schematic) illustrating radiative flattening and stability inside the BFB cone.}}{46}{figure.caption.90}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Stability and UTFANSWF consistency.}{46}{section*.91}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation within UTFANSWF.}{46}{section*.92}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {10}Conditional TCC Compliance and Inflation Gates}{47}{section.10}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Cosmological Embedding to Consistency Bounds.}{47}{section*.93}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Slow-roll dynamics and observable parameters.}{47}{section*.94}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Trans-Planckian Censorship Conjecture (TCC).}{47}{section*.95}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Implications for inflationary scale.}{47}{section*.97}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Strict TCC upper bound on the tensor-to-scalar ratio $r$ vs e-folds $N$.}}{48}{figure.caption.96}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Inflationary scale $V^{1/4}$ vs $r$ from slow-roll consistency relations.}}{48}{figure.caption.98}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF gate interpretation.}{48}{section*.99}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Role within the framework.}{49}{section*.100}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {11}Conditional TCC Compliance and Inflation Gates (Updated)}{49}{section.11}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inflation as a constrained gate.}{49}{section*.101}\protected@file@percent }
\newlabel{sec:TCC-gates}{{11}{49}{Inflation as a constrained gate}{section*.101}{}}
\@writefile{toc}{\contentsline {paragraph}{Slow-roll identities.}{49}{section*.102}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Strict TCC bound.}{49}{section*.103}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Strict TCC upper bound on \(r\) and corresponding maxima for \(H\) and \(V^{1/4}\) at \(A_s=2.1\times 10^{-9}\).}}{50}{table.caption.104}\protected@file@percent }
\newlabel{tab:TCC-r}{{4}{50}{Strict TCC upper bound on \(r\) and corresponding maxima for \(H\) and \(V^{1/4}\) at \(A_s=2.1\times 10^{-9}\)}{table.caption.104}{}}
\@writefile{toc}{\contentsline {paragraph}{Gate logic (A/B1).}{50}{section*.105}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate decision rule.}{50}{section*.106}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Branch A (Strict TCC + Curvaton) parameters consistent with all gates.}}{50}{table.caption.107}\protected@file@percent }
\newlabel{tab:TCC-A}{{5}{50}{Branch A (Strict TCC + Curvaton) parameters consistent with all gates}{table.caption.107}{}}
\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Branch B1 (Moderate TCC) parameters in tiny-\(r\) slow roll.}}{51}{table.caption.108}\protected@file@percent }
\newlabel{tab:TCC-B1}{{6}{51}{Branch B1 (Moderate TCC) parameters in tiny-\(r\) slow roll}{table.caption.108}{}}
\@writefile{toc}{\contentsline {section}{\numberline {12}Dark Matter: UTFANSWF Axion Band and Signatures}{51}{section.12}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Unified Embedding to Dark Matter Selection.}{51}{section*.109}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Axion mass and photon coupling.}{51}{section*.110}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF preferred band.}{52}{section*.111}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Relic abundance from misalignment.}{52}{section*.112}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Observational signatures.}{52}{section*.113}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF gate interpretation.}{52}{section*.115}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Axion photon coupling vs mass (DFSZ and KSVZ lines). Shaded: UTFANSWF band $m_a\in [6,60]\,\mu $eV.}}{53}{figure.caption.114}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Role within the framework.}{53}{section*.116}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {13}Neutral Zone (NZ): Hydrogen \& Stellar Ignition Correlation}{53}{section.13}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Microphysics to Macroscopic Viability.}{53}{section*.117}\protected@file@percent }
\newlabel{eq:NZ}{{95}{54}{From Microphysics to Macroscopic Viability}{equation.95}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces NZ sandwich inequality energy levels: floor $m_e+m_\nu $, middle $m_n-m_p$, ceiling $B_d-(m_e+m_\nu )$.}}{54}{figure.caption.118}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {14}Neutral Zone (NZ): full derivations and sensitivities (Expanded)}{54}{section.14}\protected@file@percent }
\newlabel{sec:NZ-expanded}{{14}{54}{Neutral Zone (NZ): full derivations and sensitivities (Expanded)}{section.14}{}}
\@writefile{toc}{\contentsline {paragraph}{Hydrogen stability \& pp exothermicity.}{54}{section*.122}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Sensitivity of $I_{\mathrm  {NZ}}$ to $\alpha _{\rm  em}$ about the observed point.}}{55}{figure.caption.119}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Sensitivity of $I_{\mathrm  {NZ}}$ to the light-quark mass splitting $\Delta q=m_d-m_u$.}}{55}{figure.caption.120}\protected@file@percent }
\newlabel{eq:NZ-sandwich}{{101}{55}{Hydrogen stability \& pp exothermicity}{equation.101}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces $I_{\mathrm  {NZ}}$ vs absolute neutrino mass $m_\nu $ (in eV).}}{56}{figure.caption.121}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Observed universe check.}{56}{section*.123}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hadronic decomposition and linear model.}{56}{section*.124}\protected@file@percent }
\newlabel{eq:mnmp-linear}{{105}{56}{Hadronic decomposition and linear model}{equation.105}{}}
\@writefile{toc}{\contentsline {paragraph}{Differential sensitivities of \(I_{\rm  NZ}\).}{57}{section*.125}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Origin in UTFANSWF.}{57}{section*.126}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF gate interpretation.}{57}{section*.127}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {15}Learning Efficiency with UTFANSWF Constraints}{57}{section.15}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{From Physical Consistency to Learning Constraints.}{57}{section*.128}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hypothesis space reduction.}{58}{section*.129}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Constrained optimization.}{58}{section*.130}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Convergence acceleration.}{58}{section*.131}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation within UTFANSWF.}{58}{section*.132}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Practical implication.}{59}{section*.133}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Learning curves: unconstrained vs UTFANSWF-constrained search, illustrating accelerated convergence within the physically admissible manifold.}}{59}{figure.caption.134}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {16}Stress tests, pass/fail matrix, and compact numeric harness (Restored)}{60}{section.16}\protected@file@percent }
\newlabel{sec:stress-harness}{{16}{60}{Stress tests, pass/fail matrix, and compact numeric harness (Restored)}{section.16}{}}
\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces UTFANSWF consistency gates: criteria and status at the benchmark slice.}}{60}{table.caption.136}\protected@file@percent }
\newlabel{tab:pass-fail}{{7}{60}{UTFANSWF consistency gates: criteria and status at the benchmark slice}{table.caption.136}{}}
\@writefile{toc}{\contentsline {section}{\numberline {17}Canonical UTFANSWF Lagrangian (Equation of Record)}{61}{section.17}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Equation of record.}{61}{section*.138}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Abelian and gravitational.}{61}{section*.139}\protected@file@percent }
\newlabel{eq:gravX}{{122}{62}{3. Portal sectors and extra $\Uone _{X}$}{equation.122}{}}
\newlabel{eq:X3}{{123}{62}{3. Portal sectors and extra $\Uone _{X}$}{equation.123}{}}
\newlabel{eq:XY2}{{124}{62}{3. Portal sectors and extra $\Uone _{X}$}{equation.124}{}}
\newlabel{eq:X2Y}{{125}{62}{3. Portal sectors and extra $\Uone _{X}$}{equation.125}{}}
\newlabel{eq:SUX2X}{{126}{62}{3. Portal sectors and extra $\Uone _{X}$}{equation.126}{}}
\newlabel{eq:SUX3X}{{127}{62}{3. Portal sectors and extra $\Uone _{X}$}{equation.127}{}}
\@writefile{toc}{\contentsline {paragraph}{Vectorlike safety.}{62}{section*.143}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Worked example: $U(1)_{B-L}$.}{62}{section*.144}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {17.1}4}{63}{subsection.17.1}\protected@file@percent }
\newlabel{mv:EHaction}{{130}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.130}{}}
\newlabel{mv:dets}{{131}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.131}{}}
\newlabel{mv:deltaGamma}{{132}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.132}{}}
\newlabel{mv:palatini}{{133}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.133}{}}
\newlabel{mv:deltaR}{{134}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.134}{}}
\newlabel{mv:EHvar}{{135}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.135}{}}
\newlabel{mv:boundary}{{136}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.136}{}}
\newlabel{mv:Gmunu}{{137}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.137}{}}
\newlabel{mv:GHY}{{138}{64}{1. Einstein--Hilbert variation and the GHY boundary term}{equation.138}{}}
\newlabel{mv:R2}{{139}{64}{2. $R^2$ (scalaron) correction}{equation.139}{}}
\newlabel{mv:fRvar}{{140}{65}{2. $R^2$ (scalaron) correction}{equation.140}{}}
\newlabel{mv:Hmunu}{{141}{65}{2. $R^2$ (scalaron) correction}{equation.141}{}}
\@writefile{toc}{\contentsline {section}{\numberline {18}Axion Sector: Strong-CP Resolution and Dark Matter Channel}{65}{section.18}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Strong-CP problem.}{65}{section*.149}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PQ symmetry and axion emergence.}{65}{section*.150}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Embedding in UTFANSWF.}{65}{section*.151}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Cosmological production.}{65}{section*.152}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Detection channels.}{66}{section*.153}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF prediction.}{66}{section*.154}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {19}AI $\leftrightarrow $ UTFANSWF Co-evolution}{66}{section.19}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Motivation.}{66}{section*.155}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Constraint embedding.}{66}{section*.156}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Learning efficiency.}{67}{section*.157}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Feedback loop.}{67}{section*.158}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation within the framework.}{67}{section*.159}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Outcome.}{67}{section*.160}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {20}Conclusion}{67}{section.20}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary of the framework.}{67}{section*.161}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Equation-to-observation closure.}{68}{section*.162}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Falsifiability as design principle.}{68}{section*.163}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Role of constraint geometry.}{68}{section*.164}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Operational program.}{68}{section*.165}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Final statement.}{69}{section*.166}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {21}Black-hole Ringdown and Echo Predictions}{70}{section.21}\protected@file@percent }
\newlabel{sec:BH-echoes}{{21}{70}{Black-hole Ringdown and Echo Predictions}{section.21}{}}
\@writefile{toc}{\contentsline {paragraph}{Kerr QNM (fundamental mode).}{70}{section*.167}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Echo generation.}{70}{section*.168}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Minimal echo model.}{70}{section*.169}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF gate relevance.}{70}{section*.170}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {21.1}Benchmark realization and signal templates}{71}{subsection.21.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Benchmark parameters.}{71}{section*.171}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Echo spacing.}{71}{section*.172}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Signal construction.}{71}{section*.173}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {22}Functional RG, PPN/GW limits, positivity bounds, and analytic Jacobians}{71}{section.22}\protected@file@percent }
\newlabel{app:FRG-PPN-positivity-analytics}{{22}{71}{Functional RG, PPN/GW limits, positivity bounds, and analytic Jacobians}{section.22}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Kerr QNM ringdown waveform for the benchmark ($a=0.68$, $M_f=60\,M_\odot $).}}{72}{figure.caption.174}\protected@file@percent }
\newlabel{fig:bh_ringdown}{{13}{72}{Kerr QNM ringdown waveform for the benchmark ($a=0.68$, $M_f=60\,M_\odot $)}{figure.caption.174}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Ringdown plus echo train with $\gamma =0.5$ and $N_{\rm  echo}=6$ for the benchmark configuration.}}{72}{figure.caption.175}\protected@file@percent }
\newlabel{fig:bh_echo}{{14}{72}{Ringdown plus echo train with $\gamma =0.5$ and $N_{\rm echo}=6$ for the benchmark configuration}{figure.caption.175}{}}
\@writefile{toc}{\contentsline {section}{\numberline {23}AI $\leftrightarrow $ UTFANSWF co-evolution (Expanded)}{75}{section.23}\protected@file@percent }
\newlabel{sec:AI-expanded}{{23}{75}{AI \texorpdfstring {$\leftrightarrow $}{↔} UTFANSWF co-evolution (Expanded)}{section.23}{}}
\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces UTFANSWF guardrails for AI-assisted search. All must remain satisfied during proposal, fitting, and simulation.}}{76}{table.caption.180}\protected@file@percent }
\newlabel{tab:guardrails}{{8}{76}{UTFANSWF guardrails for AI-assisted search. All must remain satisfied during proposal, fitting, and simulation}{table.caption.180}{}}
\@writefile{toc}{\contentsline {section}{\numberline {24}Computational Robustness Ladder (Layers 4b--9)}{77}{section.24}\protected@file@percent }
\newlabel{sec:robustness_ladder}{{24}{77}{Computational Robustness Ladder (Layers 4b--9)}{section.24}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {24.1}Overview}{77}{subsection.24.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.2}Baseline: Layer 4b Locked State}{77}{subsection.24.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.3}Layer 5: Dynamic Preservation}{78}{subsection.24.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.4}Layer 6: Localized Forcing Response}{78}{subsection.24.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.5}Layer 7: Forcing Threshold Sweep}{78}{subsection.24.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.6}Layer 8: Off-Ring / Symmetry-Breaking Forcing}{79}{subsection.24.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.7}Layer 9: Multi-Source Interference}{79}{subsection.24.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.8}Layer 9 (Extended): Aggressive Stress Regime}{79}{subsection.24.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.9}Parameter-Space Coverage and Stability Region}{80}{subsection.24.9}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.10}Behavior Hierarchy}{80}{subsection.24.10}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {24.11}Interpretation}{81}{subsection.24.11}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {25}Break UTFANSWF: Stress-Test Appendix}{81}{section.25}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs.}{81}{section*.183}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Derived.}{82}{section*.184}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Pass/Fail table (benchmark).}{82}{section*.185}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Mixed non-abelian anomalies.}{82}{section*.186}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Abelian and gravitational.}{82}{section*.187}\protected@file@percent }
\newlabel{eq:gravX_a}{{190}{83}{5. Portal sectors and extra $\Uone _{X}$}{equation.190}{}}
\newlabel{eq:X3}{{191}{83}{5. Portal sectors and extra $\Uone _{X}$}{equation.191}{}}
\newlabel{eq:XY2}{{192}{83}{5. Portal sectors and extra $\Uone _{X}$}{equation.192}{}}
\newlabel{eq:X2Y}{{193}{83}{5. Portal sectors and extra $\Uone _{X}$}{equation.193}{}}
\newlabel{eq:SUX2X}{{194}{83}{5. Portal sectors and extra $\Uone _{X}$}{equation.194}{}}
\newlabel{eq:SUX3X_a}{{195}{83}{5. Portal sectors and extra $\Uone _{X}$}{equation.195}{}}
\@writefile{toc}{\contentsline {paragraph}{Vectorlike safety.}{83}{section*.191}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Worked example: $U(1)_{B-L}$.}{83}{section*.192}\protected@file@percent }
\newlabel{eq:DR2}{{198}{85}{1. Analyticity, crossing, and subtractions}{equation.198}{}}
\newlabel{eq:PosMaster}{{200}{85}{2. Optical theorem and positivity of the integrand}{equation.200}{}}
\newlabel{eq:EFTgen}{{201}{86}{4. Mapping to EFT Wilson coefficients}{equation.201}{}}
\newlabel{eq:Acontact}{{202}{86}{4. Mapping to EFT Wilson coefficients}{equation.202}{}}
\newlabel{eq:forwardpos}{{203}{86}{4. Mapping to EFT Wilson coefficients}{equation.203}{}}
\@writefile{toc}{\contentsline {paragraph}{Single real scalar.}{86}{section*.200}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Two scalars / mixed channel.}{86}{section*.201}\protected@file@percent }
\newlabel{eq:copositivity}{{206}{86}{Two scalars / mixed channel}{equation.206}{}}
\newlabel{eq:V4}{{208}{88}{1. Field content and normalization}{equation.208}{}}
\newlabel{eq:unitarity}{{210}{88}{2. $s$--wave unitarity from the contact amplitudes}{equation.210}{}}
\@writefile{toc}{\contentsline {paragraph}{Singlet basis.}{88}{section*.208}\protected@file@percent }
\newlabel{eq:Msinglet}{{212}{88}{Singlet basis}{equation.212}{}}
\@writefile{toc}{\contentsline {paragraph}{Explicit Higgs block.}{88}{section*.209}\protected@file@percent }
\newlabel{eq:Honly}{{214}{88}{Explicit Higgs block}{equation.214}{}}
\@writefile{toc}{\contentsline {paragraph}{Mixed and adjoint blocks.}{89}{section*.210}\protected@file@percent }
\newlabel{eq:unitarity2x2}{{216}{89}{Mixed and adjoint blocks}{equation.216}{}}
\newlabel{eq:necessary}{{217}{89}{Mixed and adjoint blocks}{equation.217}{}}
\newlabel{eq:RGE1}{{218}{89}{1. RG running and matching framework}{equation.218}{}}
\newlabel{eq:comboHC}{{219}{90}{2. Heavy SU(5) thresholds and the two master combinations}{equation.219}{}}
\newlabel{eq:comboX}{{220}{90}{2. Heavy SU(5) thresholds and the two master combinations}{equation.220}{}}
\@writefile{toc}{\contentsline {paragraph}{Derivation (sketch).}{90}{section*.214}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Dimension-6 (gauge boson exchange).}{90}{section*.217}\protected@file@percent }
\newlabel{eq:tauD6}{{226}{90}{Dimension-6 (gauge boson exchange)}{equation.226}{}}
\@writefile{toc}{\contentsline {paragraph}{Dimension-5 (color-triplet Higgs exchange).}{91}{section*.218}\protected@file@percent }
\newlabel{eq:tauD5}{{228}{91}{Dimension-5 (color-triplet Higgs exchange)}{equation.228}{}}
\@writefile{toc}{\contentsline {paragraph}{Spin projectors.}{93}{section*.228}\protected@file@percent }
\citation{Saueressig:2023}
\@writefile{toc}{\contentsline {paragraph}{FRG numeric exponents (EH, Litim).}{95}{section*.234}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {26}SU(5) Threshold Sweep: Benchmark Rows 1--8}{100}{section.26}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {26.1}Master Equations}{100}{subsection.26.1}\protected@file@percent }
\newlabel{eq:C1}{{252}{100}{Master Equations}{equation.252}{}}
\newlabel{eq:C2}{{253}{100}{Master Equations}{equation.253}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {26.2}Benchmark Sweep: Rows 1--4}{101}{subsection.26.2}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces SU(5) threshold sweep (rows 1--4). Two-loop running with top--Yukawa. $\rho \equiv M_{\Sigma }/M_{X}$. $F_{D6}\propto M_{X}^{4}/\alpha _{U}^{2}$, $F_{D5}\propto M_{HC}^{2}/r^{2}$ for loop dressing $r=\{5,10,20\}$. \emph  {Normalization:} $F_{D6}$ and $F_{D5}$ are shown relative to Row 1 at $r=5$.}}{101}{table.caption.249}\protected@file@percent }
\newlabel{tab:su5sweep_1to4}{{9}{101}{SU(5) threshold sweep (rows 1--4). Two-loop running with top--Yukawa. $\rho \equiv M_{\Sigma }/M_{X}$. $F_{D6}\propto M_{X}^{4}/\alpha _{U}^{2}$, $F_{D5}\propto M_{HC}^{2}/r^{2}$ for loop dressing $r=\{5,10,20\}$. \emph {Normalization:} $F_{D6}$ and $F_{D5}$ are shown relative to Row 1 at $r=5$}{table.caption.249}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {26.3}Benchmark Sweep: Rows 5--8}{101}{subsection.26.3}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces SU(5) threshold sweep (rows 5--8). Continuation of Table~\ref {tab:su5sweep_1to4}. Two-loop running with top--Yukawa.}}{101}{table.caption.250}\protected@file@percent }
\newlabel{tab:su5sweep_5to8}{{10}{101}{SU(5) threshold sweep (rows 5--8). Continuation of Table~\ref {tab:su5sweep_1to4}. Two-loop running with top--Yukawa}{table.caption.250}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {26.4}Compact Sweep Summary}{101}{subsection.26.4}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {27}SU(5) Threshold Sweep and Proton-Decay Scaling}{102}{section.27}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {27.1}Dimension--6 Proton-Decay Trend}{102}{subsection.27.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {27.2}Dimension--5 Proton-Decay Trend}{102}{subsection.27.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {27.3}Pass/Fail Interpretation Across Rows 1--8}{103}{subsection.27.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {27.4}Verdict}{103}{subsection.27.4}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {28}PPN Constraints: $\gamma , \beta $}{103}{section.28}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {28.1}Scalar–Tensor Setup}{103}{subsection.28.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {28.2}Post-Newtonian Parameters}{104}{subsection.28.2}\protected@file@percent }
\newlabel{eq:gamma_a}{{260}{104}{Post-Newtonian Parameters}{equation.260}{}}
\newlabel{eq:beta_a}{{261}{104}{Post-Newtonian Parameters}{equation.261}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {28.3}Experimental Bounds}{104}{subsection.28.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {28.4}UTFANSWF Status}{104}{subsection.28.4}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {29}GW Propagation Speed Constraint}{104}{section.29}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces PPN Gate Status in UTFANSWF}}{105}{table.caption.251}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {29.1}Quadratic Tensor Action}{105}{subsection.29.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {29.2}Experimental Bound}{105}{subsection.29.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {29.3}UTFANSWF Implications}{105}{subsection.29.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {29.4}Gate Status}{105}{subsection.29.4}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces GW Propagation Speed Gate Status in UTFANSWF}}{106}{table.caption.252}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {30}Forward-Limit Positivity Bounds}{106}{section.30}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {30.1}Twice-Subtracted Dispersion Relation}{106}{subsection.30.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {30.2}Wilson Coefficient Constraints}{106}{subsection.30.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {30.3}Gravity-Safe Prescription}{107}{subsection.30.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {30.4}Gate Status}{107}{subsection.30.4}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Forward-Limit Positivity Gate Status in UTFANSWF}}{107}{table.caption.253}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {31}Partial-Wave Unitarity and BFB Cone (Scalar Sector)}{107}{section.31}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {31.1}Quartic Scalar Potential}{107}{subsection.31.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {31.2}s-wave Unitarity}{108}{subsection.31.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {31.3}BFB Stability Conditions}{108}{subsection.31.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {31.4}Copositivity Cone}{108}{subsection.31.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {31.5}Gate Status}{108}{subsection.31.5}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {14}{\ignorespaces Partial-Wave Unitarity and BFB Gate Status in UTFANSWF}}{109}{table.caption.254}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {32}SU(5)/SO(10) Thresholds and Proton-Decay Scaling}{109}{section.32}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {32.1}RG Running with Heavy Thresholds}{109}{subsection.32.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {32.2}Threshold Combinations}{109}{subsection.32.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {32.3}Proton Decay Scaling Laws}{109}{subsection.32.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Dimension-6 gauge-boson exchange.}{110}{section*.255}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Dimension-5 triplet-Higgs exchange.}{110}{section*.256}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {32.4}Numerical Benchmark}{110}{subsection.32.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {32.5}Gate Status}{110}{subsection.32.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {33}Axion Dark Matter: UTFANSWF Band and Signatures}{110}{section.33}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {15}{\ignorespaces SU(5)/SO(10) Thresholds and Proton-Decay Gate Status}}{111}{table.caption.257}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {33.1}Axion Mass and Coupling}{111}{subsection.33.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {33.2}Preferred UTFANSWF Band}{111}{subsection.33.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {33.3}Abundance and Misalignment Mechanism}{111}{subsection.33.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {33.4}Experimental Signatures}{112}{subsection.33.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Haloscopes.}{112}{section*.258}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Astrophysical channels.}{112}{section*.259}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {33.5}Gate Status}{112}{subsection.33.5}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {16}{\ignorespaces Axion Dark Matter Band and UTFANSWF Gate Status}}{112}{table.caption.260}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {34}Neutral Zone (NZ): Hydrogen \& Stellar Ignition Correlation}{112}{section.34}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {34.1}Hydrogen Stability}{112}{subsection.34.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {34.2}Exothermic $pp$ Chain}{113}{subsection.34.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {34.3}Neutral Zone Sandwich Inequality}{113}{subsection.34.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {34.4}Numerical Check (Our Universe)}{113}{subsection.34.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {34.5}Neutral Zone Index}{113}{subsection.34.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {34.6}UTFANSWF Embedding}{114}{subsection.34.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {34.7}Gate Status}{114}{subsection.34.7}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {17}{\ignorespaces Neutral Zone (NZ) Gate Status}}{114}{table.caption.261}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {35}Learning Efficiency with UTFANSWF Constraints}{114}{section.35}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {35.1}Constraint-Prior Hypothesis Space}{115}{subsection.35.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {35.2}Validation Error Dynamics}{115}{subsection.35.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {35.3}Comparative Learning Curves}{115}{subsection.35.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {35.4}Gate Status}{115}{subsection.35.4}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {18}{\ignorespaces Learning Efficiency with UTFANSWF Constraints}}{116}{table.caption.262}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {36}Stress Tests and Pass/Fail Matrix}{116}{section.36}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {36.1}Compact Numeric Harness (Benchmark Slice)}{116}{subsection.36.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {36.2}Pass/Fail Table (Benchmark Slice)}{117}{subsection.36.2}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {19}{\ignorespaces Pass/Fail Matrix for UTFANSWF Benchmark Slice}}{117}{table.caption.263}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {36.3}Summary}{117}{subsection.36.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {37}Canonical UTFANSWF Lagrangian (Equation of Record)}{117}{section.37}\protected@file@percent }
\newlabel{eq:UTFANSWF_Lagrangian}{{322}{118}{Canonical UTFANSWF Lagrangian (Equation of Record)}{equation.322}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {37.1}Guardrails and Consistency Conditions}{118}{subsection.37.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {37.2}Anomaly Cancellation Checks}{118}{subsection.37.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Standard Model:}{119}{section*.264}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{SU(5) Embedding:}{119}{section*.265}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{SO(10) Embedding:}{119}{section*.266}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{E$_6$ Embedding:}{119}{section*.267}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {37.3}Summary}{119}{subsection.37.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {38}Axion Primer (Concise)}{119}{section.38}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {38.1}Strong-CP Problem and PQ Symmetry}{119}{subsection.38.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {38.2}Axion Potential and Mass}{120}{subsection.38.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {38.3}Axion–Photon Coupling}{120}{subsection.38.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {38.4}UTFANSWF Band and Predictions}{120}{subsection.38.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {38.5}Phenomenological Notes}{121}{subsection.38.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {38.6}Summary}{121}{subsection.38.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {39}Axion Primer (Concise)}{121}{section.39}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {39.1}Strong-CP Problem and PQ Symmetry}{121}{subsection.39.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {39.2}Axion Potential and Mass}{122}{subsection.39.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {39.3}Axion–Photon Coupling}{122}{subsection.39.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {39.4}UTFANSWF Band and Predictions}{122}{subsection.39.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {39.5}Phenomenological Notes}{123}{subsection.39.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {39.6}Summary}{123}{subsection.39.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {40}AI $\leftrightarrow $ UTFANSWF Co-evolution}{123}{section.40}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {40.1}Motivation}{123}{subsection.40.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {40.2}Mathematical Embedding of Priors}{123}{subsection.40.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {40.3}Learning Efficiency}{124}{subsection.40.3}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Learning curves: unconstrained baseline vs UTFANSWF-constrained search. Embedding UTFANSWF gates reduces error faster and increases the yield of valid models.}}{124}{figure.caption.268}\protected@file@percent }
\newlabel{fig:learning_efficiency}{{15}{124}{Learning curves: unconstrained baseline vs UTFANSWF-constrained search. Embedding UTFANSWF gates reduces error faster and increases the yield of valid models}{figure.caption.268}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {40.4}Compact Acceptance Algorithm}{124}{subsection.40.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {40.5}Summary}{125}{subsection.40.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {41}Appendix: The Curvature Engineering Gate (CEG)}{125}{section.41}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {42}Spacetime-Engineering Consistency Gate (SECG)}{126}{section.42}\protected@file@percent }
\newlabel{sec:SECG}{{42}{126}{Spacetime-Engineering Consistency Gate (SECG)}{section.42}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {42.1}Objects under test}{126}{subsection.42.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {42.2}Primary inequalities and invariants}{127}{subsection.42.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(A) Quantum energy and causality bounds}{127}{section*.273}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(B) Ford--Roman quantum inequalities}{127}{section*.274}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(C) Chronology protection}{127}{section*.275}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(D) EFT positivity}{127}{section*.276}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(E) Hyperbolicity and stability}{127}{section*.277}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(F) Entropy consistency}{127}{section*.278}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(G) Backreaction and curvature caps}{128}{section*.279}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {42.3}Warp / effective-FTL corollaries}{128}{subsection.42.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {42.4}Artificial gravity modules}{128}{subsection.42.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {42.5}Compact pass/fail matrix}{129}{subsection.42.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {42.6}Harness (pseudo-algorithm)}{129}{subsection.42.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Status in UTFANSWF v22}{129}{section*.280}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {43}Functional RG, PPN/GW Limits, Positivity Bounds, and Analytic Jacobians}{129}{section.43}\protected@file@percent }
\newlabel{sec:FRG_PPN}{{43}{129}{Functional RG, PPN/GW Limits, Positivity Bounds, and Analytic Jacobians}{section.43}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {43.1}Functional Renormalization Group (FRG) Setup}{130}{subsection.43.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {43.2}Beta Functions and Fixed Points}{130}{subsection.43.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {43.3}PPN and Gravitational Wave Bounds}{131}{subsection.43.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {43.4}Forward-Limit Positivity Bounds}{131}{subsection.43.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {43.5}Analytic Jacobians for Compressed Cosmology}{131}{subsection.43.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {43.6}Takeaway}{132}{subsection.43.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {44}Compressed Cosmology Fit (CMB/BAO/SN/GW, $\chi ^2/\nu $ Checks)}{132}{section.44}\protected@file@percent }
\newlabel{sec:CompressedCosmo}{{44}{132}{Compressed Cosmology Fit (CMB/BAO/SN/GW, $\chi ^2/\nu $ Checks)}{section.44}{}}
\@writefile{toc}{\contentsline {paragraph}{Row 20 — run checklist (concise).}{132}{section*.281}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Row 20 — ledger linkage.}{133}{section*.282}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {44.1}Observables and Compressed Parameters}{133}{subsection.44.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {44.2}Distance Priors and BAO}{133}{subsection.44.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {44.3}Supernova (SN) Distance Moduli}{134}{subsection.44.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{SN Projection Geometry and Residual Compression}{134}{section*.283}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {44.4}Standard Sirens (GW)}{135}{subsection.44.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {44.5}Compressed $\chi ^2/\nu $ Gate}{135}{subsection.44.5}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Dataset Update Sensitivity and Constrained Recalibration.}{135}{section*.284}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Distributed Hubble Parameter Resolution (v22 Candidate)}{135}{section*.285}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Distributed Hubble Resolution Theorem (v22 Candidate)}{136}{section*.286}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {44.6}Compact Pass/Fail Matrix}{137}{subsection.44.6}\protected@file@percent }
\newlabel{stub:row21}{{44.6}{138}{Row 21 --- audit stub (verbatim)}{section*.287}{}}
\@writefile{toc}{\contentsline {paragraph}{Row 21 --- audit stub (verbatim).}{138}{section*.287}\protected@file@percent }
\newlabel{stub:row22}{{44.6}{138}{Row 22 --- audit stub (verbatim)}{section*.288}{}}
\@writefile{toc}{\contentsline {paragraph}{Row 22 --- audit stub (verbatim).}{138}{section*.288}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Status in UTFANSWF v22.}{138}{section*.289}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {45}Axion Dark Matter Gate (2025Q3 Update vs Haloscopes)}{138}{section.45}\protected@file@percent }
\newlabel{sec:AxionGate}{{45}{138}{Axion Dark Matter Gate (2025Q3 Update vs Haloscopes)}{section.45}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {45.1}UTFANSWF Axion Slice and Relations}{138}{subsection.45.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Misalignment Abundance.}{139}{section*.290}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {45.2}Detection Channels and Signatures}{139}{subsection.45.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {45.3}Current Experimental Coverage Within the UTFANSWF Band}{139}{subsection.45.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {45.4}Gate Criterion and Verdict}{139}{subsection.45.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {45.5}Near-Term UTFANSWF Forecasts}{140}{subsection.45.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {45.6}Compact Pass/Fail Matrix}{140}{subsection.45.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {46}Neutral Zone (NZ) Sandwich: Robust Sweep and Sensitivities}{140}{section.46}\protected@file@percent }
\newlabel{sec:nz-sandwich}{{46}{140}{Neutral Zone (NZ) Sandwich: Robust Sweep and Sensitivities}{section.46}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {46.1}NZ Sandwich Inequality}{140}{subsection.46.1}\protected@file@percent }
\newlabel{eq:NZsandwich}{{428}{140}{NZ Sandwich Inequality}{equation.428}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {46.2}Sensitivity Expansions}{141}{subsection.46.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {46.3}Robustness Sweep}{141}{subsection.46.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {46.4}Gate Criterion and Verdict}{141}{subsection.46.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {46.5}Implication for UTFANSWF}{142}{subsection.46.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {47}Black-Hole Ringdown and Echo Predictions (Expanded Benchmark Fits)}{142}{section.47}\protected@file@percent }
\newlabel{sec:BHringdown}{{47}{142}{Black-Hole Ringdown and Echo Predictions (Expanded Benchmark Fits)}{section.47}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {47.1}Kerr Ringdown Spectrum}{142}{subsection.47.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Benchmark Example.}{142}{section*.291}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {47.2}Echo Templates from Near-Horizon Modifications}{142}{subsection.47.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {47.3}Consistency Gates}{143}{subsection.47.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {47.4}Pass/Fail Matrix (Benchmark Case)}{143}{subsection.47.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {47.5}Verdict}{143}{subsection.47.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {48}AI $\leftrightarrow $ UTFANSWF Guardrails and Learning Efficiency (Expanded)}{144}{section.48}\protected@file@percent }
\newlabel{sec:AI_UTFANSWF}{{48}{144}{AI $\leftrightarrow $ UTFANSWF Guardrails and Learning Efficiency (Expanded)}{section.48}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {48.1}Embedding Physical Guardrails into AI}{144}{subsection.48.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {48.2}Learning Efficiency Model}{144}{subsection.48.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Unconstrained baseline.}{144}{section*.292}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF-constrained.}{144}{section*.293}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {48.3}Example: Benchmarked Learning Curves}{144}{subsection.48.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {48.4}Co-evolution Framework}{145}{subsection.48.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {48.5}Pass/Fail Gate}{145}{subsection.48.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {48.6}Verdict}{145}{subsection.48.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {49}Stress-Test Appendix: ``Break UTFANSWF'' Kill-Shot Scenarios}{145}{section.49}\protected@file@percent }
\newlabel{sec:BreakUTFANSWF}{{49}{145}{Stress-Test Appendix: ``Break UTFANSWF'' Kill-Shot Scenarios}{section.49}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {49.1}Conceptual Kill-Shot Checklist}{145}{subsection.49.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {49.2}Numeric Stress-Test Harness (Benchmark Slice)}{146}{subsection.49.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {49.3}Compact Pass/Fail Matrix}{146}{subsection.49.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {49.4}Verdict}{146}{subsection.49.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs held fixed.}{147}{section*.295}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary}{147}{section*.299}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {50}SU(5)/SO(10) Heavy Thresholds and Proton-Decay Gates}{148}{section.50}\protected@file@percent }
\newlabel{eq:C1_a}{{464}{148}{Setup and Matching Combinations}{equation.464}{}}
\newlabel{eq:C2_a}{{465}{148}{Setup and Matching Combinations}{equation.465}{}}
\@writefile{toc}{\contentsline {paragraph}{Dimension-6 (gauge bosons).}{149}{section*.303}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Dimension-5 (color-triplet Higgs).}{149}{section*.304}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {51}Gravity-Safe Forward-Limit Positivity with Spin (Projectors \& Finite-$t$)}{150}{section.51}\protected@file@percent }
\newlabel{sec:positivity_gravity_spin}{{51}{150}{Gravity-Safe Forward-Limit Positivity with Spin (Projectors \& Finite-$t$)}{section.51}{}}
\@writefile{toc}{\contentsline {paragraph}{Setup.}{150}{section*.307}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gravity-safe dispersion and positivity.}{150}{section*.308}\protected@file@percent }
\newlabel{eq:disp-P-finitet}{{472}{150}{Gravity-safe dispersion and positivity}{equation.472}{}}
\newlabel{eq:strictpos-finitet}{{473}{150}{Gravity-safe dispersion and positivity}{equation.473}{}}
\@writefile{toc}{\contentsline {paragraph}{Mapping to Wilson coefficients.}{151}{section*.309}\protected@file@percent }
\newlabel{eq:a20-positive}{{476}{151}{Mapping to Wilson coefficients}{equation.476}{}}
\@writefile{toc}{\contentsline {paragraph}{Ready-to-use bounds (canonical sectors).}{151}{section*.310}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Improved finite-$t$ bounds.}{151}{section*.311}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Causality/time-delay compatibility.}{152}{section*.312}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Implementation recipe (harness).}{152}{section*.313}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{152}{section*.314}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {52}Row 2 — PPN/GW \& Spin-2 Causality Gate (PASS)}{152}{section.52}\protected@file@percent }
\newlabel{sec:row2-ppn-gw}{{52}{152}{Row 2 — PPN/GW \& Spin-2 Causality Gate (PASS)}{section.52}{}}
\@writefile{toc}{\contentsline {paragraph}{Benchmark slice.}{152}{section*.315}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PPN parameters.}{152}{section*.316}\protected@file@percent }
\newlabel{eq:gammaDEF}{{483}{153}{PPN parameters}{equation.483}{}}
\newlabel{eq:betaDEF}{{484}{153}{PPN parameters}{equation.484}{}}
\@writefile{toc}{\contentsline {paragraph}{GW propagation speed today.}{153}{section*.317}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Spin-2 causality / time delay.}{153}{section*.318}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Verdict.}{154}{section*.320}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {53}Row 3 — SANSWF: Bounded-From-Below (BFB) \& Gauge Consistency (PASS)}{154}{section.53}\protected@file@percent }
\newlabel{sec:row3-bfb}{{53}{154}{Row 3 — SANSWF: Bounded-From-Below (BFB) \& Gauge Consistency (PASS)}{section.53}{}}
\@writefile{toc}{\contentsline {paragraph}{Scalar potential.}{154}{section*.321}\protected@file@percent }
\newlabel{eq:pot-sanswf}{{485}{154}{Scalar potential}{equation.485}{}}
\@writefile{toc}{\contentsline {paragraph}{Bounded-from-below (BFB) conditions.}{154}{section*.322}\protected@file@percent }
\newlabel{eq:bfb1}{{486}{154}{Bounded-from-below (BFB) conditions}{equation.486}{}}
\newlabel{eq:bfb2}{{487}{154}{Bounded-from-below (BFB) conditions}{equation.487}{}}
\newlabel{eq:bfb3}{{488}{154}{Bounded-from-below (BFB) conditions}{equation.488}{}}
\@writefile{toc}{\contentsline {paragraph}{Gauge consistency.}{155}{section*.323}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Partial-wave unitarity.}{155}{section*.324}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Verdict.}{156}{section*.326}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {54}Rows 4--12: Polished Consistency Gates}{156}{section.54}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.1}Row 4 --- SU(5)/SO(10) Embedding \& Seesaw}{156}{subsection.54.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.2}Row 5 --- Predictions \& SMEFT Matching}{157}{subsection.54.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.3}Rows 6 \& 7 --- Inflation + TCC Gates}{157}{subsection.54.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Branch A (Strict TCC + Curvaton)}{157}{section*.327}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Branch B1 (Moderate TCC)}{157}{section*.328}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.4}Row 8 --- Axion Band \& Signatures}{157}{subsection.54.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.5}Row 9 --- Neutral Zone (NZ) Sandwich}{158}{subsection.54.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.6}Row 10 --- NZ Sensitivities \& Robustness}{158}{subsection.54.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.7}Row 11 --- Learning Efficiency}{158}{subsection.54.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {54.8}Row 12 --- Stress Tests \& Harness}{159}{subsection.54.8}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs}{159}{section*.329}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Outputs}{159}{section*.330}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {55}Rows 13--20: Polished Consistency Gates}{160}{section.55}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.1}Row 13 --- Stress-Test Gates}{160}{subsection.55.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.2}Row 14 --- Compact Numeric Harness}{160}{subsection.55.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Benchmark input}{160}{section*.332}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Outputs}{160}{section*.333}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.3}Row 15 --- Canonical UTFANSWF Lagrangian}{160}{subsection.55.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.4}Row 16 --- Axion Sector (Primer)}{161}{subsection.55.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.5}Row 17 --- AI $\leftrightarrow $ UTFANSWF Co-evolution}{161}{subsection.55.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.6}Row 18 --- Black Hole Ringdown}{162}{subsection.55.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.7}Row 19 --- Functional RG \& Consistency Window}{162}{subsection.55.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {55.8}Row 20 --- Compressed Cosmology Fit}{162}{subsection.55.8}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{v22 note.}{162}{section*.334}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {56}Refined Predictions Post-Math Update}{163}{section.56}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {56.1}Axion Dark Matter Band}{163}{subsection.56.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {56.2}Inflation and TCC Gate}{163}{subsection.56.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {56.3}Proton Decay Lifetime}{163}{subsection.56.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {56.4}Black Hole Ringdown and Echoes}{164}{subsection.56.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {56.5}Neutral Zone Sandwich}{164}{subsection.56.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {56.6}AI $\leftrightarrow $ UTFANSWF Guardrails}{164}{subsection.56.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {57}Ordinary Solar--System Evolution (Continuity Branch)}{165}{section.57}\protected@file@percent }
\newlabel{app:solar_system_evolution}{{57}{165}{Ordinary Solar--System Evolution (Continuity Branch)}{section.57}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{165}{section*.336}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Climate thresholds.}{166}{section*.338}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Engulfment condition.}{166}{section*.340}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {58}Sourced--Tensor Gate and the \(r\!\ge \!10^{-6}\) Benchmark}{167}{section.58}\protected@file@percent }
\newlabel{app:sourced_tensor_gate}{{58}{167}{Sourced--Tensor Gate and the \(r\!\ge \!10^{-6}\) Benchmark}{section.58}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope and standing gates.}{167}{section*.344}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate check (qualitative).}{169}{section*.349}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{170}{section*.352}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {59}AI Co--Execution Protocol for UTFANSWF}{170}{section.59}\protected@file@percent }
\newlabel{app:ai_coexecution_protocol}{{59}{170}{AI Co--Execution Protocol for UTFANSWF}{section.59}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{171}{section*.353}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Stability rule.}{172}{section*.358}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {60}Spinning/Gravity Positivity \& the Cosmology Matrix Bridge}{174}{section.60}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Scope.}{174}{section*.365}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gravity handling.}{175}{section*.368}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Real scalar.}{175}{section*.370}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Photon (Euler--Heisenberg sector).}{175}{section*.371}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Dirac fermion.}{176}{section*.372}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gravity-coupled probes.}{176}{section*.373}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Example: EFT of inflation.}{176}{section*.376}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{177}{section*.378}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {61}Curvaton Transfer \& Sourced--Tensor Existence Window (Rigorous Gate)}{177}{section.61}\protected@file@percent }
\newlabel{app:curvaton_sourced_existence}{{61}{177}{Curvaton Transfer \& Sourced--Tensor Existence Window (Rigorous Gate)}{section.61}{}}
\@writefile{toc}{\contentsline {paragraph}{Budgets.}{179}{section*.381}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Strict TCC slice.}{179}{section*.383}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{180}{section*.387}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {62}Dark--Energy EFT Stability \& Screening $\to $ CPL Mapping}{181}{section.62}\protected@file@percent }
\newlabel{app:de_eft_to_cpl}{{62}{181}{Dark--Energy EFT Stability \& Screening $\to $ CPL Mapping}{section.62}{}}
\@writefile{toc}{\contentsline {paragraph}{Reconstruction.}{182}{section*.389}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Sound speed.}{182}{section*.391}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What changes here?}{183}{section*.393}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(i) Chameleon screening}{183}{section*.395}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(ii) Vainshtein screening}{183}{section*.396}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{184}{section*.398}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {63}Axion Misalignment, Isocurvature, and Small--Scale Structure Bounds}{184}{section.63}\protected@file@percent }
\newlabel{app:axion_mis_iso_small}{{63}{184}{Axion Misalignment, Isocurvature, and Small--Scale Structure Bounds}{section.63}{}}
\@writefile{toc}{\contentsline {paragraph}{What this means.}{185}{section*.400}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Nice bonus.}{186}{section*.402}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Alternate branch.}{186}{section*.403}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{187}{section*.406}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {64}GW Propagation: Redshifted Dispersion $\to $ ppE Phase Mapping}{187}{section.64}\protected@file@percent }
\newlabel{app:gw_ppe_redshift}{{64}{187}{GW Propagation: Redshifted Dispersion $\to $ ppE Phase Mapping}{section.64}{}}
\@writefile{toc}{\contentsline {paragraph}{Goal.}{187}{section*.407}\protected@file@percent }
\newlabel{eq:phase_general}{{553}{188}{B.\;Cosmological time delay and phase shift}{equation.553}{}}
\newlabel{eq:ppe_map}{{554}{188}{C.\;ppE mapping}{equation.554}{}}
\@writefile{toc}{\contentsline {paragraph}{Special cases.}{188}{section*.411}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Notes.}{189}{section*.413}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {65}Neutral--Zone Likelihood and Posterior Predictive Checks}{189}{section.65}\protected@file@percent }
\newlabel{app:nz_lik_ppc}{{65}{189}{Neutral--Zone Likelihood and Posterior Predictive Checks}{section.65}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{189}{section*.414}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{192}{section*.424}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {66}Projected Gradient, KKT Conditions, and Convergence Guarantees}{192}{section.66}\protected@file@percent }
\newlabel{app:proj_kkt}{{66}{192}{Projected Gradient, KKT Conditions, and Convergence Guarantees}{section.66}{}}
\@writefile{toc}{\contentsline {paragraph}{Problem.}{192}{section*.425}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{195}{section*.433}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {67}Solar Engulfment Decision Surface: Constants, Evolution Laws, and Monotonicity}{195}{section.67}\protected@file@percent }
\newlabel{app:solar_constants}{{67}{195}{Solar Engulfment Decision Surface: Constants, Evolution Laws, and Monotonicity}{section.67}{}}
\@writefile{toc}{\contentsline {paragraph}{Goal.}{195}{section*.434}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Mass loss (pushes Earth outward):}{196}{section*.437}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Stellar tides (pull Earth inward):}{196}{section*.438}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Monotonicity (this is the key insight).}{197}{section*.441}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{198}{section*.444}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {68}Gauge Unification and Proton-Lifetime Band: Two--Loop Running with Thresholds}{198}{section.68}\protected@file@percent }
\newlabel{app:unif_tau_full}{{68}{198}{Gauge Unification and Proton-Lifetime Band: Two--Loop Running with Thresholds}{section.68}{}}
\@writefile{toc}{\contentsline {paragraph}{Goal.}{198}{section*.445}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Semi-analytic form (just to see the structure).}{199}{section*.447}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{And this is the first gate.}{199}{section*.449}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Second gate.}{200}{section*.451}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{SUSY note (if you turn it on).}{200}{section*.452}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{201}{section*.455}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {69}FRG Truncation Stability and EFT Matching Window}{201}{section.69}\protected@file@percent }
\newlabel{app:frg_trunc_match}{{69}{201}{FRG Truncation Stability and EFT Matching Window}{section.69}{}}
\@writefile{toc}{\contentsline {paragraph}{Aim.}{201}{section*.456}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Threshold functions.}{202}{section*.458}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{First check: does adding more operators change the result?}{202}{section*.460}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Second check: does the answer depend on the regulator?}{202}{section*.461}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PMS (how we pick the best regulator).}{202}{section*.462}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Convexity check.}{202}{section*.463}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Matching error (this is key).}{203}{section*.465}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Notes.}{204}{section*.467}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{204}{section*.468}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {70}SWF--ISM: Functional Foundations, Information Geometry, and EFT Pushforward}{204}{section.70}\protected@file@percent }
\newlabel{app:swfism_functional}{{70}{204}{SWF--ISM: Functional Foundations, Information Geometry, and EFT Pushforward}{section.70}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{204}{section*.469}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Symmetry projection (this is important).}{205}{section*.471}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Why this behaves well.}{205}{section*.472}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Feasible set (what we’re actually working with).}{205}{section*.473}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Geometry (what space we’re really in).}{206}{section*.475}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Pythagorean structure (this is the clean part).}{206}{section*.476}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Positivity gate.}{207}{section*.478}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{The key condition.}{207}{section*.479}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this means in plain terms.}{207}{section*.480}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Proof sketch (what’s really happening).}{207}{section*.481}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Recipe (how UTFANSWF actually uses this).}{208}{section*.482}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{208}{section*.483}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {71}Energy Estimate and Well--Posedness for a Coupled Scalar--Tensor Sector}{208}{section.71}\protected@file@percent }
\newlabel{app:energy_wellposed}{{71}{208}{Energy Estimate and Well--Posedness for a Coupled Scalar--Tensor Sector}{section.71}{}}
\@writefile{toc}{\contentsline {paragraph}{Model.}{208}{section*.484}\protected@file@percent }
\newlabel{eq:phi_eq}{{616}{208}{Model}{equation.616}{}}
\newlabel{eq:h_eq}{{617}{208}{Model}{equation.617}{}}
\@writefile{toc}{\contentsline {paragraph}{Coercivity (this is the key stability condition).}{209}{section*.486}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this means.}{210}{section*.488}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What about long times?}{210}{section*.490}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate link.}{210}{section*.491}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {72}Population \& Control: Viability Kernel and Discrete PMP/KKT}{211}{section.72}\protected@file@percent }
\newlabel{app:population_control_viability}{{72}{211}{Population \& Control: Viability Kernel and Discrete PMP/KKT}{section.72}{}}
\@writefile{toc}{\contentsline {paragraph}{Setup.}{211}{section*.492}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Best-case scenario.}{211}{section*.494}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{More realistic case.}{211}{section*.495}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Continuous-time intuition.}{212}{section*.496}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{How do we find it?}{212}{section*.498}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{If controls are constrained.}{213}{section*.499}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{UTFANSWF link.}{213}{section*.500}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Scalar logistic case.}{213}{section*.502}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Age-structured case.}{213}{section*.503}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this means operationally.}{213}{section*.504}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{214}{section*.505}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {73}Reproducibility Lemma: Monolithic vs Row--Split Builds}{214}{section.73}\protected@file@percent }
\newlabel{app:reproducibility}{{73}{214}{Reproducibility Lemma: Monolithic vs Row--Split Builds}{section.73}{}}
\@writefile{toc}{\contentsline {paragraph}{Statement.}{214}{section*.506}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Key point.}{215}{section*.508}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Outcome.}{215}{section*.510}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Summary.}{216}{section*.511}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {74}Volcanic Hazard Gate (v22)}{217}{section.74}\protected@file@percent }
\newlabel{app:volcanic_hazard_gate}{{74}{217}{Volcanic Hazard Gate (v22)}{section.74}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{217}{section*.516}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Neutral-Zone (NZ) compression.}{218}{section*.518}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Priors.}{219}{section*.520}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Near-term eruption probability.}{219}{section*.521}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Positivity/Causality Gate.}{219}{section*.522}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hysteresis.}{220}{section*.525}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Fleet-wide FDR control.}{220}{section*.526}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {75}Affective Health Gate (v22)}{222}{section.75}\protected@file@percent }
\newlabel{app:affective_health_gate}{{75}{222}{Affective Health Gate (v22)}{section.75}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{222}{section*.533}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Neutral-Zone (NZ) compression.}{223}{section*.535}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hysteresis.}{225}{section*.538}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Alert levels.}{225}{section*.540}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Yellow/Orange:}{225}{section*.542}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Red:}{226}{section*.543}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {76}Mechatronic Health Gate (v22)}{227}{section.76}\protected@file@percent }
\newlabel{app:mechatronic_health_gate}{{76}{227}{Mechatronic Health Gate (v22)}{section.76}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{227}{section*.547}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Neutral-Zone (NZ) compression.}{228}{section*.549}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Alert levels.}{229}{section*.552}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Yellow/Orange:}{229}{section*.554}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Red:}{229}{section*.555}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {77}Capability \& Permission Gate (v22)}{230}{section.77}\protected@file@percent }
\newlabel{app:capability_permission_gate}{{77}{230}{Capability \& Permission Gate (v22)}{section.77}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{230}{section*.558}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{WARN:}{232}{section*.562}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{FAIL:}{232}{section*.563}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {78}Calibration \& Consistency Gate (v22)}{233}{section.78}\protected@file@percent }
\newlabel{app:calibration_consistency_gate}{{78}{233}{Calibration \& Consistency Gate (v22)}{section.78}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{233}{section*.566}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Calibration fixes:}{234}{section*.570}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Consistency fixes:}{234}{section*.571}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {79}Cyber--Integrity Gate (v22)}{235}{section.79}\protected@file@percent }
\newlabel{app:cyber_integrity_gate}{{79}{235}{Cyber--Integrity Gate (v22)}{section.79}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{235}{section*.574}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS:}{235}{section*.577}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{FAIL:}{235}{section*.578}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {80}Privacy \& Minimization Gate (v22)}{236}{section.80}\protected@file@percent }
\newlabel{app:privacy_minimization_gate}{{80}{236}{Privacy \& Minimization Gate (v22)}{section.80}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{236}{section*.580}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {81}Mathematical Addendum: Finite-sample NZ Calibration (v22)}{238}{section.81}\protected@file@percent }
\newlabel{app:nz_finite_sample}{{81}{238}{Mathematical Addendum: Finite-sample NZ Calibration (v22)}{section.81}{}}
\@writefile{toc}{\contentsline {paragraph}{Goal.}{238}{section*.586}\protected@file@percent }
\newlabel{eq:Fref}{{662}{239}{Hotelling $T^2$ predictive statistic (Phase II)}{equation.662}{}}
\newlabel{eq:ucl}{{663}{239}{Hotelling $T^2$ predictive statistic (Phase II)}{equation.663}{}}
\newlabel{eq:pval}{{664}{239}{Hotelling $T^2$ predictive statistic (Phase II)}{equation.664}{}}
\@writefile{toc}{\contentsline {paragraph}{When this is exact.}{239}{section*.589}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {82}Mathematical Addendum: Fleet FDR under Dependence (v22)}{242}{section.82}\protected@file@percent }
\newlabel{app:fdr_dependence}{{82}{242}{Mathematical Addendum: Fleet FDR under Dependence (v22)}{section.82}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{242}{section*.596}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{When to use this.}{242}{section*.599}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{243}{section*.601}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Use case.}{243}{section*.603}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {83}Mathematical Addendum: Hysteresis Stability for Alert Logic (PPC \#27)}{245}{section.83}\protected@file@percent }
\newlabel{app:hysteresis_stability_v19}{{83}{245}{Mathematical Addendum: Hysteresis Stability for Alert Logic (PPC \#27)}{section.83}{}}
\@writefile{toc}{\contentsline {paragraph}{Objective.}{245}{section*.610}\protected@file@percent }
\newlabel{eq:hybrid}{{676}{246}{System model (hybrid closed loop)}{equation.676}{}}
\@writefile{toc}{\contentsline {paragraph}{Mode-wise contraction.}{246}{section*.612}\protected@file@percent }
\newlabel{eq:rho-bounds}{{677}{246}{Mode-wise contraction}{equation.677}{}}
\newlabel{eq:disc-lyap}{{678}{247}{Lyapunov construction (multiple quadratic, hysteretic)}{equation.678}{}}
\newlabel{eq:iss-mode}{{680}{247}{Lyapunov construction (multiple quadratic, hysteretic)}{equation.680}{}}
\@writefile{toc}{\contentsline {paragraph}{Switching cost and hysteresis.}{247}{section*.614}\protected@file@percent }
\newlabel{thm:hybrid-iss}{{83.1}{247}{Hybrid ISS with hysteresis}{definition.83.1}{}}
\newlabel{eq:dwell}{{682}{247}{Hybrid ISS with hysteresis}{equation.682}{}}
\@writefile{toc}{\contentsline {section}{\numberline {84}Mathematical Addendum: Ordinal VEI (Proportional-Odds) Model (v22)}{250}{section.84}\protected@file@percent }
\newlabel{app:vei_ordinal_identifiability}{{84}{250}{Mathematical Addendum: Ordinal VEI (Proportional-Odds) Model (v22)}{section.84}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{250}{section*.621}\protected@file@percent }
\newlabel{eq:po}{{684}{251}{Model}{equation.684}{}}
\newlabel{eq:probs}{{685}{251}{Model}{equation.685}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is doing.}{251}{section*.623}\protected@file@percent }
\newlabel{eq:alpha_param}{{687}{251}{Ordered cutpoints (reparameterization)}{equation.687}{}}
\@writefile{toc}{\contentsline {paragraph}{Why this matters.}{251}{section*.625}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Translation.}{252}{section*.627}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this buys us.}{252}{section*.629}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Why we care.}{253}{section*.631}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Randomized PIT (cdf calibration).}{253}{section*.633}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Ordinal reliability.}{253}{section*.634}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this means.}{253}{section*.635}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Why this works.}{253}{section*.637}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{If it fails.}{254}{section*.639}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {85}Mathematical Addendum: NHPP Intensity Regularity \& Estimator Consistency (v22)}{254}{section.85}\protected@file@percent }
\newlabel{app:nhpp_regular_consistency_v19}{{85}{254}{Mathematical Addendum: NHPP Intensity Regularity \& Estimator Consistency (v22)}{section.85}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope.}{254}{section*.641}\protected@file@percent }
\newlabel{eq:intensity}{{694}{254}{Model and notation}{equation.694}{}}
\newlabel{eq:loglik}{{695}{255}{Model and notation}{equation.695}{}}
\@writefile{toc}{\contentsline {paragraph}{What these assumptions are really doing.}{255}{section*.644}\protected@file@percent }
\newlabel{prop:concavity}{{85.1}{256}{Concavity \& MLE existence}{definition.85.1}{}}
\newlabel{prop:map}{{85.2}{256}{MAP}{definition.85.2}{}}
\newlabel{thm:consistency}{{85.3}{256}{Strong consistency}{definition.85.3}{}}
\newlabel{thm:clt}{{85.4}{257}{Asymptotic normality}{definition.85.4}{}}
\@writefile{toc}{\contentsline {paragraph}{What this means operationally.}{257}{section*.647}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{If it fails.}{258}{section*.651}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {86}Mathematical Addendum: Spectral-Radius Error Bars (v22)}{259}{section.86}\protected@file@percent }
\newlabel{app:spectral_radius_bounds}{{86}{259}{Mathematical Addendum: Spectral-Radius Error Bars (v22)}{section.86}{}}
\@writefile{toc}{\contentsline {paragraph}{Setup.}{259}{section*.653}\protected@file@percent }
\newlabel{eq:norm-bound}{{703}{260}{Operator-norm error}{equation.703}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is saying.}{260}{section*.655}\protected@file@percent }
\newlabel{eq:rho-bound}{{705}{260}{Spectral-radius error}{equation.705}{}}
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{260}{section*.657}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{This is the key quantity.}{261}{section*.659}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this guarantees.}{261}{section*.660}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{If it fails.}{262}{section*.663}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {87}Mathematical Addendum: Delta-Method CIs for $p^{(\Delta t)}$ (v22)}{262}{section.87}\protected@file@percent }
\newlabel{app:delta_method_probs}{{87}{262}{Mathematical Addendum: Delta-Method CIs for $p^{(\Delta t)}$ (v22)}{section.87}{}}
\@writefile{toc}{\contentsline {paragraph}{What we are doing.}{262}{section*.664}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this means.}{263}{section*.666}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{263}{section*.668}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Edge cases.}{263}{section*.669}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Important detail.}{263}{section*.671}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{If it fails.}{264}{section*.673}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {88}Mathematical Addendum: Calibration for CCG (v22)}{264}{section.88}\protected@file@percent }
\newlabel{app:ccg_calibration_math}{{88}{264}{Mathematical Addendum: Calibration for CCG (v22)}{section.88}{}}
\@writefile{toc}{\contentsline {paragraph}{What this section is doing.}{264}{section*.674}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{ECE (de-biased).}{264}{section*.675}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What’s different here.}{265}{section*.676}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Practical settings.}{265}{section*.677}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Isotonic regression (unique minimal solution).}{265}{section*.678}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Why use it.}{265}{section*.679}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Temperature scaling (TS).}{265}{section*.680}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Key property.}{265}{section*.681}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Why use it.}{265}{section*.682}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{When to use which.}{266}{section*.683}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate thresholds.}{266}{section*.684}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{How to apply the gate.}{266}{section*.685}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Bottom line.}{266}{section*.686}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {89}Mathematical Addendum: FDR $\times $ Hysteresis (v22)}{266}{section.89}\protected@file@percent }
\newlabel{app:fdr_hysteresis_interaction}{{89}{266}{Mathematical Addendum: FDR $\times $ Hysteresis (v22)}{section.89}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is doing.}{266}{section*.687}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {90}Mathematical Addendum: Capability/Permission Lattice (v22)}{268}{section.90}\protected@file@percent }
\newlabel{app:cpg_lattice}{{90}{268}{Mathematical Addendum: Capability/Permission Lattice (v22)}{section.90}{}}
\@writefile{toc}{\contentsline {paragraph}{What this sets up.}{268}{section*.693}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Action poset.}{268}{section*.694}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Capabilities and risk.}{268}{section*.695}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Monotone policy.}{268}{section*.696}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Tokenized escalation.}{268}{section*.697}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{No-leak theorem.}{269}{section*.698}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What this really means.}{269}{section*.699}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Implementation notes.}{269}{section*.700}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {91}Mathematical Addendum: Privacy Accounting (RDP $\to $ $(\varepsilon ,\delta )$) (v22)}{269}{section.91}\protected@file@percent }
\newlabel{app:privacy_accountant_rdp}{{91}{269}{Mathematical Addendum: Privacy Accounting (RDP $\to $ $(\varepsilon ,\delta )$) (v22)}{section.91}{}}
\@writefile{toc}{\contentsline {paragraph}{What we’re tracking.}{269}{section*.701}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{RDP.}{269}{section*.702}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Convert to $(\varepsilon ,\delta )$.}{269}{section*.703}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gaussian mechanism (per release).}{270}{section*.704}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate thresholds (PMG).}{270}{section*.705}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{What to log.}{270}{section*.706}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Composition choices.}{270}{section*.707}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {92}Mathematical Addendum: Robust Covariance for NZ (v22)}{270}{section.92}\protected@file@percent }
\newlabel{app:robust_covariance_nz}{{92}{270}{Mathematical Addendum: Robust Covariance for NZ (v22)}{section.92}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is solving.}{270}{section*.708}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Tyler's M-estimator (scatter).}{270}{section*.709}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Huber shrinkage.}{270}{section*.710}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Robust NZ statistic.}{271}{section*.711}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Why this holds up.}{271}{section*.712}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Pass/Fail.}{271}{section*.713}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {93}Baseline Accounting \& NZ Calibration Logging (v22)}{271}{section.93}\protected@file@percent }
\newlabel{app:baseline_accounting_v19}{{93}{271}{Baseline Accounting \& NZ Calibration Logging (v22)}{section.93}{}}
\@writefile{toc}{\contentsline {paragraph}{What this locks down.}{271}{section*.714}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {94}Online FDR Gate (LORD++/SAFFRON) (v22)}{274}{section.94}\protected@file@percent }
\newlabel{app:online_fdr_gate_v19}{{94}{274}{Online FDR Gate (LORD++/SAFFRON) \texorpdfstring {(v22)}{}}{section.94}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {94.1}What this controls}{274}{subsection.94.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {94.2}Defaults (v22)}{274}{subsection.94.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {94.3}LORD++ (how it runs)}{274}{subsection.94.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {94.4}SAFFRON (how it runs)}{275}{subsection.94.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {94.5}Dependence backstop}{275}{subsection.94.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {94.6}Pass/Fail logic}{275}{subsection.94.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {94.7}What gets logged}{276}{subsection.94.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {94.8}Implementation constants}{276}{subsection.94.8}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {95}Stability Guard via Spectral Radius (v22)}{276}{section.95}\protected@file@percent }
\newlabel{app:stability_guard_v19}{{95}{276}{Stability Guard via Spectral Radius (v22)}{section.95}{}}
\@writefile{toc}{\contentsline {paragraph}{What this enforces.}{276}{section*.722}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {96}Robust Covariance beyond NZ Core (v22)}{279}{section.96}\protected@file@percent }
\newlabel{app:robust_cov_beyond_nz_v19}{{96}{279}{Robust Covariance beyond NZ Core (v22)}{section.96}{}}
\@writefile{toc}{\contentsline {paragraph}{What this extends.}{279}{section*.732}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Tyler (robust shape).}{279}{section*.735}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Huber shrinkage.}{279}{section*.736}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Regularized Tyler (when $n\le d$).}{280}{section*.737}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {97}Permission Lattice Concretization (v22)}{281}{section.97}\protected@file@percent }
\newlabel{app:permission_lattice_v19}{{97}{281}{Permission Lattice Concretization (v22)}{section.97}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{281}{section*.743}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {98}Privacy Accountant Wiring (v22)}{283}{section.98}\protected@file@percent }
\newlabel{app:privacy_accountant_wiring_v19}{{98}{283}{Privacy Accountant Wiring (v22)}{section.98}{}}
\@writefile{toc}{\contentsline {paragraph}{What this piece is doing.}{283}{section*.753}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {99}Uncertainty Ledger (v22)}{285}{section.99}\protected@file@percent }
\newlabel{app:uncertainty_ledger_v19}{{99}{285}{Uncertainty Ledger (v22)}{section.99}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{285}{section*.760}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Delta method (when things are smooth).}{286}{section*.763}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Bootstrap (when we don’t trust assumptions).}{286}{section*.764}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Wilson score (for probabilities).}{286}{section*.765}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Risk index $R=c-p$.}{286}{section*.766}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {100}Hysteresis Preflight (v22)}{287}{section.100}\protected@file@percent }
\newlabel{app:hysteresis_preflight_v19}{{100}{287}{Hysteresis Preflight (v22)}{section.100}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{287}{section*.771}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{How much influence actions have ($P_m$).}{288}{section*.774}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {101}Calibration Defaults (v22)}{290}{section.101}\protected@file@percent }
\newlabel{app:calibration_defaults_v19}{{101}{290}{Calibration Defaults (v22)}{section.101}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{290}{section*.779}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {102}Stress-Test Registry (v22)}{292}{section.102}\protected@file@percent }
\newlabel{app:stress_registry_v19}{{102}{292}{Stress-Test Registry (v22)}{section.102}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{292}{section*.789}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {103}Soft-Gating Math Upgrades (v22): S1--S10}{294}{section.103}\protected@file@percent }
\newlabel{app:soft_gating_v19}{{103}{294}{Soft-Gating Math Upgrades (v22): S1--S10}{section.103}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{294}{section*.794}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{How to think about all of these together.}{296}{section*.805}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {104}Moduli Space Formalism and Stabilization}{296}{section.104}\protected@file@percent }
\newlabel{sec:moduli_stabilization}{{104}{296}{Moduli Space Formalism and Stabilization}{section.104}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{296}{section*.806}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {105}Spectral Geometry and Positivity}{297}{section.105}\protected@file@percent }
\newlabel{sec:spectral_geometry}{{105}{297}{Spectral Geometry and Positivity}{section.105}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{297}{section*.813}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Illustrative moduli scalar potential with stabilized minima. Contours show mass eigenvalues consistent with stability and cosmology.}}{298}{figure.caption.812}\protected@file@percent }
\newlabel{fig:moduli_landscape}{{16}{298}{Illustrative moduli scalar potential with stabilized minima. Contours show mass eigenvalues consistent with stability and cosmology}{figure.caption.812}{}}
\@writefile{toc}{\contentsline {section}{\numberline {106}Non-Perturbative Structures}{299}{section.106}\protected@file@percent }
\newlabel{sec:nonperturbative_structures}{{106}{299}{Non-Perturbative Structures}{section.106}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{299}{section*.820}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Heat kernel coefficients $a_n$ for a representative background, illustrating positivity and spectral stability.}}{300}{figure.caption.819}\protected@file@percent }
\newlabel{fig:heat_kernel}{{17}{300}{Heat kernel coefficients $a_n$ for a representative background, illustrating positivity and spectral stability}{figure.caption.819}{}}
\@writefile{toc}{\contentsline {section}{\numberline {107}Topological Invariants in Gauge Embeddings}{301}{section.107}\protected@file@percent }
\newlabel{sec:topological_invariants}{{107}{301}{Topological Invariants in Gauge Embeddings}{section.107}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{301}{section*.828}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Profile of an $SU(2)$ BPST instanton contributing to non-perturbative dynamics and axion potential corrections.}}{302}{figure.caption.827}\protected@file@percent }
\newlabel{fig:instanton_profile}{{18}{302}{Profile of an $SU(2)$ BPST instanton contributing to non-perturbative dynamics and axion potential corrections}{figure.caption.827}{}}
\@writefile{toc}{\contentsline {section}{\numberline {108}Causal Sets and Ordering Algebras (Discrete Time Backbone)}{303}{section.108}\protected@file@percent }
\newlabel{sec:causal_sets}{{108}{303}{Causal Sets and Ordering Algebras (Discrete Time Backbone)}{section.108}{}}
\@writefile{toc}{\contentsline {paragraph}{What this is really doing.}{303}{section*.834}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Causal set Hasse diagram with a dashed Alexandrov diamond.}}{305}{figure.caption.842}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {109}Operator Algebras for Observer Dynamics}{306}{section.109}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {110}Sheaf Theory and Fiber Bundles for Gauge Patching}{306}{section.110}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces Algebra--state--gate diagram: $\mathcal  {A}\to (\pi ,\mathcal  {H})\to \Phi $ with Lindblad flow.}}{307}{figure.caption.843}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces Open cover with restrictions $s_i|_{U_i\cap U_j}=s_j|_{U_i\cap U_j}$ ensuring consistent gluing into a global section.}}{308}{figure.caption.844}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {111}Homotopy and Cobordism Classes}{308}{section.111}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces Schematic of $\pi _1$ strings, $\pi _2$ monopoles, and $\pi _3$ instantons, showing how different homotopy groups classify topological defects.}}{309}{figure.caption.845}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {112}Entropy Geometry and Information Metrics}{310}{section.112}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {113}Noncommutative Geometry (NCG) Hooks}{310}{section.113}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces Level sets of the Fisher metric, forming local information ellipsoids that describe distinguishability in parameter space.}}{311}{figure.caption.846}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces Schematic of a spectral triple $(\mathcal  {A},\mathcal  {H},D)$ and inner fluctuations generating gauge structure.}}{312}{figure.caption.847}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {114}Category-Theoretic Unification}{312}{section.114}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {25}{\ignorespaces Functors $F,G$ and a natural transformation $\eta $ encoding gate logic as a commuting structure between candidate and validated EFTs.}}{313}{figure.caption.848}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {26}{\ignorespaces Vector field sketch of a projected Langevin flow in parameter space constrained by the UTFANSWF admissible region.}}{314}{figure.caption.850}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {115}Functional Analysis and Operators}{315}{section.115}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {115.1}Densely defined operators, self-adjointness, and spectral radius guards}{315}{subsection.115.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {115.2}Example: Ornstein--Uhlenbeck generator on a weighted space}{315}{subsection.115.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {116}Functional RG (FRG) Entities}{316}{section.116}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {116.1}Wetterich equation and threshold functions}{316}{subsection.116.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {116.2}Example: $Z_k$-improved local potential (LPA$'$) for a single scalar}{317}{subsection.116.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {117}Geometry and Topology}{318}{section.117}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {117.1}Defect classification by homotopy}{318}{subsection.117.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {117.2}Čech cohomology example: $H^1(S^1,\mathbb  {Z})$}{318}{subsection.117.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {117.3}Entropy ellipsoids and differential entropy}{319}{subsection.117.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {118}Positivity and Dispersion Relations}{319}{section.118}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {118.1}K\"all\'en--Lehmann representation}{319}{subsection.118.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {118.2}Forward-limit positivity for $2\to 2$ amplitudes}{320}{subsection.118.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {119}Observer and Learning via Operator Algebras}{321}{section.119}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {119.1}C$^\ast $-algebras, states, and GNS}{321}{subsection.119.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {119.2}Spectral distance (Connes)}{321}{subsection.119.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {119.3}Stochastic differential geometry (Stratonovich on manifolds)}{321}{subsection.119.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {120}Cosmology Anchors}{322}{section.120}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {120.1}Compressed likelihood for CMB+BAO+SN (+GW)}{322}{subsection.120.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {120.2}TCC-style inflationary bound (symbolic)}{322}{subsection.120.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {120.3}Proton lifetime scaling (dimension-6)}{322}{subsection.120.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {121}Moduli Space Formalism and Stabilization}{323}{section.121}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {121.1}Set-up and Vacuum Selection}{323}{subsection.121.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {121.2}Two-Moduli Worked Example (Analytic Eigenvalues)}{323}{subsection.121.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {121.3}Cosmological Consistency Gates}{324}{subsection.121.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {121.4}Threshold Corrections and GUT Matching}{324}{subsection.121.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {121.5}Checklist for PASS}{325}{subsection.121.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {122}Spectral Geometry and Positivity Constraints}{325}{section.122}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {122.1}K\"all\'en--Lehmann Representation}{325}{subsection.122.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {122.2}Forward-Limit Dispersion and EFT Coefficients}{326}{subsection.122.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {122.3}Worked Example: Shift-Symmetric Scalar with $(\partial \varphi )^4$}{326}{subsection.122.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {122.4}Photon Example: $(F_{\mu \nu }F^{\mu \nu })^2$ and $(F_{\mu \nu }\tilde  F^{\mu \nu })^2$}{327}{subsection.122.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {122.5}No-Superluminality Gate (Small-Background Test)}{327}{subsection.122.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {122.6}PASS Ledger}{327}{subsection.122.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {123}Functional RG Fixed-Point Stability (Conceptual Truncation)}{327}{section.123}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {123.1}Dimensionless Couplings and Flow}{327}{subsection.123.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {123.2}Beta Functions (with Threshold Functions)}{328}{subsection.123.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {123.3}Fixed Point and Stability Matrix}{328}{subsection.123.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {123.4}Worked Analytic Structure (Two-Coupling Toy Slice)}{329}{subsection.123.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {123.5}PASS Conditions}{329}{subsection.123.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {124}Compressed Cosmology Jacobians (Curvature–aware, Complex–Step Verified)}{330}{section.124}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {125}P0: Compressed Cosmology Jacobians — Derivation and Validation}{333}{section.125}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {126}P0: Moduli Stabilization with Numbers}{335}{section.126}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {127}P0: Spectral Positivity and Forward Bounds}{336}{section.127}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {128}P0: FRG Toy Fixed Point}{336}{section.128}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {129}P1: Operator Algebras for Observer Dynamics}{337}{section.129}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {130}P1: Stress-Test Registry (excerpt)}{337}{section.130}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {131}P1: Category-Theoretic Commuting Square}{338}{section.131}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {132}P2: Noncommutative Geometry (explicit $S^1$ example)}{338}{section.132}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {133}P2: Sheaf Theory \& Fiber Bundles (explicit $S^2$ patching)}{339}{section.133}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {134}P2: Homotopy, Cobordism, and Defect Gates}{339}{section.134}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {135}P2: Entropy Geometry \& Information Metrics (Gaussian family)}{339}{section.135}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {136}P2: Topological Invariants (Chern number on $S^2$)}{340}{section.136}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {137}P2: Causal Sets \& Ordering Algebras (numeric check)}{340}{section.137}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {138}P2: Stochastic Differential Geometry (OU strong order)}{341}{section.138}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {139}P2: Densely Defined Operators \& Self-Adjointness (constructive)}{341}{section.139}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {140}Operator Algebras for Observer Dynamics}{342}{section.140}\protected@file@percent }
\newlabel{sec:obs-algebras}{{140}{342}{Operator Algebras for Observer Dynamics}{section.140}{}}
\@writefile{toc}{\contentsline {paragraph}{Local algebras and states.}{342}{section*.864}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{GNS construction and kinematics.}{342}{section*.865}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Observer gates as CPTP morphisms.}{343}{section*.866}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{GKLS generator and entropy arrow.}{343}{section*.867}\protected@file@percent }
\newlabel{eq:GKLS}{{821}{343}{GKLS generator and entropy arrow}{equation.821}{}}
\newlabel{eq:spohn}{{822}{343}{GKLS generator and entropy arrow}{equation.822}{}}
\@writefile{toc}{\contentsline {paragraph}{Coherence budget and consistency gate.}{343}{section*.868}\protected@file@percent }
\newlabel{eq:coh-budget}{{823}{343}{Coherence budget and consistency gate}{equation.823}{}}
\@writefile{toc}{\contentsline {paragraph}{Quantum Fisher information (QFI) bound.}{344}{section*.869}\protected@file@percent }
\newlabel{eq:qfi-contract}{{824}{344}{Quantum Fisher information (QFI) bound}{equation.824}{}}
\@writefile{toc}{\contentsline {paragraph}{Minimal Gaussian example (SWF-ISM slice).}{344}{section*.870}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Result.}{344}{section*.871}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {141}Stress-Test Registry \& Kill-Shot Harness}{345}{section.141}\protected@file@percent }
\newlabel{app:registry}{{141}{345}{Stress-Test Registry \& Kill-Shot Harness}{section.141}{}}
\@writefile{toc}{\contentsline {paragraph}{Definition (test item).}{345}{section*.872}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Acceptance.}{345}{section*.873}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Illustrative items (subset).}{345}{section*.874}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Kill-shot protocol.}{346}{section*.875}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {142}Category-Theoretic Unification Layer}{347}{section.142}\protected@file@percent }
\newlabel{sec:category-layer}{{142}{347}{Category-Theoretic Unification Layer}{section.142}{}}
\@writefile{toc}{\contentsline {paragraph}{Categories.}{347}{section*.876}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Functors.}{347}{section*.877}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Consistency square.}{348}{section*.878}\protected@file@percent }
\newlabel{eq:consistency-square}{{828}{348}{Consistency square}{equation.828}{}}
\@writefile{toc}{\contentsline {paragraph}{Theorem (UTFANSWF Consistency).}{348}{section*.879}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Proof sketch.}{348}{section*.880}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A143}P2: Geometric and Topological Hooks}{349}{section.143}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A143.1}Noncommutative Geometry (NCG) Hooks}{349}{subsection.143.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A143.2}Sheaves and Fiber Bundles}{349}{subsection.143.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A143.3}Homotopy and Cobordism}{350}{subsection.143.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A143.4}Entropy Geometry}{350}{subsection.143.4}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A144}Remaining Core Mathematics}{351}{section.144}\protected@file@percent }
\newlabel{sec:core_math}{{A144}{351}{Remaining Core Mathematics}{section.144}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A144.1}Functional RG Eigenvalue Consistency}{351}{subsection.144.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A144.2}Positivity and Dispersion Bounds}{352}{subsection.144.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A144.3}Seesaw Neutrino Embedding}{352}{subsection.144.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A144.4}Threshold Corrections in SO(10)/Heterotic Embedding}{353}{subsection.144.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A144.5}Compressed Cosmology Likelihood}{353}{subsection.144.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A145}Quantum Computing in UTFANSWF}{354}{section.145}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A145.1}Information-Theoretic Grounding}{354}{subsection.145.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A145.2}Neutral Excitations as Qubits}{354}{subsection.145.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A145.3}Symmetry-Protected Gate Operations}{355}{subsection.145.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A145.4}Neutral Zone (NZ) Sandwich in Hardware}{355}{subsection.145.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A145.5}Predictions for Platforms}{356}{subsection.145.5}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {20}{\ignorespaces UTFANSWF predictions for qubit platform viability.}}{356}{table.caption.882}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A145.6}Roadmap Implications}{356}{subsection.145.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A146}Appendix: UTFANSWF $\leftrightarrow $ Observer Dialogue}{357}{section.146}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A147}Zero-Point Modulation Clause}{359}{section.147}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.1}Vacuum as Minimal Information State}{359}{subsection.147.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.2}Modulation Operator}{359}{subsection.147.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.3}Gate Constraints}{359}{subsection.147.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.4}Worked Example: Single Mode}{360}{subsection.147.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.5}Observables}{360}{subsection.147.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.6}Pass/Fail Criteria}{360}{subsection.147.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.7}Harmonic Bubble}{361}{subsection.147.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.8}Gravity}{361}{subsection.147.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.9}Refractal Harmonics}{361}{subsection.147.9}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A147.10}Neutral Zone Horizon}{362}{subsection.147.10}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A148}Guardrails and Security}{362}{section.148}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A148.1}Clock-Skew Bug and Temporal Guard}{362}{subsection.148.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A148.2}Permission Lattice}{363}{subsection.148.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A148.3}Spectral Guard}{363}{subsection.148.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A149}Physics and Mathematics Extensions}{364}{section.149}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A149.1}SMEFT and Dispersion Positivity}{364}{subsection.149.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A149.2}Combined Constraints}{365}{subsection.149.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A150}Cosmology Fits}{365}{section.150}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A150.1}Compressed Likelihoods}{365}{subsection.150.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A150.2}Axion Dark Matter Gate}{366}{subsection.150.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A150.3}Echo Predictions}{367}{subsection.150.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A151}Applications}{367}{section.151}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A151.1}Micro-Verse Storage}{368}{subsection.151.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A151.2}Entropy-Driven I/O}{368}{subsection.151.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A151.3}Quantum Batteries}{369}{subsection.151.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A152}Outreach and Addenda}{369}{section.152}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A152.1}Reality Engine Blurb}{370}{subsection.152.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A152.2}Origin of Gravity}{370}{subsection.152.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A153}Falsifiability, Extensibility, and Communicability}{371}{section.153}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A153.1}Falsifiability: Axion Gate, Cosmology Fits, GW Echoes}{371}{subsection.153.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(i) Axion Dark-Matter Gate.}{371}{section*.888}\protected@file@percent }
\newlabel{eq:axion-band}{{873}{371}{(i) Axion Dark-Matter Gate}{equation.873}{}}
\newlabel{eq:axion-misalign}{{874}{371}{(i) Axion Dark-Matter Gate}{equation.874}{}}
\newlabel{eq:axion-test}{{875}{372}{(i) Axion Dark-Matter Gate}{equation.875}{}}
\@writefile{toc}{\contentsline {paragraph}{(ii) Compressed Cosmology Fits.}{372}{section*.889}\protected@file@percent }
\newlabel{eq:chi2}{{876}{372}{(ii) Compressed Cosmology Fits}{equation.876}{}}
\newlabel{eq:chi2-gate}{{877}{372}{(ii) Compressed Cosmology Fits}{equation.877}{}}
\@writefile{toc}{\contentsline {paragraph}{(iii) Gravitational-Wave Echoes.}{372}{section*.890}\protected@file@percent }
\newlabel{eq:echo-model}{{878}{372}{(iii) Gravitational-Wave Echoes}{equation.878}{}}
\newlabel{eq:snr}{{879}{372}{(iii) Gravitational-Wave Echoes}{equation.879}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A153.2}Extensibility: Micro-Verse Storage, Entropy I/O, Quantum Batteries}{373}{subsection.153.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(i) Micro-Verse Storage.}{373}{section*.891}\protected@file@percent }
\newlabel{eq:storage}{{880}{373}{(i) Micro-Verse Storage}{equation.880}{}}
\@writefile{toc}{\contentsline {paragraph}{(ii) Entropy-Driven I/O.}{373}{section*.892}\protected@file@percent }
\newlabel{eq:landauer}{{881}{373}{(ii) Entropy-Driven I/O}{equation.881}{}}
\@writefile{toc}{\contentsline {paragraph}{(iii) Quantum Batteries via Refractal Coherence.}{373}{section*.893}\protected@file@percent }
\newlabel{eq:q-battery}{{882}{373}{(iii) Quantum Batteries via Refractal Coherence}{equation.882}{}}
\newlabel{eq:q-coh}{{883}{373}{(iii) Quantum Batteries via Refractal Coherence}{equation.883}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A153.3}Communicability: Glossary Foundations \& Visual Stress Tests}{374}{subsection.153.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(i) Glossary $\rightarrow $ Math Consistency.}{374}{section*.894}\protected@file@percent }
\newlabel{eq:fidelity}{{884}{374}{(i) Glossary $\rightarrow $ Math Consistency}{equation.884}{}}
\@writefile{toc}{\contentsline {paragraph}{(ii) Triangle-Guard Logic.}{374}{section*.895}\protected@file@percent }
\newlabel{eq:gates}{{885}{374}{(ii) Triangle-Guard Logic}{equation.885}{}}
\newlabel{eq:tri-pass}{{886}{374}{(ii) Triangle-Guard Logic}{equation.886}{}}
\@writefile{toc}{\contentsline {paragraph}{(iii) Style-Lock (Backwards Compatibility).}{374}{section*.896}\protected@file@percent }
\newlabel{eq:style-lock}{{887}{374}{(iii) Style-Lock (Backwards Compatibility)}{equation.887}{}}
\@writefile{toc}{\contentsline {section}{\numberline {A154}Entropy Scaling Across Systems: Axion Gate $\leftrightarrow $ GW Echoes}{374}{section.154}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A154.1}Master Scaling Law}{374}{subsection.154.1}\protected@file@percent }
\newlabel{eq:entropy-scaling}{{888}{375}{Master Scaling Law}{equation.888}{}}
\newlabel{eq:entropy-invariant}{{889}{375}{Master Scaling Law}{equation.889}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A154.2}Microscopic Slice: Axion Dark-Matter Gate}{375}{subsection.154.2}\protected@file@percent }
\newlabel{eq:axion-power}{{890}{375}{Microscopic Slice: Axion Dark-Matter Gate}{equation.890}{}}
\newlabel{eq:xi-axion}{{892}{375}{Microscopic Slice: Axion Dark-Matter Gate}{equation.892}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A154.3}Macroscopic Slice: GW Echoes}{376}{subsection.154.3}\protected@file@percent }
\newlabel{eq:echo-train}{{893}{376}{Macroscopic Slice: GW Echoes}{equation.893}{}}
\newlabel{eq:xi-echo}{{896}{376}{Macroscopic Slice: GW Echoes}{equation.896}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A154.4}Unification and Cross-Predictions}{376}{subsection.154.4}\protected@file@percent }
\newlabel{eq:scaling-universal}{{897}{376}{Unification and Cross-Predictions}{equation.897}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A154.5}Decision Rules}{377}{subsection.154.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A154.6}Summary}{377}{subsection.154.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A155}Compressed Cosmology Jacobian Verification}{377}{section.155}\protected@file@percent }
\newlabel{app:compressed-jacobians}{{A155}{377}{Compressed Cosmology Jacobian Verification}{section.155}{}}
\newlabel{sec:jacobian_fix}{{A155}{377}{Compressed Cosmology Jacobian Verification}{section.155}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A155.1}Model and Observables}{378}{subsection.155.1}\protected@file@percent }
\newlabel{eq:Ez}{{899}{378}{Model and Observables}{equation.899}{}}
\newlabel{eq:Dc}{{900}{378}{Model and Observables}{equation.900}{}}
\newlabel{eq:DA_DL}{{901}{378}{Model and Observables}{equation.901}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A155.2}Jacobian Definitions and Numerical Methods}{378}{subsection.155.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A155.3}Grid, Fiducial, and Tolerance}{379}{subsection.155.3}\protected@file@percent }
\newlabel{eq:gate}{{905}{379}{Grid, Fiducial, and Tolerance}{equation.905}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A155.4}Results}{379}{subsection.155.4}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {21}{\ignorespaces Maximum relative error between central differences (CD) and complex--step (CS) Jacobians.}}{379}{table.caption.897}\protected@file@percent }
\newlabel{tab:jacobian-errors}{{21}{379}{Maximum relative error between central differences (CD) and complex--step (CS) Jacobians}{table.caption.897}{}}
\@writefile{toc}{\contentsline {paragraph}{Status.}{380}{section*.898}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A155.5}Implementation Notes}{380}{subsection.155.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A156}FRG Fixed-Point and Stability Analysis (Benchmark T0)}{380}{section.156}\protected@file@percent }
\newlabel{app:frg-t0}{{A156}{380}{FRG Fixed-Point and Stability Analysis (Benchmark T0)}{section.156}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A156.1}Setup}{380}{subsection.156.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A156.2}Fixed Point}{381}{subsection.156.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A156.3}Stability Matrix and Critical Exponents}{381}{subsection.156.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A156.4}Status}{382}{subsection.156.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A156.5}Notes and Next Steps}{382}{subsection.156.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A157}Observer Algebra: Contractivity and Spectral-Radius Guard}{383}{section.157}\protected@file@percent }
\newlabel{app:observer-guard}{{A157}{383}{Observer Algebra: Contractivity and Spectral-Radius Guard}{section.157}{}}
\newlabel{sec:observer-algebra}{{A157}{383}{Observer Algebra: Contractivity and Spectral-Radius Guard}{section.157}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A157.1}Setup (Finite-Dimensional CPTP Map)}{383}{subsection.157.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A157.2}Focus on Deviations (Traceless Subspace)}{383}{subsection.157.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A157.3}The Guard Condition}{384}{subsection.157.3}\protected@file@percent }
\newlabel{eq:observer-guard}{{918}{384}{The Guard Condition}{equation.918}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A157.4}Stability Under Perturbations}{384}{subsection.157.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A157.5}Numerical Construction}{384}{subsection.157.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A157.6}Results}{385}{subsection.157.6}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {22}{\ignorespaces Spectral radius $\setbox \z@ \hbox {\mathsurround \z@ $\textstyle \rho $}\mathaccent "0362{\rho }$ on traceless subspace for $d=4$, $r=3$, $\varepsilon =0.02$. PASS if $\setbox \z@ \hbox {\mathsurround \z@ $\textstyle \rho $}\mathaccent "0362{\rho }\le 0.98$.}}{385}{table.caption.899}\protected@file@percent }
\newlabel{tab:observer-guard}{{22}{385}{Spectral radius $\widehat {\rho }$ on traceless subspace for $d=4$, $r=3$, $\varepsilon =0.02$. PASS if $\widehat {\rho }\le 0.98$}{table.caption.899}{}}
\@writefile{toc}{\contentsline {paragraph}{Status.}{385}{section*.900}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A157.7}GNS Snapshot (Conceptual Placement)}{385}{subsection.157.7}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A158}Neutral Zone (NZ) Sandwich: Robustness Sweep and Sensitivities}{386}{section.158}\protected@file@percent }
\newlabel{app:nz-sandwich}{{A158}{386}{Neutral Zone (NZ) Sandwich: Robustness Sweep and Sensitivities}{section.158}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A158.1}Setup and Acceptance Region}{386}{subsection.158.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A158.2}Monte Carlo Sweep}{387}{subsection.158.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A158.3}Results}{387}{subsection.158.3}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {23}{\ignorespaces Binned rates over $\sigma $ bands. ``Inside'' = within $[L,U]$; ``Robust'' = within $[L+\delta , U-\delta ]$.}}{388}{table.caption.902}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {27}{\ignorespaces Neutral Zone sandwich acceptance with robustness buffer.}}{388}{figure.caption.903}\protected@file@percent }
\newlabel{fig:nz-robustness}{{27}{388}{Neutral Zone sandwich acceptance with robustness buffer}{figure.caption.903}{}}
\@writefile{toc}{\contentsline {paragraph}{Status.}{388}{section*.904}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A159}Axion Gate: Misalignment Numbers and Photon Coupling (6--60 $\mu $eV)}{389}{section.159}\protected@file@percent }
\newlabel{app:axion-gate}{{A159}{389}{Axion Gate: Misalignment Numbers and Photon Coupling (6--60 $\mu $eV)}{section.159}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A159.1}Step 1: From Mass to Decay Constant}{389}{subsection.159.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A159.2}Step 2: Match the Dark-Matter Density}{389}{subsection.159.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A159.3}Step 3: Compute the Photon Coupling}{390}{subsection.159.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A159.4}Step 4: Put It All Together}{390}{subsection.159.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A159.5}What to Notice}{390}{subsection.159.5}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {24}{\ignorespaces Required initial misalignment angle and $g_{a\gamma \gamma }$ at benchmark masses (target $\Omega _a h^2=0.12$).}}{391}{table.caption.906}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {28}{\ignorespaces Minimal initial angle $\theta _i$ vs axion mass required to saturate $\Omega _a h^2=0.12$ in the 6--60 $\mu $eV band (with anharmonic correction).}}{391}{figure.caption.907}\protected@file@percent }
\newlabel{fig:axion-theta}{{28}{391}{Minimal initial angle $\theta _i$ vs axion mass required to saturate $\Omega _a h^2=0.12$ in the 6--60 $\mu $eV band (with anharmonic correction)}{figure.caption.907}{}}
\@writefile{toc}{\contentsline {paragraph}{Status.}{391}{section*.908}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A160}Neutrino Sector: Type-I Seesaw, Observables, and Acceptance Gates}{392}{section.160}\protected@file@percent }
\newlabel{app:seesaw}{{A160}{392}{Neutrino Sector: Type-I Seesaw, Observables, and Acceptance Gates}{section.160}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A160.1}Step 1: Build the Mass Structure}{392}{subsection.160.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A160.2}Step 2: Connect to Measurable Quantities}{393}{subsection.160.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A160.3}Step 3: Build Models (Casas--Ibarra)}{393}{subsection.160.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A160.4}Step 4: Define the Gates}{394}{subsection.160.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A160.5}Step 5: What a Passing Solution Looks Like}{394}{subsection.160.5}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Status.}{395}{section*.910}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A161}Positivity and Forward-Limit Dispersion Bounds}{395}{section.161}\protected@file@percent }
\newlabel{app:positivity}{{A161}{395}{Positivity and Forward-Limit Dispersion Bounds}{section.161}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A161.1}Setup: analytic, unitary, causal $2\!\to \!2$ amplitudes}{395}{subsection.161.1}\protected@file@percent }
\newlabel{eq:hankelPSD}{{935}{396}{Setup: analytic, unitary, causal $2\!\to \!2$ amplitudes}{equation.935}{}}
\@writefile{toc}{\contentsline {paragraph}{Crossing/channel averaging.}{396}{section*.912}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A161.2}Mapping to EFT Wilson coefficients}{396}{subsection.161.2}\protected@file@percent }
\newlabel{eq:eftPSD}{{938}{397}{Mapping to EFT Wilson coefficients}{equation.938}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A161.3}Acceptance gates (referee-facing)}{397}{subsection.161.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Partial-wave unitarity sanity check.}{397}{section*.913}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A161.4}Minimal harness (pseudocode)}{398}{subsection.161.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A161.5}Reporting format}{398}{subsection.161.5}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Notes.}{398}{section*.915}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A162}PPN and Gravitational-Wave Sector: Gates and Mapping}{398}{section.162}\protected@file@percent }
\newlabel{app:ppn-gw}{{A162}{398}{PPN and Gravitational-Wave Sector: Gates and Mapping}{section.162}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A162.1}Setup and Notation}{399}{subsection.162.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PPN metric.}{399}{section*.916}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{GW sector.}{399}{section*.917}\protected@file@percent }
\newlabel{eq:gw-action}{{943}{399}{GW sector}{equation.943}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A162.2}Model-to-observable mapping (minimal recipe)}{400}{subsection.162.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A162.3}Acceptance Gates (PASS requires all applicable)}{400}{subsection.162.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PPN gates (Solar System).}{400}{section*.918}\protected@file@percent }
\newlabel{eq:ppn-gates}{{944}{400}{PPN gates (Solar System)}{equation.944}{}}
\@writefile{toc}{\contentsline {paragraph}{GW propagation gates.}{400}{section*.919}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Waveform-consistency (optional).}{401}{section*.920}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A162.4}Compact PASS/FAIL checklist}{401}{subsection.162.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A162.5}Minimal harness (pseudocode)}{401}{subsection.162.5}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Notes.}{402}{section*.922}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A163}Cosmology: End-to-End Compressed Likelihood and Gate}{402}{section.163}\protected@file@percent }
\newlabel{app:cosmo-like}{{A163}{402}{Cosmology: End-to-End Compressed Likelihood and Gate}{section.163}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A163.1}Data vector, parameters, and Jacobians}{402}{subsection.163.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Compressed summaries (examples).}{402}{section*.923}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Theory mapping.}{403}{section*.924}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A163.2}Likelihood, priors, and profiling/marginalization}{403}{subsection.163.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A163.3}Acceptance gate (referee-facing)}{403}{subsection.163.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A163.4}Robustness and stability checks}{404}{subsection.163.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A163.5}Reporting table (minimum)}{404}{subsection.163.5}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Notes.}{405}{section*.926}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A164}Black-Hole Ringdown and Echoes: Model, Fit Procedure, and Acceptance Gates}{405}{section.164}\protected@file@percent }
\newlabel{app:ringdown-echo}{{A164}{405}{Black-Hole Ringdown and Echoes: Model, Fit Procedure, and Acceptance Gates}{section.164}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A164.1}Kerr ringdown (baseline)}{405}{subsection.164.1}\protected@file@percent }
\newlabel{eq:qnm-td}{{952}{405}{Kerr ringdown (baseline)}{equation.952}{}}
\newlabel{eq:qnm-sum}{{953}{405}{Kerr ringdown (baseline)}{equation.953}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A164.2}Echo response (minimal, agnostic)}{406}{subsection.164.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Frequency-domain view (optional).}{406}{section*.927}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A164.3}Data model and noise weighting}{406}{subsection.164.3}\protected@file@percent }
\newlabel{eq:gw-noiseip}{{958}{407}{Data model and noise weighting}{equation.958}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A164.4}Fit protocol (minimal)}{407}{subsection.164.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A164.5}Acceptance gates (PASS requires all applicable)}{407}{subsection.164.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A164.6}Reporting}{408}{subsection.164.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Notes.}{408}{section*.929}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A165}Reactivation Phase: Verified Gates to Live Prediction Surface}{408}{section.165}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A165.1}From Static Validation to Dynamic Execution}{408}{subsection.165.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A165.2}Reactivation as a Controlled Phase Transition}{409}{subsection.165.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A165.3}CFGL as the Execution Backbone}{410}{subsection.165.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A165.4}Prediction Surface and Crosstalk Enforcement}{410}{subsection.165.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A165.5}Operational Interpretation}{410}{subsection.165.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A166}Row 19 — Functional RG, PPN/GW Limits, Positivity Bounds, and Analytic Jacobians}{411}{section.166}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.1}Role Within the Reactivation Phase}{411}{subsection.166.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.2}Gate Composition and CFGL Interpretation}{411}{subsection.166.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.3}Operational Summary}{412}{subsection.166.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.4}Transition to Explicit Constructions}{412}{subsection.166.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.5}Row 19.1 — FRG Truncation \& Fixed-Point Stability (Reproducibility Block)}{412}{subsection.166.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.5.1}Effective Average Action, Fields, and Scheme (v21 defaults)}{412}{subsubsection.166.5.1}\protected@file@percent }
\newlabel{eq:EAA}{{963}{413}{Effective Average Action, Fields, and Scheme (v21 defaults)}{equation.963}{}}
\newlabel{eq:scalar_potential}{{964}{413}{Effective Average Action, Fields, and Scheme (v21 defaults)}{equation.964}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.5.2}Dimensionless Variables and Flow Parameters}{413}{subsubsection.166.5.2}\protected@file@percent }
\newlabel{eq:dimensionless}{{965}{413}{Dimensionless Variables and Flow Parameters}{equation.965}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.5.3}Flow Equation (Wetterich Form)}{413}{subsubsection.166.5.3}\protected@file@percent }
\newlabel{eq:wetterich}{{967}{413}{Flow Equation (Wetterich Form)}{equation.967}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.5.4}Gauge Choice, Background Split, and Regulator}{414}{subsubsection.166.5.4}\protected@file@percent }
\newlabel{eq:litim}{{968}{414}{Gauge Choice, Background Split, and Regulator}{equation.968}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.5.5}Threshold Functions (Closed Litim Form)}{414}{subsubsection.166.5.5}\protected@file@percent }
\newlabel{eq:thresholds}{{969}{414}{Threshold Functions (Closed Litim Form)}{equation.969}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.5.6}Curvature-Quadratic Toggle (Ablation Hook)}{414}{subsubsection.166.5.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Pass rule (diagnostic).}{414}{section*.930}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{415}{section*.931}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.6}V.2 Exact Flow Objects and Beta Functions (gravity + light-scalar portal)}{415}{subsection.166.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gravitational couplings.}{415}{section*.932}\protected@file@percent }
\newlabel{eq:beta_g}{{970}{415}{Gravitational couplings}{equation.970}{}}
\newlabel{eq:etaN_general}{{971}{415}{Gravitational couplings}{equation.971}{}}
\newlabel{eq:Neta_def}{{972}{415}{Gravitational couplings}{equation.972}{}}
\newlabel{eq:Deta_def}{{973}{415}{Gravitational couplings}{equation.973}{}}
\newlabel{eq:beta_lambda_grav}{{974}{416}{Gravitational couplings}{equation.974}{}}
\@writefile{toc}{\contentsline {paragraph}{Scalar portal sector.}{416}{section*.933}\protected@file@percent }
\newlabel{eq:beta_m2}{{975}{416}{Scalar portal sector}{equation.975}{}}
\newlabel{eq:beta_lamphi}{{976}{416}{Scalar portal sector}{equation.976}{}}
\newlabel{eq:eta_phi}{{977}{416}{Scalar portal sector}{equation.977}{}}
\newlabel{eq:grav_corr1}{{978}{416}{Scalar portal sector}{equation.978}{}}
\newlabel{eq:grav_corr2}{{979}{416}{Scalar portal sector}{equation.979}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.7}V.3 Fixed Points, Stability Matrix, and Critical Exponents}{416}{subsection.166.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.7.1}Linearized Flow and Stability Matrix}{417}{subsubsection.166.7.1}\protected@file@percent }
\newlabel{eq:stability_matrix}{{981}{417}{Linearized Flow and Stability Matrix}{equation.981}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.7.2}Critical Exponents and Relevance Structure}{417}{subsubsection.166.7.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.7.3}Analytic Construction of the Stability Matrix}{417}{subsubsection.166.7.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.7.4}Interpretation for Row 19}{418}{subsubsection.166.7.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.8}V.4 Gravity-Safe Positivity, PPN/GW Windows, and Jacobian Handoff (Interfaces)}{418}{subsection.166.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.8.1}Forward-Limit Positivity (Gravity-Safe, Finite-\(t\))}{418}{subsubsection.166.8.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.8.2}PPN/GW Acceptance Window (Export to Row 20)}{419}{subsubsection.166.8.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.8.3}Analytic Compressed-Cosmology Jacobians (Handoff)}{419}{subsubsection.166.8.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.8.4}Row 19 Interface Summary}{419}{subsubsection.166.8.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.9}V.5 Compact PASS/FAIL Ledger (Row 19 export)}{420}{subsection.166.9}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.9.1}Interface: Row 19 \(\rightarrow \) Row 20}{420}{subsubsection.166.9.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.10}V.6 PPN Preliminaries and Scalar–Tensor Mapping}{420}{subsection.166.10}\protected@file@percent }
\newlabel{eq:DEF_action}{{985}{421}{V.6 PPN Preliminaries and Scalar–Tensor Mapping}{equation.985}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.10.1}PPN Parameters in the DEF Mapping}{421}{subsubsection.166.10.1}\protected@file@percent }
\newlabel{eq:gamma_DEF}{{986}{421}{PPN Parameters in the DEF Mapping}{equation.986}{}}
\newlabel{eq:beta_DEF}{{987}{421}{PPN Parameters in the DEF Mapping}{equation.987}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.10.2}Role Within Row 19}{421}{subsubsection.166.10.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.11}V.7 Observational Bounds \(\Rightarrow \) Coupling Window}{422}{subsection.166.11}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.11.1}Coupling-Space Constraints}{422}{subsubsection.166.11.1}\protected@file@percent }
\newlabel{eq:alpha0_bound}{{988}{422}{Coupling-Space Constraints}{equation.988}{}}
\newlabel{eq:beta0_bound}{{989}{422}{Coupling-Space Constraints}{equation.989}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.11.2}v21 Export Window}{422}{subsubsection.166.11.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.12}V.8 GW Propagation: Speed, Damping, and Mass Window}{423}{subsection.166.12}\protected@file@percent }
\newlabel{eq:GW_action}{{990}{423}{V.8 GW Propagation: Speed, Damping, and Mass Window}{equation.990}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.12.1}Luminosity-Distance Modification}{423}{subsubsection.166.12.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.12.2}Row 19 Export Window}{423}{subsubsection.166.12.2}\protected@file@percent }
\newlabel{eq:GW_bounds}{{995}{423}{Row 19 Export Window}{equation.995}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.13}V.9 Machine-Readable Export (for Row 20 Priors)}{423}{subsection.166.13}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.14}V.10 PASS/FAIL Checklist (logged to Row 19 ledger)}{424}{subsection.166.14}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.14.1}Interface: Row 19 \(\rightarrow \) Row 20}{424}{subsubsection.166.14.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.15}V.11 Twice-Subtracted, Finite-$t$ Dispersion}{425}{subsection.166.15}\protected@file@percent }
\newlabel{eq:twice_sub_disp}{{996}{425}{V.11 Twice-Subtracted, Finite-\texorpdfstring {$t$}{t} Dispersion}{equation.996}{}}
\@writefile{toc}{\contentsline {paragraph}{Low-energy matching.}{425}{section*.934}\protected@file@percent }
\newlabel{eq:core_pos}{{998}{425}{Low-energy matching}{equation.998}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.16}V.12 Canonical Channels and Explicit Inequalities}{425}{subsection.166.16}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{(i) Scalar \(\phi \phi \to \phi \phi \) (identical real scalar).}{425}{section*.935}\protected@file@percent }
\newlabel{eq:scalar_ops}{{999}{425}{(i) Scalar \(\phi \phi \to \phi \phi \) (identical real scalar)}{equation.999}{}}
\newlabel{eq:phi_phi_bound}{{1001}{425}{(i) Scalar \(\phi \phi \to \phi \phi \) (identical real scalar)}{equation.1001}{}}
\@writefile{toc}{\contentsline {paragraph}{(ii) Photon \(\gamma \gamma \to \gamma \gamma \) (parity basis).}{426}{section*.936}\protected@file@percent }
\newlabel{eq:photon_ops}{{1002}{426}{(ii) Photon \(\gamma \gamma \to \gamma \gamma \) (parity basis)}{equation.1002}{}}
\newlabel{eq:photon_bound_sum}{{1004}{426}{(ii) Photon \(\gamma \gamma \to \gamma \gamma \) (parity basis)}{equation.1004}{}}
\newlabel{eq:photon_bounds_split}{{1005}{426}{(ii) Photon \(\gamma \gamma \to \gamma \gamma \) (parity basis)}{equation.1005}{}}
\@writefile{toc}{\contentsline {paragraph}{(iii) Mixed \(\phi \gamma \to \phi \gamma \).}{426}{section*.937}\protected@file@percent }
\newlabel{eq:mixed_ops}{{1006}{426}{(iii) Mixed \(\phi \gamma \to \phi \gamma \)}{equation.1006}{}}
\newlabel{eq:mixed_bound}{{1008}{426}{(iii) Mixed \(\phi \gamma \to \phi \gamma \)}{equation.1008}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.17}V.12b Graviton–Scalar Channel (finite-$t$)}{426}{subsection.166.17}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.18}V.13 Finite-$t$ Guard and Limit Order}{427}{subsection.166.18}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.19}V.14 Machine-Readable Positivity Checklist (Logged in Row 19 Ledger)}{427}{subsection.166.19}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A166.19.1}Interface: Row 19 \(\rightarrow \) Row 20}{427}{subsubsection.166.19.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A166.20}V.15 Analytic Jacobians for Compressed Cosmology (Curvature–aware, Complex–Step Verified)}{427}{subsection.166.20}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A167}Row 20 — Compressed Cosmology Fit and Observables}{428}{section.167}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.1}W.0 Parameterization and Background}{428}{subsection.167.1}\protected@file@percent }
\newlabel{eq:Edef}{{1010}{428}{W.0 Parameterization and Background}{equation.1010}{}}
\@writefile{toc}{\contentsline {paragraph}{Distances and geometry.}{428}{section*.938}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Compressed CMB anchors at recombination.}{429}{section*.939}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.2}W.1 Derivatives of $E(z)$}{429}{subsection.167.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Explicit derivatives.}{429}{section*.940}\protected@file@percent }
\newlabel{eq:dX1}{{1012}{430}{Explicit derivatives}{equation.1012}{}}
\newlabel{eq:dX2}{{1015}{430}{Explicit derivatives}{equation.1015}{}}
\newlabel{eq:dX3}{{1017}{430}{Explicit derivatives}{equation.1017}{}}
\@writefile{toc}{\contentsline {paragraph}{Inverse expansion derivative.}{430}{section*.941}\protected@file@percent }
\newlabel{eq:d1overE}{{1019}{430}{Inverse expansion derivative}{equation.1019}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.3}W.2 Jacobians for $\chi (z)$ and $D_M(z)$}{430}{subsection.167.3}\protected@file@percent }
\newlabel{eq:dchi}{{1021}{430}{W.2 Jacobians for \texorpdfstring {$\chi (z)$}{chi(z)} and \texorpdfstring {$D_M(z)$}{DM(z)}}{equation.1021}{}}
\@writefile{toc}{\contentsline {paragraph}{Curvature-aware geometry.}{430}{section*.942}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Derivative of \(D_M\).}{431}{section*.943}\protected@file@percent }
\newlabel{eq:dDM_general}{{1026}{431}{Derivative of \(D_M\)}{equation.1026}{}}
\@writefile{toc}{\contentsline {paragraph}{Derivative structure.}{431}{section*.944}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Flat limit.}{431}{section*.945}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.4}W.3 Jacobians for $r_s(z_\ast )$}{431}{subsection.167.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{General parameter derivatives.}{432}{section*.946}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hubble parameter dependence.}{432}{section*.947}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Baryon contribution.}{432}{section*.948}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.5}W.4 Jacobians for Compressed Observables}{432}{subsection.167.5}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Shift parameter \(R\).}{432}{section*.949}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Acoustic scale \(\ell _A\).}{433}{section*.950}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Sound angle \(\theta _\ast \).}{433}{section*.951}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{BAO distance combinations.}{433}{section*.952}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.6}W.5 GW Standard--Siren Jacobians (for Row 20 combined fit)}{434}{subsection.167.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.7}W.6 Complex--Step Validation (Machine--Precision Check)}{434}{subsection.167.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.8}W.7 Compact PASS/FAIL Ledger (Row 19 $\rightarrow $ Row 20 Export)}{434}{subsection.167.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.9}W.8 Unit Tests (Analytic vs Complex--Step)}{435}{subsection.167.9}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{435}{section*.953}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A167.9.1}Interface: Row 19 \(\rightarrow \) Row 20}{435}{subsubsection.167.9.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A167.10}Row 19.5 — Reproducibility Block: Regulator, Scheme, and Fixed Constants}{435}{subsection.167.10}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Regulator (fixed).}{435}{section*.954}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Truncation and projection.}{436}{section*.955}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Threshold functions (locked).}{436}{section*.956}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Cosmology constants (fixed).}{436}{section*.957}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Numerical conventions.}{436}{section*.958}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Determinism and export.}{436}{section*.959}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A168}X — FRG Setup: Field Content, Gauge, and Regulator (Pinned)}{436}{section.168}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A168.1}X.1 Field Content, Split, and Gauge (Pinned)}{436}{subsection.168.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A168.2}X.2 Regulator (Pinned) and Thresholds (Closed Forms)}{437}{subsection.168.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A168.3}X.3 Dimensionless Couplings and Anomalous Dimensions (Pinned)}{437}{subsection.168.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A168.4}X.4 Beta Functions and Mode Weights (Pinned, Minimal EH\(+\)\(\phi \))}{438}{subsection.168.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gravity sector.}{438}{section*.960}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Scalar portal sector.}{438}{section*.961}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Mode assignments.}{439}{section*.962}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A168.5}X.5 Numerical Constants and Units (Pinned)}{439}{subsection.168.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A168.6}X.6 Minimal Verification Checklist (Logged)}{439}{subsection.168.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interface note.}{439}{section*.963}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A168.7}Row 19.6 — Gate Ledger (Machine-Readable Export)}{439}{subsection.168.7}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Schema.}{440}{section*.964}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Ledger (verbatim).}{440}{section*.965}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{441}{section*.966}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interface note (Row 19 \(\rightarrow \) Row 20).}{441}{section*.967}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A169}Y — Global Gate Summary and PASS/FAIL Export}{441}{section.169}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A169.1}Y.1 Compact PASS/FAIL Table}{442}{subsection.169.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{442}{section*.968}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interface note.}{442}{section*.969}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A169.2}Y.2 Minimal JSON Export (verbatim)}{442}{subsection.169.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Row 20 ingestion (pseudocode).}{443}{section*.970}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Audit note.}{444}{section*.971}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A169.3}Row 19.7 — Cross-Row Handshake: Interface to Row 20}{444}{subsection.169.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs (from Row 19).}{444}{section*.972}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Required operations (Row 20).}{444}{section*.973}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hard constraints (non-negotiable).}{445}{section*.974}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Failure conditions.}{445}{section*.975}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Reproducibility lock.}{445}{section*.976}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{445}{section*.977}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A170}Z — Execution Layer: Pipeline, Enforcement, and Run Protocol}{445}{section.170}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A170.1}Z.1 End-to-End Execution Flow}{446}{subsection.170.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A170.2}Z.2 Constraint Enforcement and Abort Logic}{446}{subsection.170.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{447}{section*.978}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A170.3}Z.3 Acceptance Rule and Outputs Returned}{447}{subsection.170.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A170.4}Z.4 Minimal Ingestion Pseudocode (Verbatim, Deterministic)}{447}{subsection.170.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Audit note.}{447}{section*.979}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A171}Row 20 — Compressed Cosmology Fit (chi2/nu ≈ 1)}{448}{section.171}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interface to Row 19.}{448}{section*.980}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A171.1}Neutral Vacuum and Compressed Cosmology Fit (UTFANSWF v22)}{448}{subsection.171.1}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Stabilized Neutral Vacuum.}{448}{section*.981}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Equation of state.}{448}{section*.983}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Vacuum energy evolution.}{448}{section*.985}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Background expansion.}{448}{section*.987}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Distance measures.}{448}{section*.989}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Compressed likelihood.}{448}{section*.992}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Neutral Zone priors.}{449}{section*.994}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Derived quantities.}{449}{section*.997}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Pipeline consistency.}{449}{section*.1000}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpretation.}{449}{section*.1001}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A172}AA — Compressed Cosmology Inputs, Parameters, and Data Provenance}{449}{section.172}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A172.1}AA.0 Overview and Inputs (from Row 19)}{450}{subsection.172.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A172.2}AA.0.1 Data Provenance (Pinned)}{450}{subsection.172.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A172.3}AA.1 Data Vectors and Model Maps}{450}{subsection.172.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{CMB compression (recombination).}{451}{section*.1002}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{BAO compression (at \(\{z_d\}\)).}{451}{section*.1003}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Type Ia Supernovae (compression).}{451}{section*.1004}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gravitational-wave standard sirens.}{451}{section*.1005}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A172.4}AA.2 Joint Objective and Constraints}{451}{subsection.172.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Likelihood.}{451}{section*.1006}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hard constraints (must hold).}{452}{section*.1007}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {25}{\ignorespaces Row 20 — Ablations at a glance (posterior stability).}}{452}{table.caption.1009}\protected@file@percent }
\newlabel{tab:ablations_glance}{{25}{452}{Row 20 — Ablations at a glance (posterior stability)}{table.caption.1009}{}}
\@writefile{toc}{\contentsline {paragraph}{Ablation checks (posterior stability).}{452}{table.caption.1009}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A172.5}AA.3 Gradients and Fisher Blocks (Analytic, from Row 19.4)}{452}{subsection.172.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A172.6}AA.4 Minimizer and Acceptance Rule}{453}{subsection.172.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Output.}{453}{section*.1010}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A172.7}AA.5 Outputs Returned and Ledger Update}{453}{subsection.172.7}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Returned quantities.}{453}{section*.1011}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Ledger linkage.}{453}{section*.1012}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Deterministic ingestion (verbatim).}{453}{section*.1013}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Determinism guarantee.}{454}{section*.1014}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A}Appendix A — Gravity-Safe Positivity and Scattering Construction}{455}{appendix.A}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}A.1 Scattering Setup, Kinematics, and Normalization}{455}{subsection.A.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}A.2 Helicity and Projector Construction}{455}{subsection.A.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}A.3 Forward-Limit Positivity with Gravity}{455}{subsection.A.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A.4}A.4 Role in UTFANSWF (Row 19 Link)}{456}{subsection.A.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A.5}A.5 Summary}{456}{subsection.A.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {B}Row 20.1 — CMB Block: R, $\ell _A$, $\theta _\ast $ (Covariance \& Checks)}{456}{appendix.B}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Data vector and covariance (from tag \texttt  {planck\_2018\_distpriors\_v1}).}{456}{section*.1015}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Theory map (Row 19.4).}{456}{section*.1016}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Sanity checks (deterministic).}{456}{section*.1017}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{457}{section*.1018}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {C}Row 20.2 — BAO • SN • GW Nodes (Lists \& Quick Tests)}{457}{appendix.C}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{BAO (tag \texttt  {desi\_dr1\_bao\_combo\_v1}).}{457}{section*.1019}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{SNe (tag \texttt  {pantheonplus\_v1\_compressed}).}{457}{section*.1020}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{GW standard sirens (tag \texttt  {o3+o4\_catalog\_v1\_compressed}).}{457}{section*.1021}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Quick sanity tests (deterministic).}{457}{section*.1022}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{457}{section*.1023}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{458}{section*.1025}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {D}Row 20.3 — Results Ledger Stub (\texttt  {row20\_results.json})}{458}{appendix.D}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{458}{section*.1026}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {E}Harmonics, Fractal Harmonics, and Refractal Harmonics}{459}{appendix.E}\protected@file@percent }
\newlabel{sec:harmonics-fractal-refractal}{{E}{459}{Harmonics, Fractal Harmonics, and Refractal Harmonics}{appendix.E}{}}
\@writefile{toc}{\contentsline {paragraph}{Harmonics (what is present).}{459}{section*.1027}\protected@file@percent }
\newlabel{eq:harmonic-expansion}{{1068}{459}{Harmonics (what is present)}{equation.1068}{}}
\@writefile{toc}{\contentsline {paragraph}{Fractal harmonics (how it scales).}{459}{section*.1028}\protected@file@percent }
\newlabel{eq:fractal-harmonics}{{1069}{459}{Fractal harmonics (how it scales)}{equation.1069}{}}
\newlabel{eq:fractal-penalty}{{1070}{459}{Fractal harmonics (how it scales)}{equation.1070}{}}
\@writefile{toc}{\contentsline {paragraph}{Refractal harmonics (how it updates).}{459}{section*.1029}\protected@file@percent }
\newlabel{eq:refractal-update}{{1071}{459}{Refractal harmonics (how it updates)}{equation.1071}{}}
\@writefile{toc}{\contentsline {paragraph}{Predictive bite.}{459}{section*.1030}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {E.1}Harmonics, Fractal Harmonics, and Refractal Harmonics}{459}{subsection.E.1}\protected@file@percent }
\newlabel{sec:harmonics-fractal-refractal}{{E.1}{459}{Harmonics, Fractal Harmonics, and Refractal Harmonics}{subsection.E.1}{}}
\@writefile{toc}{\contentsline {paragraph}{Harmonics (what is present).}{459}{section*.1032}\protected@file@percent }
\newlabel{eq:harmonic-expansion}{{1072}{459}{Harmonics (what is present)}{equation.1072}{}}
\@writefile{lot}{\contentsline {table}{\numberline {26}{\ignorespaces Refractal update procedure per dataset ingress.}}{460}{table.caption.1031}\protected@file@percent }
\newlabel{tab:refractal_update}{{26}{460}{Refractal update procedure per dataset ingress}{table.caption.1031}{}}
\@writefile{toc}{\contentsline {paragraph}{Fractal harmonics (how it scales).}{460}{section*.1033}\protected@file@percent }
\newlabel{eq:fractal-harmonics}{{1073}{460}{Fractal harmonics (how it scales)}{equation.1073}{}}
\newlabel{eq:fractal-penalty_a}{{1074}{460}{Fractal harmonics (how it scales)}{equation.1074}{}}
\@writefile{toc}{\contentsline {paragraph}{Refractal harmonics (how it updates).}{460}{section*.1034}\protected@file@percent }
\newlabel{eq:refractal-update_a}{{1075}{460}{Refractal harmonics (how it updates)}{equation.1075}{}}
\@writefile{toc}{\contentsline {paragraph}{Predictive bite.}{460}{section*.1035}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {27}{\ignorespaces Refractal update procedure per dataset ingress.}}{461}{table.caption.1036}\protected@file@percent }
\newlabel{tab:refractal_update}{{27}{461}{Refractal update procedure per dataset ingress}{table.caption.1036}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {29}{\ignorespaces Harmonic $\rightarrow $ fractal $\rightarrow $ refractal flow used by v22.}}{461}{figure.caption.1037}\protected@file@percent }
\newlabel{fig:hfr-flow}{{29}{461}{Harmonic $\rightarrow $ fractal $\rightarrow $ refractal flow used by v22}{figure.caption.1037}{}}
\@writefile{toc}{\contentsline {section}{\numberline {F}Row 20.A — Ablations: Prior \& Regulator Sensitivity (One-Page Gate)}{461}{appendix.F}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Purpose.}{461}{section*.1038}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {28}{\ignorespaces Deterministic ablation setups for prior and regulator sensitivity.}}{461}{table.caption.1039}\protected@file@percent }
\newlabel{tab:row20A_setups}{{28}{461}{Deterministic ablation setups for prior and regulator sensitivity}{table.caption.1039}{}}
\@writefile{toc}{\contentsline {paragraph}{Objective.}{461}{section*.1040}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {29}{\ignorespaces Acceptance criteria for Row 20.A ablation stability.}}{462}{table.caption.1041}\protected@file@percent }
\newlabel{tab:row20A_pass}{{29}{462}{Acceptance criteria for Row 20.A ablation stability}{table.caption.1041}{}}
\@writefile{toc}{\contentsline {paragraph}{Pass rule (hard).}{462}{section*.1042}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{462}{section*.1043}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {G}Row 20.4 — JWST Mini-Run (UVLF/SFRD/$\rho _\star $/Sizes/Lines)}{462}{appendix.G}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {30}{\ignorespaces JWST dataset tags used in the mini-run.}}{462}{table.caption.1045}\protected@file@percent }
\newlabel{tab:row20_jwst_tags}{{30}{462}{JWST dataset tags used in the mini-run}{table.caption.1045}{}}
\@writefile{toc}{\contentsline {paragraph}{Dataset tags (pinned).}{462}{table.caption.1045}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Theory map.}{462}{section*.1046}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Objective.}{462}{section*.1047}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {31}{\ignorespaces Deterministic checks for JWST mini-run integration.}}{463}{table.caption.1048}\protected@file@percent }
\newlabel{tab:row20_jwst_checks}{{31}{463}{Deterministic checks for JWST mini-run integration}{table.caption.1048}{}}
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{463}{section*.1049}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {H}Row 21 — Axion Dark Matter Gate (2025Q3 vs Haloscopes)}{463}{appendix.H}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {32}{\ignorespaces UTFANSWF axion parameter band and dataset inputs.}}{463}{table.caption.1051}\protected@file@percent }
\newlabel{tab:row21_scope}{{32}{463}{UTFANSWF axion parameter band and dataset inputs}{table.caption.1051}{}}
\@writefile{toc}{\contentsline {paragraph}{Scope \& inputs.}{463}{table.caption.1051}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Model slice (misalignment baseline).}{463}{section*.1052}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate definition (hard).}{463}{section*.1053}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Checks (deterministic).}{464}{section*.1054}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Hard exclusion rule.}{464}{section*.1055}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Setup.}{464}{section*.1057}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Interpolation envelope.}{464}{section*.1058}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {33}{\ignorespaces Row 21 robustness sweep summary (v22).}}{464}{table.caption.1059}\protected@file@percent }
\newlabel{tab:row21_results}{{33}{464}{Row 21 robustness sweep summary (v22)}{table.caption.1059}{}}
\@writefile{toc}{\contentsline {paragraph}{Reproducibility record.}{464}{section*.1061}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{464}{section*.1062}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {30}{\ignorespaces Dense robustness sweep of the axion envelope showing interpolation-stable comparison between \(g_{\rm  pred}^{\max }\) and \(g_{95}^{\min }\).}}{465}{figure.caption.1060}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{465}{section*.1063}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {I}Row 22 — Neutral Zone (NZ) Sandwich: Robust Sweep \& Sensitivities}{465}{appendix.I}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inequality (UTFANSWF NZ).}{465}{section*.1064}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Robust sweep definition.}{465}{section*.1065}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate definition (hard).}{466}{section*.1066}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Checks (deterministic).}{466}{section*.1067}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {34}{\ignorespaces Row 22 NZ sandwich diagnostic metrics (v22).}}{466}{table.caption.1068}\protected@file@percent }
\newlabel{tab:row22_metrics}{{34}{466}{Row 22 NZ sandwich diagnostic metrics (v22)}{table.caption.1068}{}}
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{466}{section*.1069}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{466}{section*.1070}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {J}Row 23 — Black-Hole Ringdown \& Echo Predictions}{466}{appendix.J}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{QNM baseline.}{466}{section*.1071}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Echo template.}{466}{section*.1072}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate definition (diagnostic).}{467}{section*.1073}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Checks.}{467}{section*.1074}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Row 23 — audit stub (verbatim).}{467}{section*.1075}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Mock audit (verbatim).}{467}{section*.1077}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{467}{section*.1078}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {K}Row 24 — AI $\leftrightarrow $ UTFANSWF: Guardrails \& Learning Efficiency}{467}{appendix.K}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Constraint-prior training.}{467}{section*.1079}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Efficiency metric.}{468}{section*.1080}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Safety rails (hard constraints).}{468}{section*.1081}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate definition (hard).}{468}{section*.1082}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Checks (deterministic).}{468}{section*.1083}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {35}{\ignorespaces Row 24 AI–UTFANSWF guardrail and efficiency metrics (v22).}}{468}{table.caption.1084}\protected@file@percent }
\newlabel{tab:row24_metrics}{{35}{468}{Row 24 AI–UTFANSWF guardrail and efficiency metrics (v22)}{table.caption.1084}{}}
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{468}{section*.1085}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{469}{section*.1086}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {L}Row 25 — Stress-Test Appendix: “Break UTFANSWF” Registry}{469}{appendix.L}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Objective.}{469}{section*.1087}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Harness rule (deterministic).}{469}{section*.1088}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Escalation rule (hard).}{469}{section*.1089}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate definition (hard).}{469}{section*.1090}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Checks (deterministic).}{469}{section*.1091}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {36}{\ignorespaces Row 25 stress-test registry summary (v22).}}{469}{table.caption.1092}\protected@file@percent }
\newlabel{tab:row25_metrics}{{36}{469}{Row 25 stress-test registry summary (v22)}{table.caption.1092}{}}
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{470}{section*.1093}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{470}{section*.1094}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {M}Row 26 — References \& Acknowledgments (Consistency Gate)}{470}{appendix.M}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Objective.}{470}{section*.1095}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Consistency checks (deterministic).}{470}{section*.1096}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Reproducibility check.}{470}{section*.1097}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Gate definition (hard).}{471}{section*.1098}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {37}{\ignorespaces Row 26 consistency and integrity checks (v22).}}{471}{table.caption.1099}\protected@file@percent }
\newlabel{tab:row26_metrics}{{37}{471}{Row 26 consistency and integrity checks (v22)}{table.caption.1099}{}}
\@writefile{toc}{\contentsline {paragraph}{Audit (verbatim).}{471}{section*.1100}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{PASS/FAIL.}{471}{section*.1101}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Scope.}{471}{section*.1103}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Global guardrails (hard).}{472}{section*.1104}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs (2025Q4).}{472}{section*.1106}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Test \& Expression.}{472}{section*.1107}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Rule (deterministic).}{472}{section*.1108}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Decision (Oct 17, 2025).}{472}{section*.1109}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Action next.}{473}{section*.1110}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Cross-gate echoes.}{473}{section*.1111}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs (2025Q4).}{473}{section*.1113}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Test \& Expression.}{473}{section*.1114}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Rule (deterministic).}{473}{section*.1115}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Decision (Oct 17, 2025).}{473}{section*.1116}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Action next.}{473}{section*.1117}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Cross-gate echoes.}{474}{section*.1118}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs (2025Q4).}{474}{section*.1120}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Test \& Expression.}{474}{section*.1121}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Rule (deterministic).}{474}{section*.1122}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Decision (Oct 17, 2025).}{474}{section*.1123}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Action next.}{474}{section*.1124}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Cross-gate echoes.}{474}{section*.1125}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs (2025Q4).}{475}{section*.1127}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Test \& Expression.}{475}{section*.1128}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Rule (deterministic).}{475}{section*.1129}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Decision (Oct 17, 2025).}{475}{section*.1130}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Action next.}{475}{section*.1131}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Cross-gate echoes.}{475}{section*.1132}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Inputs (2025Q4).}{475}{section*.1134}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Test \& Expression.}{476}{section*.1135}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Rule (deterministic).}{476}{section*.1136}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Decision (Oct 17, 2025).}{476}{section*.1137}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Action next.}{476}{section*.1138}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {38}{\ignorespaces UTFANSWF v22 — Stress-Test Headline Summary}}{476}{table.caption.1139}\protected@file@percent }
\newlabel{tab:v21_headline}{{38}{476}{UTFANSWF v22 — Stress-Test Headline Summary}{table.caption.1139}{}}
\@writefile{toc}{\contentsline {section}{\numberline {N}Row F — Compact Figures (1 page)}{477}{appendix.N}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {31}{\ignorespaces Top-left: FRG flow \& stability; top-right: gravity-safe positivity region; bottom-left: cosmology residuals with \(\chi ^2/\nu \); bottom-right: axion band vs coverage.}}{477}{figure.caption.1140}\protected@file@percent }
\newlabel{fig:compact_four}{{31}{477}{Top-left: FRG flow \& stability; top-right: gravity-safe positivity region; bottom-left: cosmology residuals with \(\chi ^2/\nu \); bottom-right: axion band vs coverage}{figure.caption.1140}{}}
\@writefile{toc}{\contentsline {section}{\numberline {O}Index of Symbols (UTFANSWF v21)}{478}{appendix.O}\protected@file@percent }
\newlabel{sec:utfa_symbols}{{O}{478}{Index of Symbols (UTFANSWF v21)}{appendix.O}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {O.1}Core Geometry \& Thermodynamics}{478}{subsection.O.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {O.2}Harmonic Bubbles \& Echoes}{478}{subsection.O.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {O.3}Axion Gate \& Cosmology}{479}{subsection.O.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {O.4}FRG \& Dispersion Positivity}{479}{subsection.O.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {O.5}Observer Algebra}{479}{subsection.O.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {O.6}Applications \& Gates}{480}{subsection.O.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {P}Acknowledgments}{481}{appendix.P}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {Q}License, Provenance, and Versioning}{481}{appendix.Q}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {R}Data, Code, and Reproducibility}{481}{appendix.R}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {S}UTFANSWF Glossary (Canonical Edition)}{482}{appendix.S}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {T}Foundational Layer --- SWF-ISM}{482}{appendix.T}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Entropy--Volume Normalization.}{482}{section*.1148}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {U}Bridge Layer --- ANSWF $\rightarrow $ SANSWF}{484}{appendix.U}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {V}Unified Layer --- UTFANSWF Core}{484}{appendix.V}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {W}Applied Layer --- Predictive and Empirical Interface}{485}{appendix.W}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {X}Integration Layer --- AI $\leftrightarrow $ UTFANSWF}{486}{appendix.X}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {Y}Stress-Test and Legacy Layer --- Endurance and Outlook}{486}{appendix.Y}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {Y.1}Limitations (v21)}{488}{subsection.Y.1}\protected@file@percent }
\bibcite{Planck2018}{1}
\bibcite{BOSS}{2}
\bibcite{Pantheon}{3}
\bibcite{LIGO2016}{4}
\bibcite{GW170817}{5}
\bibcite{GRB170817A}{6}
\bibcite{GeorgiGlashow}{7}
\bibcite{FritzschMinkowski}{8}
\bibcite{MinkowskiSeesaw}{9}
\bibcite{GRSYanagida}{10}
\bibcite{PQ77}{11}
\bibcite{WeinbergAxion}{12}
\bibcite{WilczekAxion}{13}
\bibcite{DFSZ1}{14}
\bibcite{DFSZ2}{15}
\bibcite{ADMX2021}{16}
\bibcite{HAYSTAC}{17}
\bibcite{CAPP2023}{18}
\bibcite{ColemanWeinberg}{19}
\bibcite{LQT}{20}
\bibcite{AdamsEtAl}{21}
\bibcite{deRhamTolley}{22}
\bibcite{DEF}{23}
\bibcite{Cassini}{24}
\bibcite{BGWspd}{25}
\bibcite{Echeverria}{26}
\bibcite{BedroyaVafa}{27}
\bibcite{Planck2018}{28}
\bibcite{BOSS_DR12_Alam2017}{29}
\bibcite{PantheonPlus_Brout2022}{30}
\bibcite{PantheonPlus_Scolnic2022}{31}
\bibcite{Donnan2024_PRIMER}{32}
\bibcite{Finkelstein2023_CEERS}{33}
\bibcite{TopoCensorship}{34}
\bibcite{FordRoman_QEI_1994}{35}
\bibcite{FordRoman_QInterest_1999}{36}
\bibcite{AxionLimits_OHare}{37}
\bibcite{AdamsArkaniHamed2006}{38}
\bibcite{ChenHuangWang2019}{39}
\bibcite{Sikivie1983}{40}
\bibcite{IrastorzaRedondo2018}{41}
\bibcite{CAPP2023}{42}
\bibcite{HAYSTAC_Squeezing2019}{43}
\bibcite{BennettTeleportation1993}{44}
\bibcite{KontouFewster2020}{45}
\bibcite{PetzQFI}{46}
\bibcite{AlbertiUhlmann}{47}
\bibcite{ReuterSaueressig}{48}
\bibcite{Saueressig:2023}{49}
\@writefile{toc}{\contentsline {paragraph}{}{491}{section*.1194}\protected@file@percent }
\gdef \@abspage@last{491}
