# UTFANSWF Proton-Origin / Blind Mass Closure — Archived Checkpoint

**Archived:** 2026-08-15
**Status:** PAUSED deliberately. Resume only after the active proton-stability/proton-decay task is completed.
**Purpose:** Preserve all useful proton-origin/lattice-QCD work so it can become the next UTFANSWF project without rebuilding from scratch.

## Actual project question
Can UTFANSWF produce a blind proton/nucleon mass from its upstream structure and QCD dynamics without inserting the measured proton mass, freeze that forward prediction, reveal the holdout, and reverse-diagnose any miss?

Intended chain:

UTFANSWF structure -> QCD scale/dynamics -> confined color-singlet baryon -> nucleon ground-state coordinate -> blind physical mass -> holdout -> reverse diagnosis.

This is NOT the active proton-decay/stability project. It is the next project after that work is complete.

## Blind rules
- Do not use measured proton or neutron mass as a solve input.
- Do not use proton radius/lifetime to tune the mass solve.
- Do not use measured electromagnetic alpha as a hidden normalization.
- Do not tune lattice/scale parameters to 938 MeV after looking at the holdout.
- Holdout may be used only after a forward coordinate is frozen, for diagnostic/reverse testing.

## What was established
### QCD/baryon structure
- Exact SU(3) 3x3x3 color operator spectrum selected the unique most-attractive color singlet.
- Gauge-invariant proton interpolator implemented: epsilon^{abc}(u_a^T C gamma5 d_b)u_c.
- HB/QCD variational handoff and synthetic GEVP recovery passed.
- Mini SU(3) Wilson-Dirac/baryon engine passed gauge covariance, gamma5-Hermiticity and baryon gauge invariance at ~1e-15 to 1e-16.

### QCD scale bridge architecture
- Frozen upstream alpha_s(M_Z)=0.1184, M_Z=91.1534806 GeV.
- Lambda_MSbar^(5): 1L 0.0898786, 2L 0.2166064, 3L 0.2136308, 4L 0.2132660 GeV.
- Broad leading-threshold Lambda_MSbar^(3) diagnostic ~0.330-0.349 GeV, center ~0.340 GeV.
- Correct conceptual bridge remains: alpha_s(M_Z) -> Lambda_MSbar -> nonperturbative finite-volume/step scaling -> lattice coupling/spacing -> continuum.

### Early forward/backward closure
- Plumbing runner beta -> g0^2 -> gauge -> Wilson D^-1 -> PCAC/proton correlator -> proxy -> reverse beta closed algebraically, but was not a physical mass prediction.
- Single-t proxy failed as a mass coordinate.
- Repaired PCAC-aligned GEVP on L=3,T=20 at beta=3.2 gave frozen preflight coordinate aM_N^(0)=2.5488207898123654 with spread 0.07639570798892689.
- Short sea-evolution stability held that coordinate at ~0.03% drift.
- Old perturbative bare-coupling scale aLambda_MSbar^(2)=1.27974 was rejected as a trustworthy strong-coupling scale map.
- Resulting dimensionless preflight M_N/Lambda_MSbar^(2)=1.99167080017 +/-0.05969627267 was frozen for reverse diagnosis only.

### Nonperturbative scale work
- Standard t0 failed on L/a=3 because the box was too small for the smoothing radius; do NOT call this a beta=3.2 physics failure.
- Finite-volume GF preflight numbers were generated, but L/a=3-6 resolution scans at fixed beta are not a line of constant physics and must not be interpreted as continuum step scaling.
- Wilson-flow gauge force and batched link-update implementations were accelerated and validated to numerical precision.
- Sommer/static-potential route was tested on 4^3x8 and Wilson loops were healthy, but box too small to resolve r0 and ensemble accumulation was expensive.

### beta=5.6 forward-matching work
- Same-action published N_f=2 Wilson anchor around beta=5.6 was examined.
- Important correction: single-configuration local PCAC roots (e.g. ~-1.083) are NOT equivalent to ensemble kappa_c and must not be compared directly to published equilibrated chiral anchors.
- Same-action finite-volume literature showed nucleon masses are severely inflated on small boxes; L=3 spectroscopy is not physical large-volume spectroscopy.
- Production-size 16^3x32 Wilson operator was implemented and executed successfully at 1,572,864 fermion DOF.
- Corrected Wilson operator matched trusted small-lattice implementation at relative error ~2.02e-16.
- Full 16^3x32 nontrivial SU(3) Wilson apply executed successfully; production mixed-precision D^dagger D CG preflight converged in 29 iterations with residual ~8.14e-4.
- Important correction: solving D^dagger D x=b is a conditioning/solver gate, NOT a quark propagator. Propagator requires D S=B or CGNE with D^dagger B.

### Tiled-volume control
- Tiling the same beta=5.6 local gauge field from L=3 to L=9 did NOT drive the proton mass toward a physical large-volume band.
- L=9 local proton effective-mass plateau ~2.9.
- Verdict: FAIL_TILED_VOLUME_ONLY_REPAIR. Enlarging geometry without genuine dynamical sea evolution preserves wrong local gauge physics.

### Genuine N_f=2 sea evolution
- Rebuilt dynamical Wilson/HMC engine after runtime reset.
- gamma5-Hermiticity validated ~1.20e-16.
- Full gauge+two-flavor pseudofermion force finite-difference validation ~1e-8 relative.
- Genuine 6^3x12, N_f=2, beta=5.6 branch executed with accepted HMC trajectories.
- Chronological inversion/reuse substantially reduced repeated fermion solve cost; post-first solves often fell to single-digit iterations.
- 2MN/Omelyan was validated for reversibility but was not more efficient on this branch; reject as default for current setup.

## Solver-artifact correction — CRITICAL
An apparent proton-window drop from ~2.78 to ~2.24 was initially observed during sea evolution. This was mostly caused by changing propagator accuracy.

After re-solving older states with the same tighter propagator tolerance, the fair tight-solver sequence was approximately:
- tau ~0.365: 2.2493
- tau ~0.405: 2.2441
- tau ~0.445: 2.2388
- tau ~0.505: 2.2413
- tau ~0.565: 2.2453
- tau ~0.625: 2.24374

Thus the tight branch stabilized near:

**aM_N ~ 2.244**

with essentially no meaningful monotonic drift over that short MD interval. Do NOT reuse the earlier 19.4% drop as a physics claim.

## Independent-start / thermalization diagnosis
Two independent genuine N_f=2 beta=5.6 starts were compared:
1. diagonal-SU(3)-style warm start that slowly generated non-Abelian structure,
2. fully non-Abelian SU(3) warm start tuned only to the same plaquette band.

The proton coordinates remained materially different over short MD time (roughly ~2.244 vs ~2.516), proving strong initial-condition dependence and lack of equilibration.

Raw off-diagonal-link fractions and link commutators were recognized as gauge-dependent and must NOT be used as physical thermalization diagnostics.

Gauge-invariant diagnostics replaced them:
- short 1x2 and 2x2 Wilson loops became fairly similar between starts,
- temporal Polyakov magnitudes remained very different (~0.459 vs ~0.316), indicating a slow long-distance mode / distinct unequilibrated distributions.

## Temporal-extent correction — LATEST STOPPING POINT
A major issue was identified: 6^3x12 at the beta=5.6 scale has a short temporal physical extent and may be contaminated by finite-temperature physics.

Tests:
- 6^3x20 full-SU(3) start: plaquette ~0.574520; temporal |P| ~0.28386; first genuine N_f=2 HMC accepted, post-step |P| ~0.28501.
- 6^3x24 full-SU(3) start: plaquette ~0.576043; temporal |P| ~0.30472; first large-step proposal rejected; smaller-step genuine N_f=2 HMC accepted, post-step |P| ~0.30568.

Verdict at archive:
**FAIL_NT12_AS_ZERO_TEMPERATURE_SPECTROSCOPY_BOX** (provisional but strongly indicated).

The correct next forward test is to keep N_t >=20 (preferably move toward the production-style N_t=32 geometry), evolve a genuine equilibrated N_f=2 beta=5.6 ensemble, and run the same tight 12-source proton correlator/GEVP. Compare using a fixed solver tolerance and predeclared time window. Do not spend more effort interpreting the N_t=12 mass coordinate as a physical zero-temperature result.

A 6^3x20 accepted dynamical state and 12-source propagator files exist in this archive; the proton extraction on that branch was in progress at the time the project was paused.

## What remains for this future project
1. Resume from N_t>=20/24 zero-temperature-direction branch, not N_t=12.
2. Harden/finish the 6^3x20 proton correlator result using the archived accepted gauge state and saved propagator.
3. Increase spatial volume only when needed; distinguish finite spatial volume from temporal finite-temperature effects.
4. Accumulate genuinely equilibrated N_f=2 ensemble data or ingest public equilibrated same-action configurations if accessible.
5. Require independent-start convergence in gauge-invariant long-distance observables before trusting a proton mass.
6. Restore nonperturbative scale setting / line of constant physics; do not use beta=3.2 bare perturbative aLambda conversion.
7. Freeze blind forward nucleon mass coordinate only after finite-volume, thermalization, solver-tolerance, and scale gates pass.
8. Reveal proton holdout only after freeze, then run reverse diagnosis exactly like the 1/137 workflow.

## Why this work is worth preserving
Although it was a detour from the active proton-decay task, it substantially expands UTFANSWF's executable QCD infrastructure: SU(3) baryon formation, Wilson-Dirac propagation, real N_f=2 HMC, variational spectroscopy, solver hardening, scale diagnostics, finite-volume controls, and forward/backward blind-testing methodology. It should be treated as a separate future research project, not discarded.
