UTFANSWF v22 DISTRIBUTED H0 CANDIDATE POST-RELEASE TECHNICAL RECORD Document: H0 Master Record v1 Date: July 26, 2026 Author: Ronald L. Alexander Framework: UTFANSWF v22 STATUS This document supplements but does not replace, revise, or silently alter the frozen UTFANSWF v22 publication. It preserves favorable, adverse, diagnostic, and unresolved H0 results together. Current bounded status: - V22 aggregate distributed test: PASS_CANDIDATE. - Frozen held-out DESI nodes: strong PASS. - Frozen ACT-plus-construction subset at the original v22-derived BAO node 67.933256: FAIL. - Post-hoc BAO-node scan: complete numerical-pass region identified. - Full numerical pass at BAO node 68.775 under the scanned compressed-test rules: ACHIEVED. - Independent derivation of the passing BAO node: outstanding. - Independent reproduction and external validation: outstanding. ---------------------------------------------------------------------- 1. DISTRIBUTED H0 CONSTRUCTION ---------------------------------------------------------------------- Declared local target: 73.5 km/s/Mpc Declared tolerance: +/- 1.5 km/s/Mpc Early ACT/CMB anchor: 67.400000 BAO contribution: +0.533256 Historical DESI/BAO channel node: 67.93325552376864 CMB output contribution: +1.482800 GW output contribution: +2.000000 Pre-SN distributed output: 71.416056 SN geometry contribution: +1.718147 Final distributed output: 73.1342021175366 Distance from 73.5 target: 0.365798 Target gate: PASS The final H0_dist is an emergent distributed output. It is not automatically substituted as the background H0 inside every ACT and DESI likelihood. ---------------------------------------------------------------------- 2. PRIMARY ACT + COMPLETE DESI DISTRIBUTED RESULT ---------------------------------------------------------------------- ACT/CMB H0 node: 67.400000 DESI/BAO H0 node: 67.933256 Shared Omega_m: 0.314866 Shared r_d: 146.906011 Mpc ACT Mahalanobis-squared: 3.413938 DESI chi-squared, 13 observables: 16.262811 Combined compressed objective: 19.676749 Reference degrees of freedom: 14 Reference p-value: 0.140667 Verdict: PASS_CANDIDATE This is simultaneous numerical compatibility under the distributed channel-node interpretation. It is not independent validation or proof that the Hubble tension is resolved. ---------------------------------------------------------------------- 3. REJECTED SINGLE-GLOBAL-H0 CONTROL ---------------------------------------------------------------------- Forcing H0 = 73.134202 into both ACT and every DESI background calculation fails. DESI then prefers r_d near 138.85 Mpc while ACT correlations pull toward approximately 149.44 Mpc. Training p-value: approximately 1.27e-28 Held-out p-value: approximately 4.05e-13 Maximum held-out pull: 6.10 Verdict: CATASTROPHIC FAIL This failure is preserved as a required negative control because it tests a different interpretation from the distributed framework. ---------------------------------------------------------------------- 4. FROZEN RETROSPECTIVE HOLDOUT ---------------------------------------------------------------------- Frozen ACT node: 67.4 Frozen BAO node: 67.93325552376864 Frozen distributed output: 73.1342021175366 Training redshifts: 0.510 and 0.706 Held-out redshifts: 0.295, 0.934, 1.321, 1.484, and 2.33 Fitted shared Omega_m: 0.3152886194 Fitted shared r_d: 146.8228102 Mpc Training-side result: ACT contribution: 3.064610 Four BAO training-observable contribution: 10.614779 Combined training objective: 13.679389 Reference degrees of freedom: 5 Training p-value: 0.0177795 Required threshold: p >= 0.05 Verdict: FAIL Held-out result: Conditional held-out chi-squared: 6.102346 Held-out observables: 9 Conditional p-value: 0.729633 Maximum absolute held-out pull: 1.68808 Required maximum pull: <= 3 Verdict: STRONG PASS Leave-one-held-out-redshift-group results: Removed z = 0.295: p = 0.7100 Removed z = 0.934: p = 0.8751 Removed z = 1.321: p = 0.6704 Removed z = 1.484: p = 0.5836 Removed z = 2.33: p = 0.6206 All leave-one-held-out-group diagnostics pass. Aggregate context: Training plus held-out statistic: 19.781735 Reference degrees of freedom: 14 Aggregate p-value: 0.137174 The acceptable aggregate number cannot erase the separately mandatory training-subset failure. ---------------------------------------------------------------------- 5. LOCALIZED TRAINING STRESS ---------------------------------------------------------------------- z = 0.510, D_M/r_d: Observed: 13.58758434 Predicted: 13.41115798 Residual: +0.17642636 Diagonal pull: +1.04787 z = 0.510, D_H/r_d: Observed: 21.86294686 Predicted: 22.58858697 Residual: -0.72564011 Diagonal pull: -1.69199 Joint z = 0.510 result: chi-squared: 2.964019 Observables: 2 p-value: 0.227180 Verdict: PASS z = 0.706, D_M/r_d: Observed: 17.35069094 Predicted: 17.58338673 Residual: -0.23269579 Diagonal pull: -1.29325 z = 0.706, D_H/r_d: Observed: 19.45534918 Predicted: 20.03454165 Residual: -0.57919247 Diagonal pull: -1.73478 Joint z = 0.706 result: chi-squared: 7.650760 Observables: 2 p-value: 0.021810 Verdict: FAIL The decisive stress is the correlated z = 0.706 D_M/r_d and D_H/r_d pair. ACT and the held-out DESI nodes are not the principal source of the failure. Training covariance, ordered as: 1. D_M/r_d at z = 0.510 2. D_H/r_d at z = 0.510 3. D_M/r_d at z = 0.706 4. D_H/r_d at z = 0.706 [ [ 0.02834737, -0.03260620, 0.00000000, 0.00000000 ], [-0.03260620, 0.18392804, 0.00000000, 0.00000000 ], [ 0.00000000, 0.00000000, 0.03237524, -0.02374456 ], [ 0.00000000, 0.00000000, -0.02374456, 0.11146920 ] ] Within-redshift correlations: z = 0.510: -0.45156 z = 0.706: -0.39526 The dominant covariance eigenmode is the mixed z = 0.706 mode: Mode pull: 2.3594 Chi-squared contribution: 5.5667 ---------------------------------------------------------------------- 6. LOCALIZATION CONTROLS ---------------------------------------------------------------------- ACT plus z = 0.510 refit: Objective: 5.848 Reference degrees of freedom: 3 p-value: 0.1192 Verdict: PASS ACT plus z = 0.706 refit: Objective: 10.7134 Reference degrees of freedom: 3 p-value: 0.01338 Verdict: FAIL Leave-one-training-observable diagnostics: Drop z = 0.510 D_M/r_d: p = 0.00878, FAIL Drop z = 0.510 D_H/r_d: p = 0.018998, FAIL Drop z = 0.706 D_M/r_d: p = 0.06307, PASS Drop z = 0.706 D_H/r_d: p = 0.10598, PASS Both z = 0.706 observables must remain in a scientific rerun. These removals only localize the stress. ---------------------------------------------------------------------- 7. SEPARATE ACT AND TRAINING-BAO OPTIMA ---------------------------------------------------------------------- ACT-only optimum with H0_ACT fixed at 67.4: Omega_m: 0.3158079 r_d: 146.6979 Mpc chi-squared: 2.8399 Training-BAO-only optimum with H0_BAO fixed at 67.933256: Omega_m: 0.403086 r_d: 142.0972 Mpc chi-squared: 1.348 The training BAO pair, especially z = 0.706, pulls toward higher Omega_m and lower r_d than ACT. ---------------------------------------------------------------------- 8. POST-HOC BAO-NODE SENSITIVITY SCAN ---------------------------------------------------------------------- The ACT node remained fixed at 67.4. The BAO node was scanned, shared Omega_m and r_d were refitted using the construction subset, and the held-out DESI observations were scored. BAO node Construction p Held-out p Result ---------------------------------------------------------------- 67.933256 0.0177795 0.729633 Construction fails 68.170 0.05055 0.69020 Both pass 68.200 0.05614 0.66971 Both pass 68.300 0.07633 0.57621 Both pass 68.400 0.09747 0.45077 Both pass 68.500 0.11727 0.31255 Both pass 68.600 0.13332 0.18763 Both pass 68.645 0.13874 0.14155 Balanced pass 68.700 0.14354 0.09573 Both pass 68.775 0.14655 0.05152 Boundary full pass 68.800 not decisive 0.04097 Held-out fails Approximate simultaneous-pass interval: 68.17 through 68.775 The remembered full numerical pass at approximately 68.775 occurred: Construction p-value: 0.14655 Held-out p-value: 0.05152 The more balanced diagnostic point near 68.645 gives: Construction p-value: approximately 0.13874 Held-out p-value: approximately 0.14155 Shared Omega_m: approximately 0.315803 Shared r_d: approximately 146.703637 Mpc Neither value may be adopted merely because it passed the scan. ---------------------------------------------------------------------- 9. LEADING TECHNICAL DIAGNOSIS ---------------------------------------------------------------------- The historical bridge derives its BAO contribution in an H(z)-residual representation. The official DESI likelihood evaluates the correlated observables D_M/r_d and D_H/r_d, where: D_H = c / H(z) The next derivation must propagate: - the nonlinear inverse H(z)-to-D_H relation; - shared Omega_m; - shared r_d; - the expansion function E(z); - the full Jacobian; - the complete D_M/r_d and D_H/r_d covariance. Incomplete propagation through this map is the leading explanation for the localized z = 0.706 miss. This is a diagnosis to test, not a completed repair. ---------------------------------------------------------------------- 10. NEXT-ITERATION ACCEPTANCE REQUIREMENTS ---------------------------------------------------------------------- 1. Preserve v22 and every post-release record unchanged. 2. Reproduce 67.933256 as the historical v22 BAO-node output. 3. Derive the next BAO node from UTFANSWF mathematics, not the passing scan. 4. Work directly in the official correlated D_M/r_d and D_H/r_d space. 5. Include the complete Jacobian and covariance transformation. 6. Keep Omega_m and r_d shared with ACT. 7. Recalculate every downstream H0 contribution, H0_dist, uncertainty, and correlation. Do not assume 73.134202 remains unchanged. 8. Resolve same-data residual construction, CMB-calibration, GW-proxy, and SN-target-conditioning issues before claiming a physical proof. 9. Prespecify every Critical threshold and kill condition. 10. Freeze equations, node derivation, data, code, environment, and hashes. 11. Rerun the construction subset, held-out nodes, leave-one-out tests, channel statistics, joint statistic, covariance checks, and controls. 12. Do not allow an aggregate pass to rescue a failed mandatory channel. 13. Test the frozen construction on a genuinely untouched future release. 14. Preserve favorable, adverse, and null results together. 15. Require independent reproduction before upgrading beyond candidate status. If and only if the independently derived and frozen next-iteration construction passes every requirement, it may be reported as: FULL NUMERICAL PASS OF THE SPECIFIED CORRELATED DISTRIBUTED-H0 TEST. That bounded result would not by itself be independent validation of UTFANSWF, unique confirmation of the framework, or proof that the Hubble tension is resolved. END OF H0 MASTER RECORD v1