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