Accomplishments & dated results

24 · E_DERIVATION_ONLY_CANDIDATE — NOT E_VALIDATED · 2026-10-07

Separate Hadamard derivation matches a, b, and e

Sixteen recorded checks pass. c = d = 0. The derivation was target-exposed, not blind, and is not a second Christensen/AHS implementation. Reapplying the derived e left five stored tensors unchanged to roundoff. E_VALIDATED stays false.

Match

a, b, e exact · c = d = 0

Checks

16 recorded pass

Blind

NO

E_VALIDATED

FALSE

Matching local counterterms is not a state-dependent tensor validation.

23 · NARROW COMPARISON — CHAIN STILL MRX_R_INVALID · 2026-10-03

Digitized published curves agree 12/12 at four radii

Reconciled 7 October. Component values at r=5.5, 6, 6.5, and 7 agree with digitized published Hartle–Hawking curves within stated tolerances. The full chain remains MRX_R_INVALID because r=5 failed tt n-convergence under analysis v1.0. A supplementary v1.1 pass does not replace that label.

Agreement

12/12 narrow

Chain

MRX_R_INVALID

r=5 v1.0

ANALYSIS_R_INVALID

Ward

HOLD

Digitized table values are not in the public JSON. A stored conservation diagnostic is not Ward closure.

22 · THIS PIPELINE · NOT GLOBAL ASYMPTOTICS · 2026-09-21

Unseen CNG window passes narrowly

ω∈[10.40,10.90], 51/51 angular-accepted, ε₁=37.5 fixed. The accepted record reports C1–C6 PASS. C5 was corrected to joint-H1 source transfer plus a fresh target cubic. Accepted directional R² 0.9988049064965246 and 0.9985764043986991. A 9 October replay agrees at roundoff. Discovery D=FAIL and F=CRITERIA_GAP stay.

Window

10.40–10.90 · 51/51

ε₁

37.5 fixed

Global structure

NOT ESTABLISHED

Grid file

not published

Individual C1–C4 and C6 definitions are not in the public package. Do not call this numerical CNG confirmed in the global sense.

21 · DISCOVERY EVIDENCE — NOT NUMERICAL CNG CONFIRMATION · 2026-09-20

CNG discovery scan: strong evidence for predeclared ε₁=37.5

A dense 51-point angular-gated PMR window at r=6M, ω∈[9.8,10.3], shows substantial numerical evidence for the independently predeclared first connecting-null-geodesic frequency ε₁=37.5. Fixed-ε₁ H1 explains R²≈0.997 of F_reg^tt versus ≈0.084 for a smooth cubic. The original surrogate discriminator is invalidated. Offline re-score is UNCLASSIFIED_CRITERIA_GAP. As written on this date the confirmatory window had not been computed. It later received a narrow pass; that does not change D=FAIL or F=CRITERIA_GAP.

Discovery window

9.8–10.3 · 51/51 accepted

H1 R² (tt, ε₁ fixed)

0.99722

H0 cubic R²

0.0838

Dominant |P|

ε₁=37.5 · 6.72×

Overall re-score

UNCLASSIFIED_CRITERIA_GAP

Global CNG

NOT ESTABLISHED

Window as of this date

NOT YET COMPUTED

Say substantial numerical evidence for the predicted ε₁ structure on this window. Do not say global numerical CNG confirmed. The later narrow pass is a separate entry.

18 · OPEN SCIENCE / REPRODUCIBILITY — EXTERNALLY REVIEWABLE, NOT CONFIRMED, PAUSED 2026-09-19 · 2026-09-15

Standalone Mτ sign reproducibility package

Two fresh implementations — symbolic and numerical — independently recover the analytically derived mode sign under the printed source conventions. A third internal derivation later brought the internal count to 3/3 PLUS. The result has been isolated into a public minimal reproduction pack. Public archaeology of the authors' private numerical code remains UNKNOWN. External confirmation remains open. The lane is paused pending external clarification. Production sign is not flipped.

Independent symbolic

DERIVED · no AG RSET imports

Independent numerical

DERIVED · no AG RSET imports

Internal derivations

3/3 PLUS

Tests

23/23 DERIVED · 0 PRINTED · 0 unresolved

Public pack

17 payload + FILE_HASHES.json

Confirmed

FALSE

Archaeology

UNKNOWN

Lane

PAUSED

Production sign flip

NO

A displayed-formula issue does not imply that the authors' published numerical RSET values are wrong. Not a portal claim. Not a B1 PASS. Not the live frontier.

17 · PRE-RSET STACK COMPLETE — RSET HOLD · 2026-09-15

Pre-RSET stack closed at four radii

The independent TBO extended-coordinate implementation has now passed the project's current validation gates for the radial Green function, zero mode, high-mode conditioning, complete m=6 Hadamard subtraction, ⟨φ²⟩ convergence, source-derived radial derivatives, same-ladder derivative comparison, and nested radial-spacing refinement at four benchmark radii. The renormalized stress tensor itself has not yet been assembled. B1 reproduction therefore remains unclaimed.

October 9, 2026 reassessment: this stamp keeps its original date, implementation, and tolerance. A later audit found that a blanket massless skip omitted 18 nonzero logarithmic coefficients and six nonzero rational-tail coefficients, and that the archived static-mode outer-boundary third-order coefficient had the wrong sign and denominator. Do not read “complete m=6”, “no blockers”, or a blanket TRACE PASS as a current universal claim.

Radii

ξ = 1.2, 1.8, 3.0, 5.0

h_refine_d1

PASS at all four

h_refine_d2

PASS at all four

Named blockers

NONE

RSET assembled

NO

A later PASS does not rewrite an earlier HOLD. This is a numerical-foundation closure under the implementation then in force, not an RSET result and not a physical gate.

14 · HADAMARD_MODE_SUBTRACTION = PASS · 2026-09-13

Full m=6 Hadamard mode subtraction

Full m = 0 → 2 → 4 → 6 Hadamard subtraction now runs at ξ_rad = 1.2, 1.8, 3.0, 5.0, including all higher-j Ψ⁺ terms. This is the first version of the modern engine in which those terms are actually evaluated everywhere. Infinite-mode n/ℓ convergence of ⟨φ²⟩_ren was HOLD on this date and is now recorded as PASS under the 2026-09-15 board.

ξ_rad

1.2, 1.8, 3.0, 5.0

m ladder

0 → 2 → 4 → 6

Mode-subtraction PASS does not imply an RSET reproduction.

13 · Implementation repair — not a coefficient fit · 2026-09-13

Ψ⁺ higher-j precision defect identified and repaired

The previous higher-j Ψ⁺ failure was a loss-of-precision implementation defect, not a physics divergence. The legacy path converted the Legendre product to float before high-precision differentiation, so every j ≥ 1 derivative evaluated spuriously as zero. The replacement retains the exact TBO expression and uses full arbitrary precision plus a source-derived analytic j = 1 treatment with an independent high-dps referee. Certified coefficients were not changed. The old path is retained for comparison.

j ≥ 1

previously silent; now evaluated

Not a coefficient fit. Not a physics divergence.

12 · TBO_2022_SOURCE_AUDITED · TABLE_III_SOURCE_LOCKED · 2026-09-13

Complete m=6 Hadamard coefficient families source-frozen

TBO 2022 source provenance is audited. Howard Table III scoreboard source is locked. Full m=6 D+ coefficient tables and the complete Hadamard coefficient set were ingested and source-frozen. The Wronskian conserved quantity is source-derived. Coefficients were not fitted to a numerical target.

Coefficients

source-frozen, not fitted

Source lock is not a B1 PASS.

11 · B1_EXTCOORD radial engine · 2026-09-13

Radial Euclidean Green independently HP-refereed

The radial Euclidean Green engine on the Taylor–Breen–Ottewill extended-coordinate route was independently high-precision refereed and promoted. Production Green path is source-derived log-Green only. Direct raw-amplitude path remains diagnostic-limited. The ledger preserves a FAIL_EDGE on the direct-log 5e3 crosscheck beside a PASS on the 1e2 diagnostic. Zero Matsubara mode is separately source certified.

DIRECT_LOG_5E3

FAIL_EDGE (preserved)

DIRECT_LOG_1E2

PASS

DIRECT_LOG_5E3_CROSSCHECK remains FAIL_EDGE and is not concealed.

10 · GPT REVIEW = PASS · evening sentinel · 2026-09-11

Analytic β'' method passed blind two-host certification

The corrected analytic-β'' method was subjected to a blind eight-cell sentinel independently on two different compute hosts. Both hosts returned PASS_HOST_HARD_RC, with all eight cells classified identically and no broken controls. The blind merge reported CLASS_AGREE_ALL. Promotion is scoped to the β'' evaluator.

cells

8/8 REFEREE_CONDITIONED

merge

CLASS_AGREE_ALL

hosts

primary Linux compute host + independent referee host

Process win on the historical Howard path. Not a B1 pass.

09 · Letter lock · 2026-09-07

HPS97 vacuum-log sign independently derived

HPS97 Eq. (6) and Popov Appendix B (B2) give opposite signs for the weight-zero vacuum-log contribution. A blind first-principles derivation performed before comparison agrees with the HPS97 Letter. Treated as a localized algebraic/sign discrepancy, not fraud.

Primary RHS

HPS97 Letter, not Popov B2

Not a self-consistent throat. External validation pending.

04 · B1_N2_XI5 forensic · 2026-09-11

High-ℓ derivative artifact solved with analytic differentiation

A persistent high-ℓ tail was traced to numerical evaluation of β'' by complex-step differentiation inside the WKB derivative construction. Replacing that procedure with exact symbolic / frozen-k differentiation collapsed the apparent tail. The corrected asymptotic is consistent with a decaying ℓ⁻⁶ series, not a physical nonintegrable tail.

ℓ ≈ 60 production |g|

1.51×10⁻⁷ → 8.47×10⁻¹⁰

|g| median collapse

~1266×

Historical Howard-path forensic. Not a B1 pass.

03 · LEIBNIZ_TEST n=1, ξ=1.8 · 2026-09-10

Exact treatment of adaptive WKB branch derivatives

A piecewise WKB expansion whose optimal-truncation boundaries move with the external radial coordinate cannot be differentiated as if it were globally smooth. The construction splits the continuous-ℓ integral at the moving switches and adds the Leibniz jump terms. On the primary n = 1, ξ = 1.8 cell, the independent derivative identity closed at a relative mismatch of approximately 5.94×10⁻⁷.

analytic + Leibniz

≈ 0.012945442969

independent referee

≈ 0.012945435285

relative mismatch

5.94×10⁻⁷

Closed on the tested cell. Not a B1 pass.

02 · B0-FULL thermal EOS · 2026-09-07

Independent thermal stress-energy validation

The full bitensor implementation reproduced the radiation equation of state naturally, rather than by imposing p = ρ/3 by hand. That is an independent thermal checksum on the same flat-space engine.

p / ρ

≈ 1/3 (emerged, not imposed)

Part of the B0 calibration layer.

01 · B0-FULL PASS · certification battery · 2026-09-07

Full 4D bitensor point-splitting engine

We replaced an insufficient one-dimensional differentiation model with a full two-point bitensor-jet treatment of temporal and transverse spatial derivatives. The Christensen stress-tensor operator is applied to the complete jet. The spatial vacuum residual fell from roughly 3×10⁵ to approximately 5×10⁻¹¹, with the temporal route around 2×10⁻¹¹.

Spatial vacuum residual

3×10⁵ → 5×10⁻¹¹

Temporal residual

∼ 2×10⁻¹¹

B0-FULL is a calibration layer, not a throat and not a B1 pass.