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VAL-B1-MTAU-SIGN-REPRO · PAUSED · SOURCE / LITERATURE REPRODUCIBILITY QUESTION · NOT THE LIVE FRONTIER

Mixed-Time Derivative Sign Reproducibility Check

Independently reproducible potential sign inconsistency in a displayed mixed-time derivative formula. Externally reviewable. Not confirmed. Internal derivations 3/3 PLUS. Public archaeology UNKNOWN. Lane paused pending external clarification. Production sign not flipped.

EXTERNALLY REVIEWABLENOT CONFIRMEDPAUSED3/3 PLUSARCHAEOLOGY UNKNOWN23/23 DERIVEDPRODUCTION SIGN NOT FLIPPEDPUBLIC REPRO READY

Checkpoint ladder

  1. SOURCE

    Source set frozen

    PASS

  2. SOURCE

    Δτ convention audited

    PASS

  3. SOURCE

    Matsubara derivative sign

    PASS

  4. SOURCE

    Euclidean parallel propagator

    PASS

  5. SOURCE

    W = G − K audit

    PASS

  6. REFEREE

    Point-split operator sign

    PASS

  7. REFEREE

    Point-split φ² limit

    PASS

  8. REFEREE

    Finite-Δτ Mτ referee

    PASS

  9. INDEPENDENT

    Independent symbolic implementation

    PASS / DERIVED

  10. INDEPENDENT

    Independent numerical implementation

    PASS / DERIVED

  11. INDEPENDENT

    Third internal mode-sign derivation

    3/3 PLUS

  12. INDEPENDENT

    Synthetic tests

    5/5 DERIVED

  13. INDEPENDENT

    Frozen-real mode tests

    18/18 DERIVED

  14. INDEPENDENT

    Total numerical tests

    23/23 DERIVED

  15. LITERATURE

    Literal 2022 Schwarzschild source comparison

    PASS

  16. LITERATURE

    Literal 2023 RN source comparison

    PASS

  17. EXTERNAL

    Published numerical implementation

    UNKNOWN

  18. EXTERNAL

    Archaeology of private code

    UNKNOWN

  19. EXTERNAL

    Potential sign issue

    EXTERNALLY REVIEWABLE

  20. EXTERNAL

    Confirmed

    NO

  21. EXTERNAL

    Lane

    PAUSED

  22. PACK

    Public repro pack

    READY

  23. PRODUCTION

    Production sign flip

    NO

Canonical public study: /research/mtau-sign.

Public minimal reproduction pack

MTAU_SIGN_REPRO_PUBLIC_MINIMAL

SHA256 07a1af741749a5b6b73c73ed98fe308e0903e9bba518c03ae6bd5b35690b8ad3

PASS · symbolic DERIVED · numerical 23/23 DERIVED · 0 PDFs · no AG runtime dependencies

READY17 payload files + FILE_HASHES.jsonNO PDFSNO AG RUNTIME
Download packAuthor note draft

A sign tension was identified between the displayed mixed-time coincidence formula and the sign obtained directly from the papers' own Euclidean Green-function definition, Δτ convention, W = G − K relation, and Euclidean metric.

This was not accepted on the basis of Astral Gate's production code. It was independently reproduced through a fresh symbolic derivation with no AG RSET imports, a fresh finite-Δτ numerical implementation with no AG RSET imports, and a third internal mode-sign derivation. INTERNAL_SIGN_DERIVATIONS = 3/3 PLUS.

All three internal tracks produce an overall PLUS mode contribution under our reading of the stated conventions. The displayed TBO Eq. 18 / analogous ABOT Eq. 16 carries an overall MINUS. The numerical track tested 5 synthetic modes plus 18 frozen-real modes, 23 total: 23 DERIVED, 0 PRINTED, 0 UNRESOLVED.

This earns EXTERNALLY REVIEWABLE. It does not establish that the authors' actual numerical code used the displayed sign. MT_ARCHAEOLOGY = UNKNOWN. This is not yet confirmed. Published numerical impact is unknown. We have not inspected the authors' private/original numerical code. A displayed-formula issue does not imply that the authors' published numerical RSET values are wrong.

The Mτ numerical/sign lane is paused pending external clarification. Do not present the discrepancy as a confirmed literature error. Do not flip the production sign. This lane is not the live B1 frontier.

Independent reproduction

INDEPENDENT_SYMBOLIC_MTAU_SIGN
DERIVED
INDEPENDENT_NUMERICAL_MTAU_SIGN
DERIVED
Independence grep
PASS
Synthetic
5/5 DERIVED
Frozen-real
18/18 DERIVED
Total
23/23 DERIVED
MODE SIGN
INDEPENDENTLY REPRODUCED
LOCAL/GEOMETRIC BRACE
SOURCE-ANALYTIC AUDIT

The standalone numerical referee independently verifies the MODE-SUM SIGN. It does not independently reconstruct every geometric/local brace. The geometric/local brace comparison is supported separately by the source/convention audit. Three internal PLUS derivations do not determine which sign the authors' private code used.

The 18 real samples are frozen numerical radial-Green values produced earlier in the benchmark work.

The standalone numerical referee consumes them as input data but does not import or execute the Astral Gate RSET pipeline.

Therefore this is an independent reproduction of the mathematical MODE-SIGN identity. It is not an independent full physical RSET reproduction.

The five synthetic tests plus the standalone symbolic derivation make the sign question independent of the physical origin of those frozen samples.

Source / literature scope

  • Taylor, Breen & Ottewill (2022) — Schwarzschild

    arXiv:2201.05174v3

    SHA256 91d2a0bf6c16340f9b63b116111e61e8134842cf495fc1d6daa51e1e0adbe021

    same displayed global-minus structure in the audited source (Eq. 18 mixed-time display)

  • Arrechea, Breen, Ottewill & Taylor (2023) — Reissner–Nordström

    arXiv:2307.10307

    SHA256 49f82ba89ffec977201e4d5694e161b28dfa1a7b5cc30be93df48933308834ef

    same displayed global-minus structure with κ → κ₊ (audited Eq. 16 mixed-time display)

The same displayed global-minus structure appears in the audited 2022 Schwarzschild and 2023 RN sources. Do not infer from that alone that both numerical implementations used it. Evidence identity is paper/version + literal expression + hash, not equation numbers alone.

PRINTED CONVENTION · POTENTIAL / REQUIRES EXTERNAL CONFIRMATION · LANE PAUSED

Mixed-time coincidence derivative under printed Green-function conventions

Δτ=τ′−τ\Delta\tau = \tau' - \tau
G∝exp⁡ ⁣[inκ(τ′−τ)]G \propto \exp\![i n \kappa(\tau'-\tau)]
∂τ∂τ′exp⁡ ⁣[inκ(τ′−τ)]=+n2κ2 exp⁡ ⁣[inκ(τ′−τ)]\partial_{\tau}\partial_{\tau'}\exp\![i n \kappa(\tau'-\tau)] = + n^{2}\kappa^{2}\,\exp\![i n \kappa(\tau'-\tau)]
gττ′→+1/fg^{\tau\tau'} \to +1/f
[gττ′W,ττ′]mode,analytic=+14π2∑ℓ(2ℓ+1)∑n≥1n2κ2f gnℓ[g^{\tau\tau'}W_{,\tau\tau'}]_{\mathrm{mode,analytic}} = +\dfrac{1}{4\pi^{2}}\sum_{\ell}(2\ell+1)\sum_{n\ge 1}\dfrac{n^{2}\kappa^{2}}{f}\,\mathsf{g}_{n\ell}
[gττ′W,ττ′]printed=−14π2∑ℓ(2ℓ+1)∑n≥1n2κ2f gnℓ−14π2{brace}[g^{\tau\tau'}W_{,\tau\tau'}]_{\mathrm{printed}} = -\dfrac{1}{4\pi^{2}}\sum_{\ell}(2\ell+1)\sum_{n\ge 1}\dfrac{n^{2}\kappa^{2}}{f}\,\mathsf{g}_{n\ell} - \dfrac{1}{4\pi^{2}}\{\mathrm{brace}\}

The independently reconstructed mode contribution therefore carries the analytically DERIVED plus structure. The displayed mixed-time formula carries the opposite overall sign. Three internal derivations agree on PLUS. That does not determine the sign used to generate the published tables.

Within the audited printed conventions, we did not identify a convention that accounts for the displayed overall minus. External confirmation is still required. Archaeology of the private numerical implementation is UNKNOWN. No portal claim.

Point-split validation history

  1. 2026-09-15

    Temporal point-split Mτ referee

    EXACT −1 SIGN TENSION

    Independent finite-Δτ point-split referee found Mτ_PS = − Mτ_printed at all four certification radii.

  2. 2026-09-15

    Point-split operator sign closure

    SUSPECTED REFEREE BUG REFUTED

    Hypothesis that the point-split code used +d²/dΔτ² instead of −d²/dΔτ² was tested and REFUTED. POINT_SPLIT_OPERATOR_SIGN = PASS. POINT_SPLIT_OPERATOR_CODE_EVALUATES = MINUS_D2. GPT_FINGERPRINT_PS_USES_PLUS_D2 = REFUTED. Cosine analytic, single-mode, and geometric/Hadamard operator unit tests PASS. The −1 sign tension did not originate from a bad finite-separation derivative operator.

  3. 2026-09-15

    Source-convention identity closure

    SOURCE-LEVEL GLOBAL-SIGN TENSION ISOLATED

    MTAU_SOURCE_SET = FROZEN. TIME_PARALLEL_PROPAGATOR_SIGN = PASS. MATSUBARA_SIGN = PLUS. EUCLIDEAN_LORENTZIAN_MIXED_CONTINUATION = PASS. Within the audited printed conventions, we did not identify a convention that accounts for the displayed overall minus. External confirmation is still required.

  4. 2026-09-15

    Independent reproduction / public review pack

    EXTERNALLY REVIEWABLE · NOT CONFIRMED · PACK READY

    Independent symbolic DERIVED. Independent numerical DERIVED. 23/23 tests. Public minimal pack READY (17 files, smoke PASS). Author-contact draft remains UNSENT. Production sign not flipped.

  5. 2026-09-19

    Third internal mode-sign derivation / archaeology / pause

    3/3 PLUS · ARCHAEOLOGY UNKNOWN · LANE PAUSED

    THIRD_METHOD_MODE_SIGN = DERIVED. INTERNAL_SIGN_DERIVATIONS = 3/3 PLUS. Public archaeology did not determine which sign was actually used in the private numerical implementation that generated the published tables. SIGN_VERDICT = UNRESOLVED. The Mτ lane is paused pending external clarification. Not a confirmed literature error. Production sign not flipped.

Published numerical impact

Displayed mixed-time derivative formula

POTENTIALLY_AFFECTED

Schwarzschild published numerical RSET

UNKNOWN

RN Hartle–Hawking published numerical RSET

UNKNOWN

Boulware / Unruh state-difference calculations

UNKNOWN

Downstream backreaction / energy-condition consequences

NOT_ASSESSED

Public archaeology of private numerical code

UNKNOWN

Mτ lane

PAUSED_PENDING_EXTERNAL_CLARIFICATION

ASTRAL GATE INTERNAL DIAGNOSTIC ONLY · NOT PROOF OF THE LITERATURE SIGN

Better Howard/Ward behavior did not determine the algebraic sign. The sign result comes from the printed definitions and independent reproduction. A global Ward sign patch is separately REJECTED.

Ward RMS · PRINTED-sign assembly
≈ 3.313220×10⁻⁵
Ward RMS · DERIVED-sign assembly
≈ 2.831367×10⁻⁶
Howard L2 RMS · PRINTED
≈ 47.74180
Howard L2 RMS · DERIVED
≈ 0.5551125
Trace
near machine-small in both
WARD_GLOBAL_SIGN_FIX
REJECTED

Evidence chain

  1. Published definitions

    SOURCE

  2. Source-convention audit

    FROZEN

  3. Independent symbolic derivation

    DERIVED

  4. Independent numerical referee

    23/23 DERIVED

  5. Third internal mode-sign derivation

    3/3 PLUS

  6. Public minimal pack

    READY

  7. Externally reviewable

    NOT CONFIRMED

  8. Archaeology of private code

    UNKNOWN

  9. Lane paused

    PENDING EXTERNAL CLARIFICATION

  10. Confirmation

    NOT YET

Author contact

AUTHOR NOTE = DRAFT · STATUS = UNSENT

The draft is published for inspection. It has not been sent. Authors have not confirmed anything. No contact information is published.

PUBLIC REPRO PACK = READY · AUTHOR_CONTACT_READY = YES · SHA256 07a1af741749a5b6b73c73ed98fe308e0903e9bba518c03ae6bd5b35690b8ad3

  • This is not yet confirmed.
  • Published numerical impact is unknown.
  • We have not inspected the authors' private/original numerical code.
  • A displayed-formula issue does not imply that the authors' published numerical RSET values are wrong.
  • MT_ARCHAEOLOGY = UNKNOWN.
  • The Mτ lane is paused pending external clarification. Production sign is not flipped.

Qualifiers

  • Do not say the paper is wrong, the authors made an error, or the published RSET is wrong.
  • Do not flip the production Mτ sign.
  • Author note = DRAFT / UNSENT. Authors have not been contacted.
  • PUBLIC REPRO PACK = READY. No download of third-party PDFs.
  • The sign issue is isolated from portal / gateway claims.
  • Paused is not confirmed, not refuted, and not the live instrument frontier.

Correction chain

  1. point-split

    Finite-Δτ referee: Mτ_PS = − Mτ_printed at all four radii.

  2. operator

    Suspected +d²/dΔτ² referee bug REFUTED. Operator evaluates MINUS_D2. Unit tests PASS.

  3. source

    Source-convention identity isolated a displayed global-sign tension. POTENTIAL / REQUIRES EXTERNAL CONFIRMATION.

  4. repro

    Independent symbolic + numerical packs. 23/23 DERIVED. EXTERNALLY REVIEWABLE. CONFIRMED = FALSE.

  5. pack

    Public minimal pack hardened. PUBLIC_REPRO_PACK_READY = YES. AUTHOR_CONTACT_READY = YES. Note remains UNSENT.

  6. 2026-09-19

    Third internal derivation 3/3 PLUS. Archaeology UNKNOWN. Lane PAUSED pending external clarification. Not the live frontier.

Updated 2026-09-19. All checkpoints · VAL-B1-SCALAR-TRACE-R6 · VAL-B1-PMR-CNG-CONFIRMATION · VAL-B1-PUBLISHED-HH-CURVES · VAL-B1-HADAMARD-E-CANDIDATE · VAL-B1-PMR-CNG-DISCOVERY · VAL-B1-PMR-ASYMPTOTIC-AUDIT · VAL-B1-PMR-ANGULAR-GATE · VAL-B1-EXTCOORD-HH · VAL-B1-EXTCOORD-PHI2-DERIV · VAL-B1-EXTCOORD-RSET-4PT · VAL-B1-HOWARD-242-246