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ASTRAL GATELaboratory

VAL-B1-PMR-ASYMPTOTIC-AUDIT · CLOSED ANALYTIC LANE · WAS A LIVE FRONTIER

PMR Asymptotic Expectation Audit

After Levi–Ori F_sing subtraction, F_reg is not expected to decay before the generalized integral. Sparse ω=10,12 passed the frozen adaptive gate. |F_reg^tt| grew. A decaying high-ω tail is not demonstrated. That growth is the literature pre-GI remainder, not by itself a missing F_sing term. Not Abel. Not HH RSET.

GROWTH EXPECTED PRE-GIASYMPTOTIC STRUCTURE MIXEDGLOBAL CONFIRM FALSESPARSE 10/12 PASSDECAYING TAIL FALSEASYMPTOTIC REGIME FALSEFREQUENCY SUPPORT FALSEABEL PRODUCTION FALSEHH RSET NOT CLAIMED

Checkpoint ladder

  1. SPARSE

    ω=10 ANGULAR_ACCEPTED + confirmation

    PASS

  2. SPARSE

    ω=12 ANGULAR_ACCEPTED + confirmation

    PASS

  3. SPARSE

    L_ceiling

    180

  4. DOMAIN

    Certified pointwise domain to ω=12

    PASS CONDITIONAL ON ℓ GATE

  5. OBSERVATION

    |F_reg^tt(10)|/|F_reg^tt(8)|

    2.18019

  6. OBSERVATION

    |F_reg^tt(12)|/|F_reg^tt(8)|

    4.02997

  7. OBSERVATION

    Decaying high-ω tail demonstrated

    FALSE

  8. AUDIT

    Raw F(ω) identified

    Levi F_μν(ω)

  9. AUDIT

    F_sing componentwise

    (1/6)a ω³ − b ω · c=d=0

  10. AUDIT

    Leading ω³ omission

    DISFAVORED · ω=8 |F_reg|/|F|≪1

  11. AUDIT

    Pre-GI remainder

    GROWTH / OSCILLATION EXPECTED

  12. AUDIT

    Literature r=6M F_rr^Reg

    amplitude ∝ ω^{5/2}

  13. AUDIT

    Power-law fit on {8,10,12}

    FORBIDDEN

  14. AUDIT

    Asymptotic structure

    MIXED

  15. AUDIT

    Mixed-structure global confirm

    FALSE

  16. AUDIT

    Asymptotic regime identified

    FALSE

  17. AUDIT

    Frequency support converged

    FALSE

  18. ABEL

    Abel production validated

    FALSE

  19. FRONTIER

    B1 HH reproduction

    NOT CLAIMED

  20. FRONTIER

    Physical gate

    NOT REACHED

Canonical public study: /research/pmr-asymptotic-audit.

Levi–Ori t-splitting subtracts only the local coincidence singularity of the Christensen / DeWitt–Schwinger counterterm. That subtraction removes a polynomial in ω (ω³ and ω for the Schwarzschild RSET). It does not cancel remote null-geodesic / caustic singularities of the two-point function.

Those remote singularities Fourier-transform into undamped oscillations of F_reg(ω). For ⟨φ²⟩ the published envelope is ∼ω^{1/2}. For the RSET, Levi (2017) shows at the same diagnostic radius r=6M that F_rr^Reg is dominated by oscillations with amplitude proportional to ω^{5/2}. The ordinary integral ∫ F_reg dω therefore need not converge. The remainder is defined to be taken as a generalized integral (Abel / self-cancellation).

|F_reg^tt(10)| / |F_reg^tt(8)|
2.18019
|F_reg^tt(12)| / |F_reg^tt(8)|
4.02997
  • This is not frequency-support convergence.
  • This is not Abel production.
  • This is not an HH RSET reproduction.
  • The ω=8,10,12 ratios are not a derived envelope power.
  • ASYMPTOTIC_REGIME_IDENTIFIED = FALSE.
  • ASYMPTOTIC_STRUCTURE_MIXED_GLOBAL_CONFIRM = FALSE.
  • The production PMR source was not line-audited in this website freeze.

Qualifiers

  • Do not fit |F_reg| ∼ ω^p on {8,10,12} and call that a derivation.
  • Do not say the high-ω tail has been shown to decay.
  • Do not say frequency support has converged.
  • Do not say Abel production is validated.
  • Do not say Schwarzschild Hartle–Hawking RSET has been reproduced.
  • Do not say certified growth proves a missing F_sing term.
  • This website freeze does not contain a line-by-line production-source dump.

Correction chain

  1. 2026-09-19

    Adaptive angular gate prospectively validated at ω=7. Historical high-ω FAIL retained as ℓ-support.

  2. sparse-10-12

    SPARSE_EXTENSION_PASS. ω=10 and ω=12 ANGULAR_ACCEPTED + confirmation. L_ceiling=180.

  3. ratios

    |F_reg^tt(10)|/|F_reg^tt(8)|=2.18019. |F_reg^tt(12)|/|F_reg^tt(8)|=4.02997. Decaying tail not demonstrated.

  4. audit

    Analytic Levi–Ori mapping frozen before reading the ratios as a power. GROWTH_EXPECTED_PRE_GI.

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-ANGULAR-GATE · VAL-B1-MTAU-SIGN-REPRO · VAL-B1-EXTCOORD-HH · VAL-B1-EXTCOORD-PHI2-DERIV · VAL-B1-EXTCOORD-RSET-4PT · VAL-B1-HOWARD-242-246