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ASTRAL GATELaboratory

VAL-B1-PMR-ANGULAR-GATE · CLOSED INSTRUMENT GATE · WAS A LIVE FRONTIER

PMR Adaptive Angular-Convergence Gate

Insufficient angular-mode support is the supported cause of an earlier apparent high-ω PMR subtraction failure. An adaptive angular-convergence gate was implemented and prospectively validated at unused ω=7. Sparse ω=10,12 later passed the same frozen gate. This is numerical-method progress, not an HH RSET reproduction or gateway result.

ADAPTIVE GATE PROSPECTIVE PASSSPARSE 10/12 PASSANGULAR PLATEAU PASSℓ-SUPPORT CAUSE SUPPORTEDABEL PRODUCTION FALSEHH RSET NOT CLAIMEDGATE NO

Checkpoint ladder

  1. DIAGNOSTIC

    Fixed low-ℓ high-ω probe

    FAIL (historical)

  2. DIAGNOSTIC

    Precision / rtol ladder

    NOISE DISFAVORED

  3. ISOLATION

    ℓ-support isolation (ω=8, r=6M, ξ=5)

    CAUSE SUPPORTED

  4. ISOLATION

    Cancellation at L=75

    HEALTHY tt/rr/θθ

  5. PLATEAU

    ω=8 L=75 vs 60

    FAIL

  6. PLATEAU

    ω=8 L=90 vs 75

    PASS

  7. PLATEAU

    ω=8 L=105 vs 90

    PASS

  8. PLATEAU

    ANGULAR_PLATEAU_STATUS

    PASS

  9. GATE

    Adaptive angular-support gate

    IMPLEMENTED

  10. GATE

    Silent accept forbidden

    ANGULAR_UNRESOLVED IF CEILING

  11. PROSPECTIVE

    Unused ω=7 start L=30

    FAIL then recovered

  12. PROSPECTIVE

    ω=7 L*=90

    ANGULAR_ACCEPTED

  13. PROSPECTIVE

    ω=7 L=105 confirmation

    TRUE

  14. SPARSE

    ω=10 and ω=12

    ANGULAR_ACCEPTED + confirmation

  15. DOMAIN

    PMR pointwise domain to ω=12

    PASS CONDITIONAL ON ℓ GATE

  16. DOMAIN

    PMR high-ω beyond ω=12

    UNESTABLISHED

  17. ABEL

    Abel math/synthetic referee

    PASS_DIAGNOSTIC

  18. ABEL

    Abel production validated

    FALSE

  19. NEXT

    Analytic large-ω expectation audit

    CLOSED 2026-09-19

  20. FRONTIER

    B1 HH reproduction

    NOT CLAIMED

  21. FRONTIER

    Physical gate

    NOT REACHED

Canonical public study: /research/pmr-angular-gate.

  1. Observed high-ω failure

    HISTORICAL FAIL

  2. Precision / tolerance noise disfavored

    REPRODUCIBLE

  3. ℓ-support isolated

    CAUSE SUPPORTED

  4. Cancellation restored

    L=75 HEALTHY

  5. ω=8 angular plateau demonstrated

    PASS

  6. Adaptive ℓ gate implemented

    ANGULAR_ACCEPTED RULE

  7. Prospective ω=7 validation

    PASS · L*=90

  8. Sparse extension ω=10,12

    ANGULAR_ACCEPTED

  9. Decaying high-ω tail

    NOT DEMONSTRATED

  10. Analytic asymptotic-expectation audit

    MIXED · GROWTH EXPECTED PRE-GI

  11. Dense CNG discovery scan

    STRONG EVIDENCE

  12. CNG independent confirmation

    NARROW PASS · 21 SEP

  13. Global CNG structure

    NOT ESTABLISHED

  14. Finite-support self-cancellation

    IMPLEMENTED · NOT INFINITE

  15. Infinite-support generalized integral

    NOT PROVED

  16. Independent HH benchmark reproduction

    ONLY LATER

ℓ-support isolation · ω=8 · r=6M · ξ=5

ℓ_max

25

|F_reg|/|F|_tt

8.698

F/F_sing_tt

0.103

cancellation

FAIL

ℓ_max

35

|F_reg|/|F|_tt

3.775

F/F_sing_tt

0.209

cancellation

FAIL

ℓ_max

50

|F_reg|/|F|_tt

1.011

F/F_sing_tt

0.497

cancellation

MARGINAL

ℓ_max

75

|F_reg|/|F|_tt

0.0124

F/F_sing_tt

1.013

cancellation

HEALTHY

Prospective ω=7

L

30

D_tt

0.191

cancel_ok

FALSE

gate

FAIL

L

45

D_tt

0.913

cancel_ok

FALSE

gate

FAIL

L

60

D_tt

38.25

cancel_ok

TRUE

gate

ANGULAR FAIL

L

75

D_tt

5.20×10⁻⁶

cancel_ok

TRUE

gate

PASS

L

90

D_tt

0

cancel_ok

TRUE

gate

PASS · L*
  • This is numerical-method progress, not an HH RSET reproduction or gateway result.
  • An ANGULAR_ACCEPTED point is merely eligible to enter a future controlled frequency-integration dataset.
  • It does not mean frequency support Ω → ∞ has been demonstrated.
  • It does not mean a decaying high-ω tail has been demonstrated.
  • It does not mean generalized-integral convergence has been demonstrated.
  • It does not mean Abel ε → 0+ has been validated.
  • It does not mean absolute HH RSET has been reproduced.
  • The latest PMR numbers are not physical RSET measurements.
  • The ω=8,10,12 |F_reg| ratios are not a derived envelope power.

Qualifiers

  • Do not describe this as proof that the full PMR RSET is correct.
  • Do not say Abel production is validated.
  • Do not say Schwarzschild Hartle–Hawking RSET has been reproduced.
  • Do not say the latest PMR numbers are physical RSET measurements.
  • Do not promote Branch G or a physical gate from this instrument result.
  • Preserve the historical high-ω FAIL. Do not rewrite it as if it never occurred.

Correction chain

  1. historical

    Fixed low-ℓ high-ω probe failed. Residuals grew; |F_reg|/|F| became O(1).

  2. precision

    Precision/rtol ladder: failure reproducible. Ordinary float64/ODE noise disfavored.

  3. ℓ-isolation

    Controlled ℓ staircase at ω=8, r=6M, ξ=5. ELL_SUPPORT_CAUSE_SUPPORTED = TRUE.

  4. matched re-probe

    Cancellation restored at L=75. ω=8 not yet plateaued between L=60 and 75.

  5. plateau

    Dedicated ω=8 staircase L=75→90→105. ANGULAR_PLATEAU_STATUS = PASS.

  6. gate

    Adaptive angular-convergence gate implemented. Silent accept forbidden.

  7. 2026-09-19

    Prospective unused ω=7 validation PASS. L*=90. confirmation_ok TRUE.

  8. sparse-10-12

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

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