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VAL-B1-SCALAR-TRACE-R6 · LIVE FRONTIER · EMPIRICAL BUDGET · NOT FULL RSET

Repaired scalar trace at r = 6M

The massless scalar subtraction was repaired and compared with the stored PMR trace at one radius, r = 6M, under minimal coupling. Status TRACE_R6_NUMERICAL_PASS_UNDER_EMPIRICAL_BUDGET. The residual exceeds the scalar-only allowance and is covered only by a combined empirical allowance dominated by the inherited PMR estimate. This website did not re-run the calculation.

EMPIRICAL PASSSCALAR ALLOWANCE DOES NOT COVERINHERITED PMR ALLOWANCE DOMINATESNOT A TAIL BOUNDNOT NINE TRACE TESTSE NOT VALIDATEDFULL RSET FALSEGATE NO

Checkpoint ladder

  1. SCALAR

    φ² at r=6M

    1.9571596066001755e-4
  2. SCALAR

    Box(φ²)

    3.1414970956971594e-7
  3. TRACE

    Scalar-inferred minimal trace

    −1.2088044476173205e-7
  4. TRACE

    Stored PMR trace

    −1.2086496991741827e-7
  5. TRACE

    Absolute residual

    1.5474844313788875e-11
  6. BUDGET

    Scalar-only allowance

    DOES NOT COVER
  7. BUDGET

    Combined empirical allowance

    COVERS RESIDUAL
  8. METHOD

    Primary quadrature

    DUFFY 256 · RECTANGLE EXCLUDED
  9. METHOD

    Nine radii 5.92–6.08M

    DERIVATIVE SUPPORT ONLY
  10. LOCK

    Independent tensor components

    NOT THIS RESULT
  11. LOCK

    HH independent RSET

    FALSE
  12. LOCK

    Physical gate

    NO

Coupling for this comparison is minimal, ξ = 0. On Ricci-flat Schwarzschild the variance φ² does not depend on coupling. The stress tensor does. Do not relabel older conformal B1 trace stamps as this check.

Relation used, with ℏ = 1: trace(T) = −Box(φ²)/2 + M²/(60 π² r⁶). The conformal anomaly-only relation is a different check.

Two implementation corrections are recorded. A blanket massless skip omitted 18 nonzero logarithmic coefficients and six nonzero rational-tail coefficients. The archived static-mode outer-boundary third-order coefficient had the wrong sign and denominator: correct γ = −α(3α+2)/(2α+1), archived +α(3α+2)/(2α−1), with α = ℓ+1 and M = 1.

Fresh static modes use exact Legendre solutions. For ℓ = 0, exact g00 = log(r/(r−2))/8 = 0.05068313851352055 against an archived 0.05068410711710673. That single mode shifts φ² by about 1.22675×10⁻⁸, most of the old/new scalar difference of about 1.22716×10⁻⁸. The archived first derivative is close to the exact one, so the scalar offset is not itself the earlier derivative or trace discrepancy.

The allowance protocol is retrospective and target-exposed. There is no fitted normalization, constant, or counterterm. It is not a statistical confidence interval and not a rigorous infinite-tail bound. Local or second-host agreement is reproducibility, not external peer review.

Mode outputs, coefficient tables, and server logs are not in the public package. The figures are the editorial summary.

Qualifiers

  • Do not say the scalar-only allowance covers the residual.
  • Do not treat the nine nearby radii as nine independent trace validations.
  • Do not carry a blanket TRACE PASS forward as a current universal claim.
  • Do not say this website recomputed the integrals.

Correction chain

  1. 2026-09-14

    Nested-h derivative closure under the then-current implementation and tolerance. Preserved.

  2. 2026-10-07

    Stored-tensor Box prediction 3.141187598810884e-7. Distinct from the 9 October independent Box.

  3. 2026-10-09

    Repaired scalar comparison. TRACE_R6_NUMERICAL_PASS_UNDER_EMPIRICAL_BUDGET.

Updated 2026-10-09. All checkpoints · 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-MTAU-SIGN-REPRO · VAL-B1-EXTCOORD-HH · VAL-B1-EXTCOORD-PHI2-DERIV · VAL-B1-EXTCOORD-RSET-4PT · VAL-B1-HOWARD-242-246