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.
Checkpoint ladder
SCALAR
φ² at r=6M
1.9571596066001755e-4SCALAR
Box(φ²)
3.1414970956971594e-7TRACE
Scalar-inferred minimal trace
−1.2088044476173205e-7TRACE
Stored PMR trace
−1.2086496991741827e-7TRACE
Absolute residual
1.5474844313788875e-11BUDGET
Scalar-only allowance
DOES NOT COVERBUDGET
Combined empirical allowance
COVERS RESIDUALMETHOD
Primary quadrature
DUFFY 256 · RECTANGLE EXCLUDEDMETHOD
Nine radii 5.92–6.08M
DERIVATIVE SUPPORT ONLYLOCK
Independent tensor components
NOT THIS RESULTLOCK
HH independent RSET
FALSELOCK
Physical gate
NO
| Layer | Checkpoint | Status |
|---|---|---|
| SCALAR | φ² at r=6M | 1.9571596066001755e-4 |
| SCALAR | Box(φ²) | 3.1414970956971594e-7 |
| TRACE | Scalar-inferred minimal trace | −1.2088044476173205e-7 |
| TRACE | Stored PMR trace | −1.2086496991741827e-7 |
| TRACE | Absolute residual | 1.5474844313788875e-11 |
| BUDGET | Scalar-only allowance | DOES NOT COVER |
| BUDGET | Combined empirical allowance | COVERS RESIDUAL |
| METHOD | Primary quadrature | DUFFY 256 · RECTANGLE EXCLUDED |
| METHOD | Nine radii 5.92–6.08M | DERIVATIVE SUPPORT ONLY |
| LOCK | Independent tensor components | NOT THIS RESULT |
| LOCK | HH independent RSET | FALSE |
| 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
2026-09-14
Nested-h derivative closure under the then-current implementation and tolerance. Preserved.
2026-10-07
Stored-tensor Box prediction 3.141187598810884e-7. Distinct from the 9 October independent Box.
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