TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/ROOT-RELATIVE-HEAT-MEASURE-CHECK.json
Original file SHA-256: 898bc827358e7b048e6c38615ecd41898173f1aaaa823c69c3c06014f2b85651
Inclusive original lines: 1-10
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | {
000002 |   "relative_pair": "A_1/4^2 versus A_1/2^2 on same circle",
000003 |   "flat_measure_integral": "log(2)",
000004 |   "positive_alternative_measure": "dt/t + c exp(-t)dt, c>0",
000005 |   "extra_integral": "pi sinh(2pi)/(cosh(2pi)(cosh(2pi)+1))",
000006 |   "extra_integral_numeric": "0.0116897064161940837367048",
000007 |   "consequence": "Both measures give convergent relative integrals. UV cancellation does not select dt/t; extra term is strictly positive.",
000008 |   "proof": "Integrating exp(-t)Delta(t) gives resolvent trace difference. Sum_n 1/((n+a)^2+1)=pi sinh(2pi)/(cosh(2pi)-cos(2pi a)).",
000009 |   "scope": "Only rejects convergence implies unique original scale measure. Flat logarithmic integral and supplied reference calculation remain valid."
000010 | }