TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/native-arc-charge-source-interface-20261026/CONFORMAL-TRACE-REVIEW.txt
Original file SHA-256: ac8d7282712059c7ba465a088ea9f8fdd023b3e2e31cb13fb01de271d0f80ad9
Inclusive original lines: 1-62
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | Independent scoped mathematical review
000002 | 26 October 2026
000003 | 
000004 | Reviewed claim: UR.NATIVE.ARCCHARGE.CONFORMAL-TRACE.01
000005 | Verdict: ACCEPT_EXACT_STATED_SCOPE. No material correction required.
000006 | 
000007 | Read CONFORMAL-TRACE-AND-WICK.txt and check_conformal_trace_wick.py fully.
000008 | Checked the orthogonal Cauchy-data definition and conformal Dirac law against
000009 | Guillarmou/Moroianu/Park, arXiv:1009.3179, Section3.1 and Proposition7.
000010 | The original BOUNDARY-SOURCE.txt and ELLIPTIC-GREEN-RP.txt were also read.
000011 | 
000012 | 1. Analytic theorem
000013 | With the canonical conformal spin-bundle identification understood, the
000014 | harmonic solution factor exp(-(d-1)sigma/2) is exactly canceled by the
000015 | boundary L2 unitary exp((d-1)sigma_boundary/2). Thus the unitary maps the
000016 | smooth Cauchy-data spaces onto one another, and by closure maps their
000017 | orthogonal Calderon projections onto one another. The argument is not a
000018 | finite-regulator extrapolation. Fixed geometric boundary components and
000019 | regional supports are preserved by this scalar multiplication.
000020 | In the common bulk L2 picture, exp(-sigma/2) D exp(-sigma/2) and the corrected
000021 | trace exp(-sigma_boundary/2)Tr are consistent with that same theorem.
000022 | 
000023 | 2. Source and operator scope
000024 | The original quarter/fold map is correctly applied AFTER boundary transport.
000025 | No commutation of the boundary multiplier with Fourier/quarter projections
000026 | is assumed. Wick and current-functional invariance refer to the retained
000027 | free conditional CAR source and correctly transported observables. Native
000028 | composites retain their original subtraction, domains and smearing; a stress
000029 | tensor defined anew by each metric is explicitly outside this identification.
000030 | This does not prove invariance of spectra, APS data, spectral actions,
000031 | physical time, or a primitive P1 measure/source map.
000032 | 
000033 | 3. Geometry averaging
000034 | For an identical normalized conditional source functional, arbitrary
000035 | source-independent weights, including determinants and anomalies, factor
000036 | from normalized correlators when the stated integrals exist and their
000037 | denominator is nonzero. The four-field determinant and all higher Wick
000038 | words therefore remain fixed. The conclusion does not follow for a varying
000039 | conformal class, connection, mass, cut, source covariance, primitive higher
000040 | vertex, or untransported metric-dependent observable. The text preserves
000041 | these distinctions, including possible effective-weight changes when other
000042 | geometric data are integrated as well.
000043 | 
000044 | 4. Independent replay
000045 | Ran both python3 -B check_conformal_trace_wick.py and python3 -B -OO
000046 | check_conformal_trace_wick.py without an output path. Both exited0 and
000047 | returned the same result as conformal_trace_wick_results.json. RuntimeError
000048 | checks remain active. The raw-trace compression defect is nonzero for
000049 | different positive face factors; the varying-covariance control is -v^2/4.
000050 | These symbolic and finite graph checks are diagnostics of the analytic
000051 | closed-space proof, not a replacement for it. No other files were changed.
000052 | 
000053 | Reviewed SHA256:
000054 | CONFORMAL-TRACE-AND-WICK.txt
000055 | 77a6bffa2192b809f0264406afe7dd57d4718576f7f6632c107a7036de6ff5d1
000056 | check_conformal_trace_wick.py
000057 | c30f3058a971b28d17ba3af73f6cbb63fbac43d94a4640ad58d8c64fe613271d
000058 | conformal_trace_wick_results.json
000059 | 84cbf70dba2439348d6f450a57b6852ea1779bcc0882b718e7abc2feabee8238
000060 | 
000061 | Experiment-only review. No ledger, empirical, interaction or physical-source
000062 | promotion is implied.