Scoped exclusion
Positive spectral weight alone does not establish original-source reflection positivity
In the question: Common clock sectors, quartic geometry and operational reconstruction
Counterproof only to the generic positive-weight preservation inference in cited original passages,not the entire geometric/BRST measure theorem under all additional conditions. Finite test is no full P1/P2 countermodel,no TFPT prediction,and no newly chosen physical source. Source Bernstein cone means completely monotone profile,not a general Bernstein function. No actual original field map or completeT1-T8 goal closed. Preserve existing given-source paths,positive transfer constructionv330,Schur/projector/Weyl results. Do not introduce full ambient geometric measure construction as a prerequisite for every neutral local response;direct local OS embedding remains possible. P1 already assumesRP;only a proposed derivation shortcut is excluded.
Read the exact result, assumptions and evidence
Result
The generic RP preservation inference in the old constructive-measure proof is false. A strictly positive RP base with eigenvalues19,1 becomes non-RP under w=exp(-Tr exp(-D²)),despite positive weights,reflection covariance and gap>=1. Exact Delta=e^-1(1-e^-4)²>75/256>1/9>log(10/9);normalized reflected sign response changes from1/19 to-0.12394264612509166625. General nonconstant positive Laplace profiles haveDelta>0;generic failure uses r in(exp(-Delta),1),while fixed9/10 base requires the stated threshold. Finite W>=0 is the universal Schur-multiplier preservation criterion;for a fixed base K0 elementwise-times W>=0 is exact. A suitable reflected factorization is sufficient for repair. Source-independent positive reference denominator cancels in normalized responses and repairs neither false RP nor missing cross coherence.
Required assumptions
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
- Finite test of the generic spectral RP preservation inference
Test only the generic inference used in old measure proofs that a pointwise positive reflection-symmetric spectral weight exp(-Tr f(D²)) preserves existing RP. Test class: classical reflected finite halves,K0=[[10,9],[9,10]],D(s,t)=[[2s,1],[1,2t]],s,t=plus/minus1,f(u)=exp(-u). No full geometric/BRST/branch or P1/P2 realization of these data assumed. General-profile formula uses finite positive Laplace measure;the9/10 threshold is not asserted for arbitrarily small profiles.
Original evidence
- PROOF.txt lines 1–184
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261029/PROOF.txt
9b6ed0c36862913dac9762c0d1a6cd1e9f9c9a5f6b4b905ac8de5dccc25424b1
- check_spectral_weight_rp.py lines 1–123
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261029/check_spectral_weight_rp.py
9cf7bc1c265ef42a6e56ce364cfa98f62a48b81e9986e0ac12a13bc2e0d9b8d8
- spectral-weight-rp-results.json lines 1–73
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261029/spectral-weight-rp-results.json
c90b0f3274565b0a96df43217aa7f85de6395547bd90bd7b85ed113396279d25
- INDEPENDENT-REVIEW.txt lines 1–142
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261029/INDEPENDENT-REVIEW.txt
a6232d863bf730a98c4d499326cd9457f866ad8896bfcaba726b46b33b1aab06
- REVIEW-ADDENDUM.txt lines 1–61
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261029/REVIEW-ADDENDUM.txt
a3ee717842af75b6fad26d1ab15741c83ea9e228fb0579efe20e57a72d2b14a7
- STAND-EINFACH-DE.txt lines 1–50
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261029/STAND-EINFACH-DE.txt
9fdd29c32942b4f142e82385f8162f9d19362cb2218274c6b2de3ca89270a4ce
- 005-section-absolute-dimensionless-metrology-from-the-bounda.tex lines 65–181
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Original location and fingerprint
documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/005-section-absolute-dimensionless-metrology-from-the-bounda.tex
b19c58deb3ee905c16e659dd26b15ca8d1998bab6f703cd350e04e54129a9a4c
- 016-section-closure-architecture-b-yukawas-masses-flavor-had.tex lines 108–151
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Original location and fingerprint
documents/archive--paper-latex--tfpt-42/sections/016-section-closure-architecture-b-yukawas-masses-flavor-had.tex
87eb0d32b6b0794efc2e27127e8f09839161b97b478c03dbd36557fcad08f729
- 002-section-closure-theorems-from-the-admissibility-complex.tex lines 256–310
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Original location and fingerprint
documents/archive--tfpt-45--source_extracts--04_qft_source/sections/002-section-closure-theorems-from-the-admissibility-complex.tex
61ecee7727bdec47936bbffc028d3dbac5260a025b6dbcce30124a60d635fc9c
- 001-section-primitive-core-and-carrier-interface-handoff.tex lines 302–342
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Original location and fingerprint
documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex
7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
- v330_qgamb_admissible_measure.py lines 42–132
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Original location and fingerprint
verification/v330_qgamb_admissible_measure.py
21cbeb2b96d9ee581da3a9c45be400d77d232730ba37bbb19cb4cec07fb5e5be
- PROOF.txt lines 271–326
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Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce
finding:positive-spectral-reweighting-does-not-establish-original-source-rp