Established in scope
OS step requires full moments rather than connected cumulants
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact counterexample and mathematical repair of the specified OS step. The original full Z_adm and its boundary word transport are not thereby constructed. Uniform growth and symmetric contraction time hypotheses must actually hold for full reconstruction.
Read the exact result, assumptions and evidence
Result
Archived sources define S_n^T=delta^n log Z and use it directly as the full OS family. An RP Gaussian functional gives full Gram determinant 2c²>0 for 1,X², but cumulant replacement gives -a²<0. Repair: Z/Z0=exp W and the full graded moment-cumulant expansion, followed by RP on all reflected words. A unital graded reflection/time compatible word map preserving the full functional induces an OS isometry.
Required assumptions
- Original seam operators and explicit moment definition in the OS passage
Source basis: the original boundary core supplies selfadjoint tangential B_Sigma; the seam has winding and stated spectral flow one. EM later names an allegedly selected rank-one line. QFT defines S_n^T as log-Z derivatives and uses them as the OS family. These statements and operator identifications are audited at the originals, not assumed proved.
Original evidence
- 005-subsection-admissible-schwinger-functions-minkowski-loca.tex lines 144–184
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--04_qft_source/sections/005-subsection-admissible-schwinger-functions-minkowski-loca.tex
8bf0a37157505ca12b90154dbe41a29c49a503686a8493dffd63945f205e0af6
- 008-section-relative-reflection-positivity-with-fermions.tex lines 179–254
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex
898aa879cf6a3eb6464d3180274bc2fc028408aeec9676af70a862dad9c3f4dc
- OS-SOURCE-REPAIR.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/OS-SOURCE-REPAIR.txt
50bc771398e8a363a617c677f503f556c9f2adccf6e40cfcb460ca4eb9f55ba6
- OS-SOURCE-REPAIR.txt lines 201–375
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/OS-SOURCE-REPAIR.txt
50bc771398e8a363a617c677f503f556c9f2adccf6e40cfcb460ca4eb9f55ba6
- identification-results.json lines 1–43
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/identification-results.json
ed089bdaf31a99eb21c46d67adee58aa0021779529c824f4001d0fa895885a80
finding:original-os-step-needs-full-moments-not-connected-cumulants