Scoped exclusion
Full neutral source time has different spectral growth from finite-rank geometric Dirac
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact occupation-count proof in the already existing infinite limiting source,no new model or numerical asymptotics. No divergence claim for a fixed finite microscopic lattice. No exclusion of abstract Hilbert unitaries,compact resolvent,finite thermal heat traces,separately defined D_coll or correct one-particle extraction. Primitive P1 definition does not require the excluded equality or explicitly all comparison summability assumptions. No general P1 no-go or rejection of the already complete chosen source. This test only prevents unproved identification of full OS/GNS time generator with geometric one-particle operator.
Read the exact result, assumptions and evidence
Result
Actual neutral even pairs b*_{-r}d*_{r+1}=a*_{-r}a_{r+1} have energy2r+1. Each subset of the first m disjoint pairs yields a distinct orthonormal Q=0 state of energy at most m². Thus N_H,Q0(m²)>=2^m and Tr_Q0(1+H)^(-p)>=2^m/(1+m²)^p diverges for every finite p>0. This entire many-body time generator therefore cannot be time-intertwining unitarily identified with |D| in the tested finite p-summable geometric type,even after neutral/even selection or positive affine energy rescaling.
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.
- Given quarter many-body source and tested compact Dirac comparison
Given the already constructed limiting source in toe_research_20260909.tex with H=sum |j-1/4| n_j^exc and Q=sum n_b-sum n_d. Test only the added direct unitary identification of this FULL many-body time generator,including neutral/even sector,with |D| or positive affine energy rescaling in the usual compact finite-dimensional elliptic Dirac type with finite coefficient rank and finite p-summability. This identification is neither asserted as an original P1 theorem nor assumed true. Primitive boundary definition does not explicitly prescribe D_coll=H or every summability hypothesis.
Original evidence
- HILBERT-TYPE-TEST.txt lines 1–63
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/charge_transport/HILBERT-TYPE-TEST.txt
b46c43edbc7eb10530aacc6b61463f565668e860212d8655773be785978cf6fa
- REVIEW-HILBERT-TYPE.txt lines 1–48
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/charge_transport/REVIEW-HILBERT-TYPE.txt
e6a5a386e4c87b0dc7a662d1405f72c41ff4c8043532208e7c341dc0aa2e8f8a
- toe_research_20260909.tex lines 67–95
Source checked at this snapshot
Original location and fingerprint
tex-artefacts/toe_research_20260909.tex
361c3843779f78c66ff7e19b610152f38d5dc4f6623ed9017c9d515f1dc94433
- 001-section-primitive-core-and-carrier-interface-handoff.tex lines 65–91
Source checked at this snapshot
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
- 002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex lines 103–143
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex
1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e
finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac