Established in scope
Field response and unnormalized factor from the same free integral
In the question: Automated construction of operator maps and sources
Exact for supplied free K, measure and source coupling. The example integrates a hole mode, not a geometric collar interior. Coherent source contraction K^-1 is not normal-ordered occupation. No general no-go for a separate bosonic spectral action plus fermion determinant and no original P1/P2 quantization.
Read the exact result, assumptions and evidence
Result
Direct Grassmann integration gives det K exp(bareta K^(-1) eta). Schur reduction jointly retains det K_ii and the inverse effective boundary/mode matrix. Two collars of the actual lowest quarter particle/hole pair under the supplied fermionic trace give det K=69649/65536 and occupations1/17,1/4097. Direct identification of the primitive spectral action with integrated complex fermions requires x f'(x)+1=0, hence a logarithmic profile; arbitrary f is insufficient.
Required assumptions
- Explicit complex-fermion source quantization
Given the actual invertible free kinetic operator K, its reference, Grassmann source couplings and oriented Berezin measure with integral exp(-barpsi psi)=1. A mode partition is not a spatial boundary decomposition without geometric identification. Neither comparison part D_rel nor a general spectral profile is automatically identified with this K or -log det K; this quantization is not presumed derived from P1/P2.
Original evidence
- PROOF.txt lines 271–326
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce
finding:joint-fermionic-source-schur-functional