Established in scope
Exact field variation of the existing covariance reconstruction and its boundary faces
In the question: Automated construction of operator maps and sources
Analytic finite/regulated derivative result plus exact reuse of the given positive particle/hole collar. No general non-Gaussian state reconstruction, Phi provenance, statement for noncommuting sector projectors or unchecked unbounded limits.
Read the exact result, assumptions and evidence
Result
The Frechet derivative of the actual v258 reader multiplies each matrix element in an eigenframe by the strictly negative divided difference of h. For fixed sector projectors commuting with the background covariance, each sector block vanishes iff its covariance-variation block vanishes. A moving carrier embedding has additional derivative terms. The Calderon projection is not already a faithful mixed occupation: restriction to its own range gives I. The existing two-face construction correctly gives n=1-A and h(n)=2ell B, thus recovering the variation already present in B without selecting it.
Required assumptions
- Given differentiable faithful covariance chart with explicit sector embedding
Finite or explicitly regulated CAR one-particle chart with 0<C<I; h(C)=log(I-C)-log C. The individual sector-block statement requires fixed sector projectors commuting with the background covariance; moving embedding, grading, scale and source must be differentiated separately. Interpretation as a complete state uses the quasi-free hypothesis. No physical P1 source or Phi insertion is selected.
- Complete data of both product-collar faces
A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.
- 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.
Original evidence
- P1-INSERTION-TANGENT.txt lines 34–132
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/P1-INSERTION-TANGENT.txt
b49aa4ec77bc22029545c4f8f2584e80e63fd8bb6b8a0ce8536baf4137d3ea55
- p1_insertion_tangent.py lines 27–113
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/p1_insertion_tangent.py
70b3d0790f40a4834644c806db90fc27402967563e6e8888a8f1192ec539ad00
- v258_dirac_covariance_induction.py lines 65–150
Source checked at this snapshot
Original location and fingerprint
verification/v258_dirac_covariance_induction.py
16c60e831dceba773f3629466895f1009654827286e5b760ae01bd755fd5c0b1
finding:source-covariance-jet-and-mixed-face-interface