Established in scope
Old seam factor remains exact in faithful KMS polarization class
In the question: Common clock sectors, quartic geometry and operational reconstruction
Proved operator persistence on the same circle,no fitted thermal scale or limit. Physical seam kernel,time,OS and EM readout still need identification. No full-E8 quasifree state.
Read the exact result, assumptions and evidence
Result
Trace-class C-P implies det_F[(I-z uCu*)(I-zC)^-1]=1-z on|z|<1 by exact three-factor cancellation; u^m gives(1-z)^m. C_beta is faithful with trace-class C_beta-P and h(C_beta)=beta B_a on DomB_a. D_beta is positive trace class,infinite rank and trace1; its product telescopes at every finite beta. Full A4 NS cover winding gives1-z,its square(1-z)^2 without a single-quarter choice.
Required assumptions
- Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
- Same original circle with trace-class changed polarization
For the mathematical continuation retain H,B_a psi_n=(n+a)psi_n,0<a<1,u psi_n=psi_(n+1),P=1_(B_a<0),uPu*=P+Pi. C is a positive contraction with trace-class C-P; actual functional-calculus C_beta=(I+exp(beta B_a))^-1,beta>0 belongs to this class. Physical KMS/OS/EM source identification is not presumed.
Original evidence
- KMS-AND-CARRIER-TRANSPORT.txt lines 38–159
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/KMS-AND-CARRIER-TRANSPORT.txt
9efcfb0d68e16db842aab97b7171b2d667e7b065cb4c6ab8138102acc4c8fb68
- GRADED-DETERMINANT-SOURCE.txt lines 435–566
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/GRADED-DETERMINANT-SOURCE.txt
9cadaa53b70ebb666109f9cc7a02c07292a6faacf03eae79bf3d235682bf6952
- RELATIVE-PAIRING-REVIEW.txt lines 411–475
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/RELATIVE-PAIRING-REVIEW.txt
ef280950f70a108ecff5dde9f57c67d097494e3824fdd65aea2ca176b5b83a34
- PROOF.md lines 11–32
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collar-current-source-bridge-20261021/PROOF.md
2dae051bb6a3ee77cc96bc0d63470ac4875950b46057865d1177e4ed3322e5ac
finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class