Established in scope
Schur transport with carrier and complement preserves the relative determinant
In the question: Common clock sectors, quartic geometry and operational reconstruction
Sufficient exact operator transport once actualF and source intertwiner are supplied. Does not construct an unknown physicalF,infer autonomous carrier time,or assume multiplicativity of arbitrary separate zeta determinants.
Read the exact result, assumptions and evidence
Result
For A=I-zC,A'=I-z uCu*,Q=I-F,QQ and Schur blocks are invertible on|z|<1. Exactly1-z=det(S'_F S_F^-1)det_F(A'_QQ A_QQ^-1),with S_F=I_F-zC_F-z²C_FQ(I_Q-zC_QQ)^-1C_QF. Unipotent factors are finite rank with determinant1; the QQ difference is trace class. The complement comes from the same supplied source.
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.
- Supplied finite orthogonal carrier on the same source space
In the carrier-transport theorem F is an actually supplied finite-rank orthogonal projection on the same circle H,Q=I-F. Physical application additionally needs the original map into active seam space and carrier isometry. A finite internal index retaining infinitely many spacetime modes is not this finite rank. No freely chosen F establishes origin.
Original evidence
- KMS-AND-CARRIER-TRANSPORT.txt lines 194–220
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 568–646
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/GRADED-DETERMINANT-SOURCE.txt
9cadaa53b70ebb666109f9cc7a02c07292a6faacf03eae79bf3d235682bf6952
- GRADED-DETERMINANT-SOURCE.txt lines 696–749
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/GRADED-DETERMINANT-SOURCE.txt
9cadaa53b70ebb666109f9cc7a02c07292a6faacf03eae79bf3d235682bf6952
- covariance_compression_review_20260921.md lines 166–221
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/source-yukawa-forward-gate-20260921/covariance_compression_review_20260921.md
0a460e9272a6da78e2bc199cd512807582c83dbccc4fedf08e51f8ab14c88f22
finding:schur-carrier-plus-complement-preserves-original-relative-determinant