Scoped exclusion
Finite circle compression cannot retain the whole thermal factor
In the question: Common clock sectors, quartic geometry and operational reconstruction
Only naive finite-rank compression on the same circle. Not exclusion of the entire carrier program,infinite spacetime fibers with finite internal index,or another justified original source map.
Read the exact result, assumptions and evidence
Result
For pure C=P the compressed relative determinant is1-z<v,(I-zC_F)^-1v>,v=Fpsi0. It equals1-z on an open set iff psi0 lies in RanF,forcing endpoint eigenvalues0/1 and singular log odds. For C_beta,D_beta>0,TrD_beta=1 and Tr(FD_betaF)<1 for every finiteF. Already its derivative at0=-Tr(FD_betaF)>-1 rules out1-z.
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 161–192
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 289–433
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 652–794
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/GRADED-DETERMINANT-SOURCE.txt
9cadaa53b70ebb666109f9cc7a02c07292a6faacf03eae79bf3d235682bf6952
finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor