Excluded in the stated class
Finite NS circle contains a UV partner and gives no determinant limit1-z
finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index
Sampling original M_z gives exactly the diagonal site phase and the cyclic shift in the actual v519 NS Fourier window. Negative sea obeys U_N P_N U_N*=P_N+Pi0-Pi_-M. Hence the complete ordinary finite relative determinant equals1 for everyN. Pi_-M escapes strongly but retains trace normone; a Fredholm determinant limit1-z is therefore invalid. Canonical sampling becomes exact on every fixed Fourier core; finite cyclic u_N admits no exact intertwining with bilateral M_z.
Scope: Excludes only passage from ordinary finite NS determinants by strong convergence. Positive full sampling proof for all evenN plus directN8/16/32 controls. Does not exclude separately defined original infinite relative factor,a justified different UV rule or all P1 sources. Finite alias,carrier complement and reflected physical pair stay distinct.
Required premises and original source excerpts
- Actual finite NS kernel and sampled original winding
Comparison uses the unchanged free NS kernel in v519/v524/v526 and sampling of original u=M_z on N=2M circle sites. Fourier modes n=-M,...,M-1 are cyclic. No UV contribution is removed and no ordinary finite determinant is declared an already renormalized continuum determinant.
premise:actual-finite-ns-kernel-and-sampled-original-winding - 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.
premise:historical-original-circle-and-transfer-source-passages - Trace-class polarization pair with actual unitary action
P,Q are orthogonal projections on the same H,Q-P in L1. The covariance theorem additionally assumes Q=UPU*,U unitary,0<=C<=I,C-P in L1. The theorem is on this common space; physical source membership is not inferred from index alone.
premise:trace-class-polarization-pair-with-restricted-unitary
- experiments/theory-contracts/original-admissible-source-closure-20261025/NS-CONTINUUM-WINDING-LIMIT.txt, lines 1–200
Source SHA256: 4a61f9604bb51f0d13419606d7d8c64fa2cfc840b417a7297403db7d6706f916
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/original-admissible-source-closure-20261025/NS-CONTINUUM-WINDING-LIMIT.txt, lines 201–304
Source SHA256: 4a61f9604bb51f0d13419606d7d8c64fa2cfc840b417a7297403db7d6706f916
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/original-admissible-source-closure-20261025/ACTUAL-KERNEL-FORWARD-MAP.txt, lines 143–260
Source SHA256: f94c5faee612af1deed8a1516b01fb9aa48f3c21196af825b070c6dab084f4ab
bounded-excerpt · current-at-snapshot