Established within the stated premises
Full original NS orientation cover has charged Green RP in all modes
finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp
Original doubled Pin deck action forces beta2 in the existing length convention. H=i sigma3 partial_w is selfadjoint on the same b boundary domain,with simple spectrum nπ/2,n inZ. For L=partial_x+H,S(t)=e^(−tH)(1+e^(−2H))^−1 is the entire antiperiodic Green kernel. Both charge blocks factor exactly:−S(−t−s)=B_t*B_s and S(t+s)=Btilde_t*Btilde_s,with B_t=e^(tH)(1+e^(2H))^−1/2 and Btilde_t=e^((1−t)H)(1+e^(2H))^−1/2 for0<t,s<1. Both are bounded. Explicit source-order minus and charge-exchanging word reversal give full free CAR RP through Wick/Gibbs limits. Relative thermal Z=2 product_n≥1(1+e^(−nπ))² converges. Linear Clifford reflection exchanges the actual c=±i deck spaces;their zero kernels jointly give NS value±1/2. Every transverse excitation is retained.
Scope: Proved for the given free charged Green quantization on the existing whole orientation cover. No additional field-species doubling,no mixture of independent complex states,no identification with P1 kernel or previous W8 vacuum. Cover trace period2 is not the global relative C12 cover result. Jaffe/Ritter is not applied with unchecked boundary hypotheses;the concrete proof is direct.
Required premises and original source excerpts
- Given free Green quantization of the flat Pin Dirac operator on its NS cover
Given is the free charged Gaussian field realization with the Green operator of the concrete flat Dirac boundary family D=−i(sigma1 partial_x+sigma2 partial_w),w in[-1,1],sigma1 psi at boundary=b psi,b=±1. Original Pinminus c=±i forces psi(x+2,w)=−psi(x,w) on the orientation cover. The tested Euclidean kernel belongs to L=i sigma1 D=partial_x+H,H=i sigma3 partial_w. This Green quantization and x as Euclidean time are named premises,not identified with the D spectral sea,the old quarter Hardy state or original P1 kernel.
premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover - 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.
premise:typed-source-structures
- experiments/theory-contracts/original-admissible-source-closure-20261025/NS-COVER-FULL-DIRAC-RP.txt, lines 1–186
Source SHA256: a18c7589ac87b0ea875af7a2a46790989c80c836369b9ee001b0417dda6ab154
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/original-admissible-source-closure-20261025/NS-COVER-GREEN-RP-INDEPENDENT-REVIEW.txt, lines 1–199
Source SHA256: 3579d118cdaf036aed24ab5ee20bdc2889023a49b9a44efaebc3dce14b46d01a
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/original-admissible-source-closure-20261025/check_ns_cover_dirac_rp.py, lines 1–121
Source SHA256: 2eaf564d895d70abf3a2974268de7b178f05196ea784515babcf650e5fa25b21
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/original-admissible-source-closure-20261025/ns-cover-dirac-rp-results.json, lines 1–135
Source SHA256: d1844d0c16d7868f38ab2342f3568b53d1d59c3fa56552a0db33815127101862
bounded-excerpt · current-at-snapshot