Established within the stated premises
Cover Green state and quarter Hardy vacuum require an actual time and state map
finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum
The full cover Green realization quantizes x as Euclidean time and has thermal covariance C=(1+exp(2H))^−1 on the w-section L2 space,with simple zero-mode value1/2. The D sea on L2(x,w) and old quarter Hardy state on the longitudinal circle are spectral projections. Mere covariance-preserving one-particle unitary identification is impossible:projections have only0,1 while C has1/2. Spaces and time coordinates must be transported. Enlarged purification or local net embedding is not excluded. v526 already assumes the chiral NS kernel and half algebra;its thermal success does not supply this original two-dimensional P1 identification.
Scope: Type check of the specified free sources. No ban on local state maps in enlarged cyclic spaces and no requirement of surjective full Hilbert-space identification. Same geometry or numerical temperature is not yet same field action and time.
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 - Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
premise:given-flat-mobius-dirac-boundary-family-and-full-sea - Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
premise:original-quarter-car-fold-current-subalgebra - 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 134–186
Source SHA256: a18c7589ac87b0ea875af7a2a46790989c80c836369b9ee001b0417dda6ab154
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/original-admissible-source-closure-20261025/NS-COVER-GREEN-RP-INDEPENDENT-REVIEW.txt, lines 130–199
Source SHA256: 3579d118cdaf036aed24ab5ee20bdc2889023a49b9a44efaebc3dce14b46d01a
bounded-excerpt · current-at-snapshot