Scoped exclusion
A single fixed Pinminus Green kernel fails the neutral OS word
In the question: Common clock sectors, quartic geometry and operational reconstruction
Only this given charged Gaussian Green realization and standard charge-exchanging word reflection on a single fixed Pinminus sector. No P1 no-go,no exclusion of the positive NS cover source or arbitrary other kernels. Sector exchange prevents transporting the neutral witness as an isolated OS square in the cover state.
Read the exact result, assumptions and evidence
Result
The actual invariant simple transverse branch has D0=−i b partial_x,q=cb=±i. Its exact Green kernel Gq is q/(q−1) for0<s<1 and1/(q−1) for−1<s<0. The equivalent normalized one-mode trace has z=−q^−1 and omega(N)=1/(1−q)=(1±i)/2. The neutral number word is phase-independent under standard antilinear charge-exchanging word reflection. Its smeared positive-time OS square is not real. Thus the complete free Green realization in one fixed Pinminus sector is not RP. Linear Clifford reflection sends c to−c and is not an endomorphism there;K R_x as D-sea symmetry does not replace it.
Required assumptions
- 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.
- 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.
Original evidence
- MOBIUS-ZERO-MODE-RP-REVIEW.txt lines 1–177
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/MOBIUS-ZERO-MODE-RP-REVIEW.txt
3c9bab8a98ee6cf425ec52de0ad0fd2006701b56fa1f31cb40c0fead2f108752
- check_mobius_zero_mode_rp.py lines 1–101
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/check_mobius_zero_mode_rp.py
9554a64c350e9b444c52093f328e0688c29ab968e5adbc934f1e562747c62b70
- mobius-zero-mode-rp-results.json lines 1–35
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/mobius-zero-mode-rp-results.json
f15582e3e800492c208cd7dee83fefd2e81ed73603482c405dc65c8748d5f800
finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity