Established in scope
Longitudinal reflection preserves the fixed Pin domain and full Dirac sea
In the question: Common clock sectors, quartic geometry and operational reconstruction
Concrete flat boundary family and its given D sea. State invariance does not imply Green reflection positivity;P1 locality,time and kernel need an actual map. Do not identify the three reflection types.
Read the exact result, assumptions and evidence
Result
Theta_x=K R_x is an antiunitary involution of the same(c,b) H1 domain for both c=±i and b=±1. Deck inversion compensates conjugation:bar(c)^−1=c. Exactly D Theta_x=Theta_x D;all real spectral functions,the complete D sea and quasifree vacuum ray are preserved. Block-diagonal antiunitary Fock implementation needs no PH mixing or HS repair. D time and longitudinal translations are reversed. Original operational Theta is distinct from normal deck lift and Calderon polarization;longitudinal reflection is a correctly typed candidate,not yet an identified P1 field map.
Required assumptions
- 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.
- Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
- 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
- P1-LONGITUDINAL-REFLECTION-REVIEW.txt lines 1–167
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/P1-LONGITUDINAL-REFLECTION-REVIEW.txt
135ba18d617bf9a5f88fae3bc9f96a51d3632985a4de9165de5bb0d231a5d8a2
- P1-LONGITUDINAL-REFLECTION-REVIEW.txt lines 168–210
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/P1-LONGITUDINAL-REFLECTION-REVIEW.txt
135ba18d617bf9a5f88fae3bc9f96a51d3632985a4de9165de5bb0d231a5d8a2
finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea