TFPT scientific source excerpt Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/two_face_source_20261029/REVIEW.txt Original file SHA-256: 1e21acc2b106d5b7d1895a5de57c91b70c2b239144cfb7cb61ffa14f26147a75 Inclusive original lines: 1-112 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000001 | Independent review: existing two-face source and typed reflections 000002 | 29 October 2026 000003 | 000004 | Verdict: ACCEPTED IN THE STATED GIVEN-SOURCE SCOPE. 000005 | 000006 | Read check_two_face_source.py in full, then executed it directly with 000007 | python3 and independently with python3 -B -OO. Both exited 0 and produced 000008 | the same result. The source test uses two positive NS modes pi and 3pi, 000009 | with z=exp(-pi/12), W=1/2 and beta=1. Its four-dimensional exterior Fock 000010 | space must not be described as four distinct one-particle source modes. 000011 | 000012 | The checker correctly reuses the old source lift, graph projection and 000013 | graded double implementations. The two sewing null relations, all four 000014 | covariance blocks, midpoint Green values, graded odd partner, occupation 000015 | hole image, neutral current orientation, noncommuting neutral insertions, 000016 | bounded cross Gram and ordered reflected histories are checked on the 000017 | same thermal source. Finite matrices are expressly not claimed to realize 000018 | a nonzero central current CCR. The +/- mode graph-reflection control is 000019 | separate from the two positive-mode thermal control. 000020 | 000021 | Independent analytic sign review 000022 | 000023 | For J_HS X=X*, J_HS L_A J_HS=R_(A*) is conjugate-linear multiplicative. 000024 | With W_L(f)=R_(W(f)*), right multiplication reverses products, so W_L has 000025 | the opposite Weyl cocycle. Neutral even partners need no Klein factor. 000026 | The odd CAR partner retains the original whole-GNS parity Gamma. For a 000027 | Hermitian finite-mode quadratic current with the displayed subtraction, 000028 | j_L(A)=-R_(j(A)) and J n_R J=I-n_L are correct, including complex 000029 | Hermitian off-diagonal A such as sigma_y. 000030 | 000031 | For any normal density rho, not necessarily Gaussian, 000032 | Tr(sqrt(rho) W_i* sqrt(rho) W_j) 000033 | is the Hilbert-Schmidt Gram of rho^(1/4) W_i rho^(1/4). 000034 | Boundedness of W_i and Schatten Holder make these vectors Hilbert-Schmidt. 000035 | This establishes positivity of the joint bounded pairing without asserting 000036 | that an arbitrary density has the free projector occupation covariance. 000037 | 000038 | For H>=0 and Z_beta=Tr exp(-beta H)(-t,s). Its ordinary spatial 000053 | profile map is -I on reflected neutral Weyls, not minus spatial reflection. 000054 | The previous single-chiral spatial-reflection obstruction therefore does 000055 | not exclude this already existing elliptic OS source. The independently 000056 | derived right-current orientation does not identify a geometric P1 second 000057 | face with the modular partner. 000058 | 000059 | This review accepts the analytic theorem supplied with the review request. 000060 | At this stage PROOF.txt was not yet present in the output directory; no 000061 | claim is made to have reviewed a later saved exposition. No physical P1 000062 | measure, field coupling, source map, physical time or full TFPT completion 000063 | is proved by the finite checks or by these general HS identities. 000064 | 000065 | SHA256: 000066 | check_two_face_source.py 000067 | c5075473da6daeb5284cb7d4f16fa4f6c82d53a88945b856c2a8fa348c1549ce 000068 | two-face-source-results.json 000069 | e862327f829aa1721e505865ee785657c4c8a4bf08a07a0c89ca9453cf284f98 000070 | 000071 | Only this review was added. No original source or ledger was changed. 000072 | 000073 | Completed saved-text review 000074 | 000075 | Subsequently read the now saved PROOF.txt and STAND-EINFACH-DE.md in full. 000076 | This completed review supersedes the earlier interim note about PROOF.txt 000077 | not yet being present. No additional checker run was needed or performed. 000078 | 000079 | The bounded extension in PROOF.txt is valid under its explicit premise 000080 | that the neutral current Weyls already belong to the given source von 000081 | Neumann algebra. Kaplansky density supplies uniformly bounded strong-star 000082 | approximating nets from the generating even CAR star algebra. All heat 000083 | durations in a strictly interior history are positive. Each corresponding 000084 | heat operator lies in its stated finite Schatten class. Approximate these 000085 | heat operators by finite-rank operators in those Schatten norms. With 000086 | finite-rank factors, bounded strong-star convergence of the insertions 000087 | gives norm convergence of the history; Schatten Holder bounds the remaining 000088 | tails uniformly. Thus K_F converges in Hilbert-Schmidt norm and 000089 | Tr(K_F* K_G)/Z converges. The same reasoning with rho^(1/4) in Schatten4 000090 | gives Hilbert-Schmidt convergence of the bounded joint-pairing vectors. 000091 | No norm approximation of a von Neumann Weyl by CAR polynomials is asserted. 000092 | 000093 | The saved proof retains every intermediate heat factor, distinguishes 000094 | time ordering from an ordinary unordered opposite-time product, and 000095 | explicitly does not assume bounded imaginary-time conjugates. It limits 000096 | the bounded operator theorem to neutral even insertions and does not 000097 | extend it to odd Schwinger words without their graded conventions. 000098 | 000099 | The geometric Schottky time reflection and the antiunitary modular 000100 | conjugation have distinct stated product types. The particle-hole formula 000101 | belongs to the latter partner construction. A small ambiguity in the 000102 | simple-language text was pointed out: wording about a particle-hole change 000103 | in a generic reflection could blend these two types. Read back the corrected 000104 | text: it now explicitly refers to the correspondence of the representation 000105 | sides and distinguishes it from geometric time reflection. This is 000106 | consistent with the accepted proof. 000107 | 000108 | No scientific overclaim was found in PROOF.txt. Its P1 field/sewing map, 000109 | primitive source measure and physical time identification remain open. 000110 | The saved all-mode conclusions concern the given source representation; 000111 | the two-mode computation is not used as their proof. Final review verdict: 000112 | ACCEPTED WITH THE STATED GIVEN-SOURCE AND NORMAL-REPRESENTATION PREMISES.