Established in scope
Old scalar clutch separates bulk C0,boundary adjoint and product reflection
In the question: Automated construction of operator maps and sources
Actual old product collar with specified complex structures and theta-fixed R_geo. No general reflection no-go;additional original base pullbacks/fiber lifts can give different common operation and must be transported explicitly. Existing open-source reflection positivity,whole Cauchy graph and source state/time remain intact. Bulk adjoint,boundary CAR and geometric reflection are not interchangeable names. Correction rejects The reviewed first C0/U inference,not every physical P1 Real structure.
Read the exact result, assumptions and evidence
Result
Actual C0=i_old N is old-complex-linear and commutes with U=e^{i_oldθ}I. New antilinearity for Ical does not allow C0UC0=U*. Whole T chart clutch is diag(U,barU). Oriented T_faces conditions are v1=Uv0,w1=−Uw0. Bulk C0 preserves this closed kinetic domain;C_faces maps unitary clutch subspace to orthogonal complement. Actual theta-fixed product reflection instead transports whole domain to U^-1. SF+1 alone does not assign four original boundary pieces to F5 faces. Reuse old NS/quarter dictionary;The reviewed mixed1/4,3/4 mass toy does not replace actual same-Aα source.
Required assumptions
- Geometric Clifford boundary with explicit changed complex structure
Assume the existing free product class B=Gamma A or actual smooth tangential odd finite coefficient B_Phi=Z A-S Phi with total grading Z tensor gamma_F. Apply the standard Clifford boundary functor on the underlying real space with NEW complex structure Ical=i_old Gamma_tot and real structure C0=i_old gamma_n; the dual face has -C0. C0 is old-linear and new-antilinear,not identified with original charge J. This differs from full complex CAR quantization of both independent normal copies. State conclusions use the full graph as the actual quantum covariance in this functor. Its physical selection from P1/P2 is not presumed proved; Phi is a fixed classical background. Keep the fixed normal-independent product collar; a(theta) is smooth Hermitian and even,Phi(theta) smooth Hermitian and odd. No quantization of these bosonic backgrounds.
- Relative unit seam on explicitly assigned collar faces
In existing product collar,test original relative unit gluing v1=Uv0 on an explicitly assigned pair of labeled faces. Scalar block has h e_n=(n+α)e_n and U e_n=e_(n+1),α=1/4 or3/4. Actual original Γ±-to-face assignment,orientation and three-cabled spin trace map are not assumed derived.
- 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
- CLAUDE25-CLUTCH-REAL-TYPE-REVIEW.txt lines 1–100
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE25-CLUTCH-REAL-TYPE-REVIEW.txt
7cc827c6925676e8570d5279b33897050dc24efdce8bfa16dea3e3197ec19314
- CLAUDE25-CANDIDATE.txt lines 1–117
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE25-CANDIDATE.txt
5a7349f3040b85650865b152d4e8c13b54389e60a6fbb1435a6d6f9126bf2806
- PROOF.txt lines 20–140
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/PROOF.txt
708dad21942cc00dd56d3348eacee3f0d90ccfc53e3f4987e39ded00ddc70841
- FINITE-COUPLED.txt lines 14–100
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/FINITE-COUPLED.txt
61d3d524801aff0147d393c518ad554e3ab550271165e2000d9efbf613b90234
finding:old-complex-scalar-clutch-separates-c0-and-product-reflection