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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

Canonical Spin2 lift carries the whole annulus source with reversed time

In the question: Automated construction of operator maps and sources

A complete image-source map for the given original F5 family, without claiming physical P1 selection. Constant-normal graph formulas retain their stated scope; general normal-dependent data are transported as existing Cauchy data. Distinguish this time-reversing linear geometric lift from the earlier linear Kswap plus-time map without face exchange and The reviewed antilinear plus-time face map. No identification of circle, modular and physical time.

Read the exact result, assumptions and evidence

Result

The existing collar Clifford product is i_old Z. The pure geometric half-turn, both coordinate inversions and endpoint exchange transport the entire given collar operator, oriented real structure, four field/adjoint slots, full graph covariance and CAR state. In the charged chart its generator relation is T hq T^-1=−hp, so the actual circle parameter reverses. This OLD/NEW linear map squares to minus identity and needs no particle swap or independently fitted p coefficient.

Required assumptions

  • 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.

  • Complete data of both product-collar faces

    A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.

  • 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.

  • Actual full v252 gauge lift and original P2 comparison

    Given the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed.

  • Constant odd circle-source coefficient with existing sea and full boundary graph

    In the existing Clifford chart on L2(S1,K) with finite K let h0=(-i∂theta+alpha)gamma,alpha=1/4 or3/4,gamma*=gamma,gamma²=I. Supply constant selfadjoint odd Phi,{gamma,Phi}=0,and V=-i gamma Phi,h=h0+V on common periodic H1. Compare given CAR sea projectors P_-(h0),P_-(h) and complete pure two-face projector G_ell(h),ell>0,including crossings. This is the existing source class with classical background, not physical selection from P1 or quantization of dynamic bosons.

Original evidence

  • SPIN2-ANNULUS-WHOLE-SOURCE-REVIEW.txt lines 1–200

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SPIN2-ANNULUS-WHOLE-SOURCE-REVIEW.txt

    7f6b63b83be1e440fb870885f17a54aea799084be96c7b784d6f7c30774354f7

  • SPIN2-ANNULUS-WHOLE-SOURCE-REVIEW.txt lines 201–249

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SPIN2-ANNULUS-WHOLE-SOURCE-REVIEW.txt

    7f6b63b83be1e440fb870885f17a54aea799084be96c7b784d6f7c30774354f7

  • NATIVE-SPIN2-ANNULUS-PULLBACK-REVIEW.txt lines 1–164

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/NATIVE-SPIN2-ANNULUS-PULLBACK-REVIEW.txt

    2bdb013daad58a696abf36d62a6d8c9d4e7f314cc167013502e38a3f3298f6ed

  • ROOT-SPIN2-ANNULUS-CHECK.json lines 1–56

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPIN2-ANNULUS-CHECK.json

    fef9cb8cc0c9544063051719dfbd50b6617aeafb6c2b3afd98d3a7679a6c9b42

finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time