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

Established in scope

Actual spin-product weight has canonical trace-class form pairing

In the question: Automated construction of operator maps and sources

Do not promote the unsandwiched singular multiplier to a bounded L2 operator. Retain full coefficient ends, actual deweighted jets and cancellations. Clifford type alone does not prove admissibility of arbitrary family Hom coefficients as original central one-forms. A finite form trace or derived response operator is not automatically the original full CAR composite or physical P1 selection.

Read the exact result, assumptions and evidence

Result

Original divisors give explicit mixed spin products and their actual Clifford type. Their base boundary coefficient has an integrable but non-L2 power singularity at all four ramification marks; source/target half-densities cancel in the multiplier. The exact surviving-channel L2 criterion retains deweighted jets. The original smoothing cross kernel still yields an absolutely convergent form pairing and canonical two-sided trace-class realization, with no new cutoff or kernel.

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.

  • Recovered genus2 cover with retained coefficients

    Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.

  • Unchanged A0* Fuchsian equation and actual C4 clock

    Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is 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

  • SPIN-PRODUCT-BOUNDARY-WEIGHT-REVIEW.txt lines 1–192

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SPIN-PRODUCT-BOUNDARY-WEIGHT-REVIEW.txt

    530b76ce72037cfb83ecb9bd04bb4472cfd47cfc494ef5ef29f3f05ed67e2fcc

  • F5-QP-REVERSE-HOM-KERNEL-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/F5-QP-REVERSE-HOM-KERNEL-REVIEW.txt

    07b31e029aef2bb4f51ffd3c65a6f659da29581c203df2101dd6556c4c7be2b9

  • ROOT-REVERSE-KERNEL-AND-C3-CHECK.json lines 1–14

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-REVERSE-KERNEL-AND-C3-CHECK.json

    b28ae1e183a2173fa38a818e4b2c438fa8780e1cba313e4c5429e4c57a6228f6

  • F5-REVERSE-HOM-FORM-TRACE-ADDENDUM.txt lines 1–62

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/F5-REVERSE-HOM-FORM-TRACE-ADDENDUM.txt

    a7517ca562a83a6647828721ae764e253c6d6f5e85fc6a2ee2aaed727b9bf067

finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing