Read the result in its research context.

Result

The already proved whole transport J=Swap tensor j gives a uniquely specified reverse comparison B=Gq J*. Its same-face blocks are precisely the original smoothing cross-face coherence Xq followed by geometric return. The entire G/W kernel composition retains endpoints, half-forms, metrics and adjoint slots. No reverse kernel or state is fitted. The q/p field labels refer to the same source with a non-diagonal redundant CAR metric, not independent duplicated species.

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.

• 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.

Original evidence

• 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

• F5-QP-REVERSE-HOM-KERNEL-REVIEW.txt lines 201–227

  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

finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel