Scoped exclusion
Fully descended covariant reverse kernel removes rho form channel
In the question: Automated construction of operator maps and sources
Exclude only the specified fully descended covariant rho insertion with this actual kernel. Marked open arcs, actual additional original reader legs or a different sewing consumer change the premise. No automatic identification of native internal Zc with this descent and no general physical CP exclusion. Retain the positive inverse-character/Hom pairing results without counting their factors a second time.
Read the exact result, assumptions and evidence
Result
Original normalized lifts calibrate c=R_V squared to the entire Hom action, not a bare geometric character counted twice. On the fully descended source, a reader covariant for this same total action compresses every nontrivial character to zero. Thus the rho form channel is removed by the canonical equivariant reverse kernel. The invariant ranks are two off-diagonal and three in the full family; the whole source does not vanish.
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.
Original evidence
- F5-QP-REVERSE-HOM-KERNEL-REVIEW.txt lines 137–200
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
finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel