Established in scope
Concrete transverse force couples gradients and mixed Yukawa contact
In the question: New constructive routes to the original common field integration
New concrete derivation within the stated older geometric contract;known R032 S/T differences remain. No identification with every primitive S_adm realization or addition of distinct action conventions. The gradient test excludes automatic scalar closure of this component;cancellation by other parts would need proof. Primitive full contacts are not yet evaluated.
Read the exact result, assumptions and evidence
Result
In the printed constant-scale residue branch,the radial Higgs component is integral[chi0²u/(4π²)+|D_AH|²/(8π²)+u²/(4π²)+Ru/(48π²)],in addition to actual boundary/eta/rest derivatives. Profiles with equal u and different gradients distinguish this component;on the circle product chart the difference is h²k²/(4π). The original contact before fermion integration requires <x_j barpsi V_i psi>,gradient two-point,H four-point and the whole spectral/reference/eta force. The general operator spectral derivative and both reference roles are explicitly retained.
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.
- Printed constant-scale residue-action component
Older Gamma_grav=-6chi0²E_D+Gamma_D4 contract per WEIGHT:62-132 at fixed g,A,chi0;retain boundary/eta/remaining terms. Keep R032 reference/operator differences and primitive Sspec distinct.
Original evidence
- transverse-whole-force-and-first-mixed-contact.txt lines 1–89
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-paper-source-reconciliation-20261102/hypotheses_20261105E/fieldint_hypotheses1/transverse-whole-force-and-first-mixed-contact.txt
2da2e34285c1b794b140f50f39a0637810f3058d7c7c7938abec687eacff137a
- WEIGHT.txt lines 62–132
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/WEIGHT.txt
7857f9185fc245b3de23789bcf1020b0b88e64dfd814d6ba71004e7d185fd345
- REFERENCE.txt lines 89–156
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/REFERENCE.txt
9f99952b6a75c28d65de9de9d45d2c409ac6135d2b82f39ba4f4bee35620e328
- ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt lines 49–128
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt
13e79f2be052ca918fd2be8faf8cf6f1669fc3ad535ccf9a3fdff5b7c0b1b3c5
finding:hyp20261105e-transverse-force-couples-gradients-and-yukawa-contact