Established in scope
Whole cubic Gram differential retains Hardy phase and mixed resonance
In the question: Automated construction of operator maps and sources
Exact response of the existing uncompressed cubic block to a declared direction. Original EM5 requires actual Pstr commutation and a gap norm bound; it does not select this V_adm. Conditional length threshold is not a derived physical length. PositiveC6 block is not physical seam projection, nor P0 the structural projector. Finite response differs from its derivative, with22.65% relative control error near the bound. No physical source insertion, CP or time origin is claimed. Preserve prior bareK3 reality and actual wedge consumer.
Read the exact result, assumptions and evidence
Result
The complete inverse-Gram-square-root derivative is given exactly by its two spectral projectors, including cross blocks. For declared V=-kappa M0P0 the fixed-line coefficient is exactly Re(kappa)/(3g²), but mixed operator response diverges as |kappa|/(sqrt6 g), not a bounded remainder. Actual Hardy phase gives rank3, Frobenius17.9916735432 and fixed-line amplitude share0.890301077, squared share0.792636008. The quoted99.3% applies only to an artificially real direction. Independent root two-projector calculation confirms the full eigenvector divided-difference result.
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.
- 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 hard-holonomy contract with pure closed-triangle trace
Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.
- Original closed real delta transport action
Original EM3 action on its invertible closed epsilon0 branch with real delta, fixed U6 and all three cusps. Use actual common Gbase dictionary U6=diag(M0,-M0) and fixed marked P0. This is not a newly chosen independently projected physical variation.
- Declared Hardy direction for the original cubic Gram differential
Comparison at the original unregulated positive cubic block with declared V=-kappa M0P0, actual y/delta and already calculated Hardy phase. This is not a claim that the original physical source selects this whole V_adm. Preserve actual Pstr commutation and other C6 branches at the original source contract.
Original evidence
- CLAUDE46-GRAM-RESPONSE-AND-VADM-REVIEW.txt lines 1–150
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE46-GRAM-RESPONSE-AND-VADM-REVIEW.txt
6df3e624f781d6884de0c8c2c2ad09cd9f0aa3572048e9057ff2a4f16a89dbed
- CLAUDE46-GRAM-RESPONSE-AND-VADM-REVIEW.txt lines 151–247
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE46-GRAM-RESPONSE-AND-VADM-REVIEW.txt
6df3e624f781d6884de0c8c2c2ad09cd9f0aa3572048e9057ff2a4f16a89dbed
- ROOT-FULL-GRAM-RESPONSE-REVIEW.txt lines 1–49
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-FULL-GRAM-RESPONSE-REVIEW.txt
bdf5b023a617154c9c7766c84664cadd9671dd03a37ebf0879a731b93aa7f3e8
- ROOT-TWO-PROJECTOR-GRAM-RESPONSE-CHECK.json lines 1–16
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-TWO-PROJECTOR-GRAM-RESPONSE-CHECK.json
ac4ad2f6d36eb63f448f22892b453edd5a17087b5654905ab2d8e5d3803293a1
- claude46-gram-response-results.json lines 1–77
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/claude46-gram-response-results.json
5fb8567b9195a973d0b65a24bf71d25e5127e05a4d754aee699d81191c1ee896
- 005-source.tex lines 1–100
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/005-source.tex
786d2619e775775d70adf177794138485b261968042a880b2f0f617bb0111814
- 003-subsection-discrete-phase-operator-and-transport-grammar.tex lines 90–125
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/003-subsection-discrete-phase-operator-and-transport-grammar.tex
00a2cf1b249b77280dbbf6dfb41c91c77e08aa63e0f30b682d1a8a621f3dd7ec
- SPINE-ORIGINAL-PQ-FOLD-KERNEL-ADDENDUM.txt lines 1–143
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SPINE-ORIGINAL-PQ-FOLD-KERNEL-ADDENDUM.txt
d98da73f0023e1de696a31874d73b1df547564cec70205c07e5a54f3e0dc0fc5
finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance