Established in scope
Finite source modular mixing preserves integrated native Cartan matrices
In the question: Common clock sectors, quartic geometry and operational reconstruction
Finitely tested modular one-particle response. No continuum reconstruction,pointwise quartic-field invariance,physical-time identification,or F_a to delta D_rel map.
Read the exact result, assumptions and evidence
Result
The actual source class was restricted on rings64 and128 for both quarter phases to eight equally spaced arcs. h=log((1-C)/C) has nonzero interarc transfers but numerically commutes with all four actual integrated native Cartan matrices. Removing interarc covariance removes the witness while changing the state. Normal and-OO produce byte-identical results.
Required assumptions
- Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
- Original displayed J-equivariant root isometry
Use existing S=_SIMPLE and T=_TARGET_SIMPLE from cartan_source._glue_deck_character_certificate: O=T S^-1/sqrt2 maps actual Construction-A roots r/sqrt2 to original Chevalley roots r/2, preserving metric and J. This is the existing concrete map, not a newly fitted embedding; physical P1 selection stays separate.
- Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
- 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.
Original evidence
- PROOF.txt lines 86–124
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/PROOF.txt
17e05220f16d70049c949cfe1b9639fd27defcf196d106869e8b8673ae0903a6
- results.json lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/results.json
aa418563617de5dd2d66575792afb7488f4dc4d1d4b94f7d1c4d9785d44a75df
- results.json lines 201–239
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/results.json
aa418563617de5dd2d66575792afb7488f4dc4d1d4b94f7d1c4d9785d44a75df
- REVIEW.txt lines 1–9
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/REVIEW.txt
ba59b19746bf5188f3f10e6b6863aa017273fe1829ab0e6d3ef71b128afac9dc
finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan