Established in scope
Entire reflected quadratic regulator class decided by negative cross matrix
In the question: Automated construction of operator maps and sources
Complete universal preservation theorem only for specified bosonic two-half class. Known RP-cone mathematics specialized to original IR caller. Not necessary for every regulator of one fixed source, not full P1 countermodel or proof of original S_adm RP.18 controls together with source flow; analytic class proof separate. No new physical model optimization.
Read the exact result, assumptions and evidence
Result
In specified finite class exp(-phi R phi/2) preserves every original positive RP measure iff C is negative semidefinite. Bounded reflected feature expansion gives sufficiency; RP product Gaussian with Gcross=((I+A+C)^-1-(I+A-C)^-1)/2 and inversion order gives necessity, without simultaneous diagonalization. Cone closed under addition; R_k to zero recovers original source by finite dominated convergence. Exact RP baseline C0=[[1,1/2],[1/2,1]],R=ones,P_adm=I gives reflected response-1/16 despite ordinary positivity and structural commutation. Existing generic spectral-weight exclusion is reused, not recounted as new proof.
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.
- Finite reflected positive quadratic IR regulator class
Two real bosonic halves with no fixed-plane fields, reflection swaps them. Real symmetric A,C and PSD R=[[A,C],[C,A]]. Universal preservation over all finite positive RP original measures; no silent extension to complex/graded fermionic cases. A fixed original source can admit additional regulators. IR regulator is not a physical selector.
Original evidence
- FULL-SOURCE-REGULATOR-PROOF.txt lines 104–175
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FULL-SOURCE-REGULATOR-PROOF.txt
589a9054dd0af97934ff572ad3a5e1b18d8a0e3ed9cfb848f450b509dbf48df0
- check_full_source_regulator.py lines 1–85
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_full_source_regulator.py
694718775b75428ce173a281c688881d9e39176c37b217bcfa52a868ae3e2dae
- FULL-SOURCE-REGULATOR.json lines 1–102
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FULL-SOURCE-REGULATOR.json
6cfd1b8664627bd3cd8e036c1b542383fc66ca98997101b554a0f294fe4b0f90
finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source