Established in scope
Linear mixed-source identity without positivity
In the question: Automated construction of operator maps and sources
Only the specified R096 branch under its jointly required premises. No derived physical Higgs measure, general H(x) field theory or P1 source completion.
Read the exact result, assumptions and evidence
Result
The conditional identities <O>_H=24m(H)^2 and <N>_H=3m(H) give Z[O]=8Z[mN] with the same integrable unnormalized weights. Positivity is unnecessary for this branch. Actual origin of the mixed insertion in the original solver remains open.
Required assumptions
- Same constant Higgs and two-face carrier
R096 compares the same original constant Higgs parameter on the same actual two-face CAR carrier and fixed source caller. Face labels are not internal chiral L/R labels. This is a conditional source comparison, not derivation of the primitive P1 identification.
- Actual R054 color-symmetric quasifree fibers
The four-word connection uses the actual constant color-symmetric conditionally quasifree R054 fermion fibers on the same carrier: <O>_H=24m(H)^2 and <N>_H=3m(H). The averaged source is not assumed quasifree.
- Identical integrable unnormalized weights and insertions
The linear identity Z[O]=8Z[mN] uses identical integrable unnormalized weights and conditional fiber values on both sides. Positivity or finite complex normalization is not assumed for this linear statement. Physical use still requires deriving the mixed insertion from the original alphabet.
Original evidence
- JOINT-HIGGS-TWOFACE-SOURCE-CONSTRAINT-20261102.txt lines 46–62
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/JOINT-HIGGS-TWOFACE-SOURCE-CONSTRAINT-20261102.txt
db30b33db3c1d4528c65e0ffb6951ef1276710b5958afa10f06a04990c6dbd33
finding:r096-unnormalized-mixed-source-linear-identity