Established in scope
Quantitative joint positive two-face bound
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
For Pbar=integral P_H dmu and m=Tr(L P_H L), Tr L(Pbar-Pbar²)L>=Var_mu(m)/6. Under the additional named R054 fiber premises Delta_O=24Var_mu(m), giving the same lower bound Delta_O/144. Var(m)>0 excludes projection of Pbar; a pure primitive state before H integration remains possible.
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.
- Positive normalized mixture of covariance contractions
For the quantitative two-face defect mu is positive normalized, each conditional covariance P_H is self-adjoint with 0<=P_H<=1 on the same CAR space, and L is the fixed rank-six projector. Pbar uses precisely these weights.
- 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.
Original evidence
- JOINT-HIGGS-TWOFACE-SOURCE-CONSTRAINT-20261102.txt lines 15–44
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-positive-twoface-fourword-defect-bound