2253 - Spectral Pinching Is a Mathematical Flavor Selector but Not a Physical One (WP54)
The (H_u)-spectral conditional expectation
is the first tested candidate with a proper quotient-level image. Exact matrix algebra proves it is unital, positive, idempotent, and covariant under the full common-left weak-basis action. Its image is the commutant of (H_u).
Thus it is a genuine mathematical selector on physical16, not a chart
rigidifier. But its fixed locus has ([H_u,H_d]=0), hence trivial physical CKM
mixing and (J=0) for nondegenerate spectra. One nonzero off-diagonal entry of
(H_d) in the up spectral frame is the smallest exact falsifier; observed CKM
mixing and CP violation exclude the locus.
More importantly, the declared flavor source supplies the Gram spectral data but no action, channel, threshold process, or instrument that applies this pinching. Imposing its fixed locus would insert selection by hand. The result therefore realizes the hostile distinction: mathematical distinction and a proper image do not establish a physical selector.
Artifacts:
research/flavor/flavor-spectral-conditional-expectation.mdresearch/flavor/checkers/wp54_spectral_conditional_expectation.pyresearch/flavor/results/wp54_spectral_conditional_expectation.json- updated
research/flavor/flavor-programme-index.md
Verification: exact SymPy checker, 6/6 gates, exit 0. Epistemic admission
ev-000000003122-ed6ce6b7-1f26-45ca-9c95-0c9e83b7c229.