Conditional result
Weighted clock index reduces to the full chiral trace under commutation assumptions
In the question: Automated construction of operator maps and sources
Finite matrix class and named independent original sources; no general P1 index theorem, automatic P1/neutrino relation, prior physical selection of λ or self-duality derived from P1.
Read the exact result, assumptions and evidence
Result
For finite-dimensional γ=γ*=γ⁻¹ and V=V* with {γ,V}=0, and λ=λ* with [λ,γ]=[λ,V]=0, tr_ker(V)(λγ)=tr(λγ), since V pairs opposite chiralities with the same λ charge off its kernel. Periodicity, actual integral charge normalization, and Fermi/sea covariance remain additional clock and relative-determinant conditions. C=I/2 shows the missing general covariance assumption in the supplied index claim. Full-fiber λ=I index zero and quarter variance 1/(8π) at the self-dual theta function are already in the record; original selection of the quarter and β=4π is a new hypothesis to test.
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.
Original evidence
- SYNTHESE-2026-11-02-QUELLENPFAD.md lines 1–45
Source checked at this snapshot
Original location and fingerprint
docs/research/fundamental-plan/SYNTHESE-2026-11-02-QUELLENPFAD.md
d5193c3b8281bc612998ad0f05ee0b2142a67adbb736ade4c6ef00d53acee27c
finding:weighted-index-trace-and-selfdual-theta-require-original-selection