Established in scope
Full free projector forces factorization with a commuting source
In the question: Common clock sectors, quartic geometry and operational reconstruction
Necessary theorem about the same joint state and specified algebras. Does not exclude every interaction or future entanglement. Full projection and commutation are not inferred from a thermal face or incomplete neutral data. In a finite full Slater block, commutation with its entire even part already suffices via rank1 support. Positive conditional mixtures need actual positive disintegration; complex eta weights are not one. The source identity presupposes an actual bilinear action/integration and is not a derivation from P1. Physical joint response remains open.
Read the exact result, assumptions and evidence
Result
The existing full CAR projection-covariance theorem gives a pure restriction omega_P. For b>=0 from a commuting algebra, phi_b(a)=omega(ab) is positive and dominated by ||b||omega_P; purity forces omega(ab)=omega_P(a)omega(b). All equal-time connected mixed responses of those algebras vanish. A positive mixture of conditional CAR states with full mean projector P consists almost everywhere of the same state. An actual original coupled source with nonzero mixed response therefore cannot have that full free reference projector; it needs its own joint response or a proved independent source sector. The correct conditional complex source identity retains K(phi), or its J derivatives.
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.
- Full projector covariance in a positive joint source
Conditional theorem: a positive normalized joint state has full projection covariance P on the actually fully realized CAR algebra. The further unital C* algebra commutes with this CAR algebra. These assumptions are a source contract to test, not already derived P1 data; one face or incomplete neutral measurements do not replace them.
Original evidence
- PROOF.txt lines 1–195
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/fermionic_source_type_20261029/PROOF.txt
46af047b5d8f80d7cfab5eb9f4aaac964f116b9e03fea63a99fc07ed2de35d68
- INDEPENDENT-REVIEW.txt lines 1–37
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/fermionic_source_type_20261029/INDEPENDENT-REVIEW.txt
a6067a969660c06520b119fb26c06743b81168810ae98f768570ae2e577cd306
- PROJECTOR-STATE-RIGIDITY.txt lines 1–173
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/PROJECTOR-STATE-RIGIDITY.txt
2e14e8875c263d71bd6bda61d005461cb718bdf30fdf34a6312db53167cd80c6
finding:full-free-projector-forces-joint-commuting-source-factorization