Established in scope
Full projection covariance and positivity force all CAR words
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact infinite CAR-state theorem under actual full projection covariance,not a new general CAR theorem and requiring no extra Gaussian premise. GNS uniqueness gives no implementability in an arbitrarily prechosen old Fock representation. A geometric Cauchy projection is not automatically presented as a physical covariance;P1 and its real joint field carrier remain to be identified.
Read the exact result, assumptions and evidence
Result
For an arbitrary positive CAR state with full covariance C=P=P*=P²,GNS zero norms force a(f)Omega=0 onkerP and a*(f)Omega=0 onranP. CAR normal ordering uniquely determines all finite words and hence the full state as the pure Fock/Slater state omegaP. Quasifreeness,gauge invariance and zero anomalous pairs follow instead of being assumed. This is the charged application of Araki1970 Lemma4.3. A positive ensemble mean with projection covariance P forces that same covariance and state almost surely;complex weights are outside this ensemble argument.
Required assumptions
- Test a positive joint CAR source against the full geometric projection
Consider an arbitrary normalized positive state on the specified joint charged two-face CAR algebra,without assuming quasifreeness or U1 invariance. The geometric target is the existing closed chiral annulus graph P_A with both marked faces,W=1/2 and original NS B_Sigma. Actual identity C_source=P_A is an explicit condition of the uniqueness theorem and an unresolved P1 source equation,not a fact inferred from geometry or RP. A finite error test applies only on a genuinely P_A reducing CAR block. Complete Dirac vector source,OS Padm and physical time are not identified with this chiral scalar target. No freely chosen purification supplies missing physical cross correlations.
- 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
- 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
- check_projector_state_rigidity.py lines 1–107
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/check_projector_state_rigidity.py
8439a30ad767f138f9269aa2bc6beca1f2d3d7088e92862bcd76fbf40d5a7c16
- projector_state_rigidity_results.json lines 1–22
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/projector_state_rigidity_results.json
40737f35ef6967cdfa2742f5f79d722f677a1adbb5a3770b9b0ee12bd190fe75
- PROJECTOR-STATE-REVIEW.txt lines 1–72
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/PROJECTOR-STATE-REVIEW.txt
4b9abbcb3b3f0dcf9a99a4ec09640b28aaa938d1f78b47cc409cc89f81aaf934
finding:full-projector-covariance-and-positivity-force-all-car-words