Established in scope
Positive finite-word state extension
In the question: Constructive seam search: operators, state and source compatibility
No complete concrete Finsupp kernel instantiation, physical state selection or automatic K-invariance of the bare shift algebra.
Read the exact result, assumptions and evidence
Result
E0(y*y)=a0*a0+phi^-1(a1*a1) proves positivity of omega0 o E0. General algebra/star/positivity and dual uniqueness theorems are Lean-checked; concrete finite-lattice transfer is analytically proved.
Required assumptions
- Fixed CAR source and adjoined half sector
Ordered eight-channel cocycle, s=(1/2)^8, Q, quarter phase and K_alpha=N+|p|²/2+delta_alpha.p are supplied; alpha=1/4,3/4. Parity equivalence is in the global operator envelope without a separately marked physical X. Neither source nor extension is derived from P1/P2.
- Positive base functional and explicit observable algebra
For finite crossed words omega0 is positive; dual Z2 invariance is additionally required for unique algebraic extension. Comparing physical densities must retain the actual Cartan observables and the common normal ground space of supplied K.
Original evidence
- SOURCE_BRIDGE.md lines 1–106
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-constructive-search-20261015/continuation/state_expectation/SOURCE_BRIDGE.md
501a88a57ad0bc00e4207533e0fd90760df8543135a3402ebbe40dd4c9313664
finding:constructive-positive-state-extension