Established in scope
The same shift functional hides distinct ground states
In the question: Constructive seam search: operators, state and source compatibility
Normal ground densities in the supplied K space; no state selection from P1/P2. The ground space was already known.
Read the exact result, assumptions and evidence
Result
All dual-invariant ground mixtures diag(a,1-a) on {0,r0} give the same shift functional. Original Cartan vacuum values select |0><0|; additional Rc invariance requires I2/2. These two conditions conflict.
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
- SYNTHESIS.md lines 58–96
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-constructive-search-20261015/SYNTHESIS.md
d112d0054cd1558c0a64f8aebfaa98c942beab9e5688cc9704d31b15cdacb252
- PROOF.md lines 176–292
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-constructive-search-20261015/continuation/ground_state/PROOF.md
b32a58aa4c3f1a30a78d25c88d5931898842ce67b8f75101f8f8de53a6332922
finding:constructive-state-algebra-resolution-and-source-test