Established in scope
E8 current group conditionally determines the P sign
In the question: Constructive seam search: operators, state and source compatibility
Only the stipulated even E8 lift; full odd-Z8 sectors remain additional. No transfer of the different (9,1) source. The ±i path orientation is not selected.
Read the exact result, assumptions and evidence
Result
In the supplied positive E8 module X=E_s commutes with SU8 root currents because alpha.s=Q(alpha)=0; oscillators are fixed. C=Z_e0 R gives CXC^-1=±iX and P sign+1. This is a direct global operator bridge, not X=Y(s).
Required assumptions
- Stipulated even E8 completion with actual Klein signs
Assume the E8 extension of the even D8 CAR sector constructed in seam-joint-ward-state, with original ordered cocycle, retained quarter transition and explicit P-lift convention. An ordinary-local inclusion of odd CAR fields is not assumed.
- 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.
Original evidence
- PROOF.md lines 29–178
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-constructive-search-20261015/continuation/current_group/PROOF.md
f43ab51961cc19fb39dc2feab427463391d38962c4ba58276056787f3cae563a
finding:constructive-current-group-selects-positive-p-lift