Established in scope
Full root product contains the normalized octic component
In the question: Common clock sectors, quartic geometry and operational reconstruction
Assumes the additional full E8 algebra; no exclusivity, executed projection or physical preparation. The classical invariant identity is not claimed as new. This extension is unnecessary for the original CAR mechanism.
Read the exact result, assumptions and evidence
Result
In the supplied E8 vertex closure, the phase-correct dual-root product has a full weight8 coefficient S8 with all22 oscillator partitions. Exactly <F8hat,S8>=sqrt140/56=sqrt35/28 and ||S8||²=15600. Actual polarization gives moments2,4,6 zero and moment8=(15/2)I8.
Required assumptions
- Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
- Original displayed J-equivariant root isometry
Use existing S=_SIMPLE and T=_TARGET_SIMPLE from cartan_source._glue_deck_character_certificate: O=T S^-1/sqrt2 maps actual Construction-A roots r/sqrt2 to original Chevalley roots r/2, preserving metric and J. This is the existing concrete map, not a newly fitted embedding; physical P1 selection stays separate.
Original evidence
- NATIVE-FOLDED-OCTIC-ORIGIN.txt lines 145–189
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-octic-seam-origin-20261025/NATIVE-FOLDED-OCTIC-ORIGIN.txt
c694cb1cee45e65145fdbf144925e45178a7d0ee29adb7142400a00a970e259b
- native_folded_octic_origin_results.json lines 185–199
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-octic-seam-origin-20261025/native_folded_octic_origin_results.json
2387a356a4da818ff4dd455475e35c5718e0c4b5823ab3c4b703b1d163ed48d5
finding:full-root-ope-has-normalized-native-octic-component