Established in scope
One native representation forces the actual quartic code and erasure action
In the question: Historical: common source, state and event selection
Shared mathematical cause within the given core. The physical symmetric rule, origin of the core data, and an E8-current/fermion identification are not derived.
Read the exact result, assumptions and evidence
Result
P64 is characteristic as O2(G31). Fix_P64(Sym^4 V4) is exactly the actual five-code; the original codeword sums give its real intertwiner rather than a fitted embedding. The existing erasure intertwiner forces rho20(g)=rho5(g) tensor bar(rho4(g)) for the same words. The full fourth tensor power has Pauli fixed rank16, whereas the symmetric fourth power has rank5.
Required assumptions
- Actual native G31 event representation
Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round.
- Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
Original evidence
- PROOF.md lines 11–56
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/PROOF.md
dd94d9a85e61618bfabbfd462e0fca9f8ecc58e5b961c09a9c8656886793b5e8
- operator_audit.md lines 1–85
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/operator_audit.md
f1849345563b8d81cd3861a5a5eaa96f1355ff7d5d55bdbc00e73ab90b7b64e5
finding:native-symmetric-quartic-erasure-common-object