Established in scope
Joint block algebra, normalizer and intrinsic2+3 orbit
In the question: Historical: common source, state and event selection
No unique physical3+2 marking, no spacetime dimension29 and no physical5/4 normalization derived from dimension ratios. The associative-algebra normalizer is larger than the group normalizer. The existing physical mark is therefore not simply an as-yet-unselected member of those15 responses.
Read the exact result, assumptions and evidence
Result
The actual4-,5-,20-representations are distinct irreducibles. Their group algebra is M4+M5+M20 with commutant C^3 and group normalizer U(1)^3 rho(G31). The algebra quotient preserves these word representations but is not tensor-closed by itself. The15 original matching involutions yield a canonical transitive family of rank2 projectors with rank3 complements. Joint group-invariant states retain free positive block weights. The decisive exact comparison nevertheless gives P2 != Q_t for ALL15 projectors of the native response orbit: color-S3 commutation excludes this identification structurally.
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 58–98
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/PROOF.md
dd94d9a85e61618bfabbfd462e0fca9f8ecc58e5b961c09a9c8656886793b5e8
- operator_audit.md lines 87–125
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/operator_audit.md
f1849345563b8d81cd3861a5a5eaa96f1355ff7d5d55bdbc00e73ab90b7b64e5
finding:joint-native-algebra-normalizer-and-response-orbit