Established in scope
Actual native-four Galois clock and one marked representation orbit
In the question: Historical: common source, state and event selection
Explicit operator identification and one logical equivalence class, not six independent physical options. A common native-four/P1 clock continuation and the twenty-lift of a specified coherent R polynomial are not thereby derived.
Read the exact result, assumptions and evidence
Result
For each of the six remaining F20 representatives actual native C,G satisfy C^5=G^4=I and GCG^-1=C^2. Simultaneous intertwiners to the original v419 carrier have solution dimension1 and rank4. The six representatives form ONE orbit of the existing logical stabilizer, already S2×C3 acts regularly. R5 is not a native group word by an exact centralizer test; the compiler clock instead maps to an order3 operator on the quartic code. The canonical cyclotomic trace metric is carried isometrically into the native four-metric by normalized intertwiners, leaving an overall phase.
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.
- Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Original evidence
- PROOF.md lines 100–110
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/PROOF.md
dd94d9a85e61618bfabbfd462e0fca9f8ecc58e5b961c09a9c8656886793b5e8
- operator_audit.md lines 127–220
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/operator_audit.md
f1849345563b8d81cd3861a5a5eaa96f1355ff7d5d55bdbc00e73ab90b7b64e5
- galois_metric_results.json lines 1–63
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/galois_metric_results.json
910c47bbe4c54b7d521b24e25dee57581353c0f6926c41c99a1da21e4ed97d11
finding:native-galois-intertwiner-unique-logical-marked-orbit