Established in scope
Complete four/five generators determine the60 native rates
In the question: Historical: common source, state and event selection
Unique continuation within exactly this menu, not selection of that menu, complete generators or their physical time scale from P1. A few populations or a single finite-time channel are weaker inputs.
Read the exact result, assumptions and evidence
Result
The native rate map has rank55 on the four and15 on the five, jointly rank60 with60 columns. Its joint nullity is0: fixing complete generators excludes a hidden twenty-rate twin inside the60-reflection Poisson menu. The old coherent S3 sign twin belongs to a different event menu and additionally violates the actual branchwise erasure contract, with trace distance1/4 for an explicit input.
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.
- Complete four/five generators with exactly60 reflection jumps
Consider only Poisson generators sum_j lambda_j(Ad_rj-id) over the actual60 native reflections, with complete continuous-time four- and five-generators fixed. No extra Hamiltonians, coherent algebra events, or generators inferred uniquely from one finite-time channel.
Original evidence
- PROOF.md lines 112–128
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/PROOF.md
dd94d9a85e61618bfabbfd462e0fca9f8ecc58e5b961c09a9c8656886793b5e8
- operator_audit.md lines 190–220
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/operator_audit.md
f1849345563b8d81cd3861a5a5eaa96f1355ff7d5d55bdbc00e73ab90b7b64e5
finding:native-reflection-full-four-five-generators-rate-injectivity