Established in scope
Decoder and same native clock polynomial act differently
In the question: Historical: common source, state and event selection
This excludes exactly the stated native polynomial continuation with the fixed decoder P220, not every coherent common-clock lift. The logical decoder does not prove original physical permission for the collective intervention.
Read the exact result, assumptions and evidence
Result
The existing three-register decoder derives encoded R5 tensor I4. Substituting actual sigma20 and all four native tau20 into the same R polynomial with original decoder marking gives unitarity and the correct square but fails common erasure action. The pure input rho=(I-F_sigma5)(I+s23)/2 yields output-difference eigenvalues +1/4,+1/4,-1/4,-1/4 and16 zeros: trace distance1/2 for all four lifts.
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 simplex and positive polar rule
Use the actual W6 simplex and raw metric, unchanged native three-clock and original positive polar prescription at one of its three marked fixed points. The prescription and its physical selection are not derived from P1.
- Original decoder and same native quarter polynomial
Fix original erasure decoder D(A)=W(A tensor I4)W* and its mark P220=P2 tensor I4. Substitute actual sigma20=sigma5 tensor bar(sigma4) and all four native reflection lifts of original tau5 into the existing R polynomial. This tests that continuation, not all coherent lifts.
Original evidence
- MARKED-CLOCK-LIFT.md lines 123–160
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/MARKED-CLOCK-LIFT.md
da0d56aeb94f078f496a0748911ad559fa5835d77757fc7d1879c2eb70123468
finding:original-decoder-versus-native-quarter-polynomial-erasure-test