Read the result in its research context.

Result

Actual mixed Chevalley brackets give Q(H)|F20=H tensor I4, Q(H)|C4=trH/3 and kappa=trHK-trH trK/9. Noncommuting E+ responses exist. Separated Ward responses distinguish original polar and countermarks. Clock-current norm25/18 is constant throughout CP1 and selects no point. Three gl5 lifts of given R5 have full orders12,4,12; a genuine order4 source clock exists. All60 actual finite event charts match the native erasure twenty-action on the coupled determinant cover.

Required assumptions

• Given local E8_1 vacuum representation and explicit cocycle

  Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.

• 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 clock/simplex without an imposed polar mark

  Retain actual normalized W6 simplex, sigma=(234), tau=(01), q=5. Consider ALL Hermitian rank2 projectors P with RanP inside Fixsigma, [P,tau]=0 and one positive/one negative tau eigenvalue on RanP. The original polar rule is a comparison point, not an imposed condition of this compatibility class.

• Original coupled determinant event lift

  Compare all60 original events with h=exp(-i pi/4)r and A5=-rho5(r) on the coupled finite SU4 cover. This is not the unchanged order2 G31 word or a selected physical pulse.

Original evidence

• CURRENT-RESPONSE-AND-DICTIONARY.md lines 10–92

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/CURRENT-RESPONSE-AND-DICTIONARY.md

  db9163de1017810818e104f651e531247378a4c8295580c8936cb19e594b4b73

finding:original-e8-current-response-and-full-quarter-lifts