TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/MIXED-ORDERED-RETURN.md
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000060 | ## 3. Actual five-code return: nontrivial, but wrong marking and clock
000061 | 
000062 | The exact sparse calculation uses the ORIGINAL five code polynomials with
000063 | normalization squares(96,8,8,8,1). It keeps original v_beta coefficients.
000064 | All194 nonzero first-response directions give positive definite rank5
000065 | return matrices; none is scalar or commutes with the original P2. The
000066 | remaining46 first responses and return matrices are zero.
000067 | 
000068 | The sum over the original unit-norm root-current INPUT basis is
000069 | 
000070 |     K_sum=diag(3581,4191,3419,3419,3790).
000071 | 
000072 | The W_beta response states have NOT been separately normalized. This is
000073 | an original-R-weighted derivative-response Gram, not a selected physical
000074 | equal-rate event ensemble. The eight Cartan input derivatives are zero.
000075 | Its exact characteristic polynomial is
000076 | 
000077 |     (x-4191)(x-3790)(x-3581)(x-3419)^2.
000078 | 
000079 | It commutes with original tau, but not original sigma or P2. Exact witnesses:
000080 | 
000081 |     [K_sum,sigma]_(1,2)=772,
000082 |     [K_sum,P2]_(0,1)=(488 sqrt2-61 sqrt3)/5 !=0.
000083 | 
000084 | Indices are zero-based. The original P2 has entry
000085 | (P2)_(0,1)=(sqrt3-8sqrt2)/50. This compares ACTUAL operators, not only
000086 | degeneracy counts. The response has spectral multiplicities1+1+1+2;
000087 | collecting selected eigenvectors would add a new rule, and its unique
000088 | two-dimensional eigenspace is not the required original marked plane.
000089 | 
000090 | All FOUR original `omitted_family` choices give EXACTLY THE SAME K_sum in
000091 | the held native chart. Choosing another supplied family representative
000092 | therefore does not repair this marking/clock mismatch. This says nothing
000093 | about a different original process with different derived contraction data.