TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt
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Inclusive original lines: 183-207
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000183 | 6. Complete seam-graded energy response does not yield a sharp3+2
000184 | 
000185 | Use ALL actual positive-mode density response matrices G_m, m=1,...,32,
000186 | already independently computed on the full five inputs, both quarters.
000187 | The original seam fixes four characters, without fitting a profile:
000188 |  G_rho=sum_(1<=m<=32,m=rho mod4) G_m, rho=0,1,2,3.
000189 | Exactly sum_rho G_rho=32 B4, with B4 the ACTUAL source input metric.
000190 | All four G_rho are positive definite (rank5) in BOTH quarters, independently
000191 | checked by exact Gaussian-rational Sylvester minors. So for the normalized
000192 | mathematical response effects E_rho=(32B4)^-1/2 G_rho (32B4)^-1/2,
000193 |  0<E_rho<I, sum E_rho=I.
000194 | Every nonempty proper coarsening also lies strictly between0 andI. In
000195 | particular deck-even G0+G2 and deck-odd G1+G3 both have rank5. This is an
000196 | energy-response decomposition, NOT an executed POVM or filtering rule.
000197 | The exact common commutant of (32B4)^-1 G_rho has dimension1 overQ(i).
000198 | Thus no common reducing3+2 input-spectrum is hidden in these four forms.
000199 | 
000200 | EXCLUSION SCOPE: only a sharp deterministic character/deck input-sector
000201 | reading, and a common reducing spectral split of this complete response
000202 | decomposition. There is NO new axiom that a physical mark must commute
000203 | with every response; no exclusion of all nonlinear intrinsic event
000204 | relations, other full-field histories, admissibility rules or P1. The
000205 | existing original global event-label pair, intrinsic six rays and60 flags
000206 | are retained. The original physical q/S and polar3+2 selection remain open.
000207 |