TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/SEAM-STATE-EVENT-POLAR-SELECTION.txt
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000217 | 6. Original determinant lift: coherent phase and full lattice test
000218 | 
000219 | Keep the already existing determinant cover h=lambda r, lambda=e^-i pi/4,
000220 | separate from native order-two r. On the native quartic it acts as
000221 | lambda^4 rho5(r)=-rho5(r). Incident coherent differences are therefore
000222 | 
000223 |     -n_j-n5,        G_det=I5+J5/3,
000224 | 
000225 | with eigenvalues8/3,1,1,1,1. Their positive polar prescription gives a
000226 | rank2 mark at squared distance48/25 from original P2. Nonincident events
000227 | also respond, now by -2n5. Summing all60 raw native response outer products
000228 | gives eigenvalues24,4,4,4,4; the determinant version gives144,4,4,4,4.
000229 | These sums are algebraic diagnostics, not assumed probabilities or rates.
000230 | The relative minus against identity is coherent data, not a removable
000231 | projective ray phase.
000232 | 
000233 | More decisively, the same h cannot be used as a literal automorphism of
000234 | the FULL original lattice fields with that Cartan action. The original
000235 | Construction-A raw roots are integer vectors of norm squared4. Rotation
000236 | lambda sends (2,0,...,0) to(sqrt2,-sqrt2,0,...), not a lattice vector.
000237 | Native r preserves the lattice, so lambda r does not preserve it. The
000238 | checker tests all60 r on all240 roots and gives a root failure for each
000239 | lambda r. An automorphism preserving the original Heisenberg Cartan must
000240 | transport its charge spectrum E8 onto itself; the failed charge image
000241 | already precludes this extension, before any cocycle repair.
000242 | 
000243 | This is NOT an exclusion of other full-source operations, twists between
000244 | different modules, or the previously constructed inner E8 lift on the
000245 | different CHARGED C4/F20 current blocks. Finite representation agreement
000246 | on that coupled cover remains correct. It cannot supply the missing
000247 | identical Cartan-four/local-quartic dictionary by changing the phase alone.
000248 | The charge-spectrum argument uses the standard lattice vertex formula;
000249 | see Tuite-Zuevsky2011 Eq55, https://arxiv.org/pdf/1106.6149 .