TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/FOLD-COVARIANCE-TO-NATIVE-FIELD-RESPONSE.txt
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Inclusive original lines: 198-229
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000198 | 6. THE SMALLEST ACTUAL MARKING TESTS FAIL, WITHOUT A FIT
000199 | 
000200 | Use the six previously source-derived simplex rays and all60 P(q,S), with
000201 | their literal original N coordinates only for comparison after response
000202 | construction. Neither old q5, sigma, P2 nor an angle is an input to D_r.
000203 | For BOTH retained alpha values:
000204 |   -- The one-point Riesz ray matches none of the six native rays.
000205 |   -- D1 has rank4; its one-dimensional kernel matches none of those rays.
000206 |   -- No one of60 P(q,S) commutes with D1.
000207 |   -- No one of60 P(q,S) commutes with the complete B4.
000208 |   -- Therefore none reduces the entire D0..4 two-point response family.
000209 | All statements are exact symbolic equality tests, not proximity thresholds.
000210 | 
000211 | Any spectral projector of a Hermitian B commutes with B. Consequently no
000212 | P(q,S) can be obtained as a spectral projector of this actual B4 or D1.
000213 | No chosen pair of eigenvalues, minimum/maximum overlap or nearest flag
000214 | repairs the literal mismatch. A generic rank2 spectral subspace is not a
000215 | physical dictionary simply because its dimension is two.
000216 | 
000217 | This excludes ONLY those stated direct mean/kernel/spectral identifications.
000218 | A physically relevant projector need not commute with every possible
000219 | source response. We do NOT impose that as a new physical principle, demand
000220 | closed code dynamics, or conclude that the original state cannot select a
000221 | mark through a different source-derived observable or charged history.
000222 | Particular profiles might give special Grams, but must be supplied by the
000223 | original source law rather than tuned after this test.
000224 | 
000225 | All D_r are unchanged under b->-b, since partial^nu f_i is homogeneous of
000226 | degree4-r. Complex conjugation conjugates the matrices and transports the
000227 | real candidate flags consistently. The negative/positive current convention
000228 | cannot convert these failed tests into a successful one.
000229 |