TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/recursive-mirrored-source-20261103/ADMISSIBILITY-AND-MEASURE-REVIEW.txt
Original file SHA-256: de2ccd65bc3070d969182a62e274e219595cdcb77db7c7d3a282699f45c2171e
Inclusive original lines: 181-211
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000181 |  including its ordinary linear Higgs-volume premise and exclusions.
000182 | It already says a bounded finite-rank spectral seed alone does not
000183 | normalize that noncompact volume. This is REUSE, not a fresh discovery
000184 | or R080 replay.
000185 | 
000186 | In that SAME declared class the boundedness is uniform even when all
000187 | geometry/A/reference coefficients vary: rank<=N and bounded f imply
000188 |  |Tr f(D)-Tr f(D_ref)|<=2N ||f||_infinity,
000189 |  e^(-2N||f||)<=|exp(-S_spectral)|<=e^(2N||f||)
000190 | for a real eta phase. The actual bounded-rank spectral reference alone
000191 | does not create radial damping. Its entire field dependence is retained
000192 | in this uniform inequality, not frozen.
000193 | 
000194 | The actual finite affine fermion Pfaffian and ordinary Grassmann ghost
000195 | determinant, where that original source prescription holds, are finite
000196 | polynomials. If their joint leading coefficient is nonzero on an actual
000197 | open angular/nonradial tube, continuity gives a uniform polynomial lower
000198 | bound there at large radius. If the actual original base element has
000199 | the stipulated nondecaying linear Higgs volume on that positive-volume
000200 | tube, the coupled absolute integral diverges. All those interactions
000201 | are retained; no zero-measure slice proves this statement.
000202 | 
000203 | But this does NOT decide a source whose actual base/conditional density,
000204 | bosonic auxiliary integration, extra original action, physical selector,
000205 | or joint rank limit changes those hypotheses. Gaussian/Hermitian graph
000206 | geometry alone and the named gap/index constraints do not supply a new
000207 | measure by themselves. An actual supplied full omega already fixes its
000208 | commutative field laws; it is to be evaluated, not replaced with linear
000209 | volume or an arbitrarily chosen Riemannian measure. The full primitive
000210 | source/integration equality and its normalizing conditional density are
000211 | not declared computed by this review.