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at its declared finite cutoff.", "Primitive searches are complete only for the declared rational flat lattices and radii using exact coordinate bounds.", "Gaussian identities concern moduli-averaged affine observables; the companion does not sample curve counts or construct genus-two models.", "Independent numerical formulas share mpmath; precision agreement and residual tolerances are not interval certificates.", "Analytic series and integral tail bounds exclude quadrature and roundoff errors; their numerical evaluations are uncertified.", "Increasing finite rank-one sums do not prove divergence or turn a truncated raw product into an L2 observable.", "No rectangle clipping, optional elementary gap plots, arbitrary affine-quotient mixing, or nonsquare-stratum classification.", "No torus spectrum enumeration, full length-8192 campaign, historical-data recovery, or conditional sensitivity enclosure is performed here.", "Author formula contracts are pinned in fixture data; concurrent manuscript edits are not part of this source freeze." ], "elapsed_seconds": 1.689166291966103 }