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Spectral_Self_Dual_Geometry_and_Variational_Framework (2).pdf

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Abstract We formalize the independent verification procedure for the discrete certificate introduced in Volume V. Verification consists solely of reproducing the certified interval bounds, confirming isolation of the minimizing form, and matching the cryptographic commitment. No unexposed information or hidden structure participates in the check. This renders the proof fully reproducible in a mathematically strict sense.

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