Abstract
Restricted response equivalence does not determine the response to a different source or the output of a different observation. We study this distinction in two linked, explicitly specified superconducting model comparisons. A conserving, particle–hole-symmetric density model gives identical linear responses for a two-point form factor and a smooth angular form factor with the same first two moments. Its diagonal cubic response contains the fourth moment. A supplied additional singlet channel modifies that dependence, and a smooth family approaching the two-point distribution eliminates a uniform cubic-coefficient separation on bounded, pole-separated domains. We then turn to distinct finite-energy optical completions, retaining their actual dispersion, pairing regulator, gap feedback, occupied-sea currents, and electromagnetic attachment. Their lower optical responses can already differ; seventh order is not asserted to be the first optical discriminator. For a fixed two-tone, same-incident-field comparison, inherited computer-assisted continuum enclosures certify a nonzero selected seventh-degree coefficient, two ninth-degree corrections, and an all-order remainder. The resulting relative-error bounds hold at explicitly very small normalized amplitudes and do not establish practical detectability. Finally, we distinguish phase selection from square-law detection and state the waveform and preparation conditions under which a sign-reversal pilot estimator preserves a finite linear query. The result is a model-specific, source-explicit comparison with auditable error accounting, not universal band identification or a derivation of the superconducting interaction from complementarity.
The supplement contains the declared model/proof notes, curated numerical source and inputs, all seven accuracy cases, historical failure and replay records, and the accepted repaired Lean source with statement/axiom evidence and correspondence. The completed local Lean review covers 57 selected theorem declarations and ten supporting definitions/types. It is not a formalization of the entire microscopic derivation, continuum-enclosure producer, all-order tail, or physical detector preparation. A final separately organized AI-assisted technical review repeated the original saved-endpoint checks; it was not an independent external referee review. Mathematical accuracy at very small normalized amplitudes is not demonstrated experimental sensitivity.
Where it sits in the release
The release’s single superconducting-response paper. It is a model-specific, source-explicit comparison with auditable error accounting — not universal band identification, and its very small normalized amplitudes do not establish practical detectability.
Download paper (Zenodo) — CC-BY-4.0.