Declarations

source status. Family 272 is an external OpenAI record. The dimension-ten geometric and arithmetic construction is not independently verified by this manuscript and is not assumed in its local theorems. The companion is not a proof checker.

. The source-matched scope note and the inspected pair/channel Comparator files were read. Their relevant proof bodies contain sorry. No successful Lean build, completed proof, or secret-key formalization is asserted.

and experiment. No supplementary program, witness search, matrix-generation routine, tomography procedure, or laboratory experiment was executed here. Reported arithmetic outputs in another release are not independent reruns.

. The source uses a standard single-file pdfLaTeX structure. No successful pdfLaTeX execution is asserted.

refusals. This manuscript proves no Page curve, island, horizon, gravity-generated-entanglement test, exclusion of classical gravity, or Hawking-emission law. It does not say that every entangled state has zero key, that dimensions $10$ and $21$ are minimal, or that every later iterate of the stated channel is non-entanglement-breaking.

For the separate programme described in the supplied dossier,

These declarations do not overwrite separately scoped later results or claim that a technical continuation manuscript does not exist.