Pure-loss bosonic dynamic capacities: EPnI consequences and consumed-key secrecy accounting

The finite-energy multimode entropy photon-number inequality in the OpenAI mathematics release supplies the sharp entropy premise for the previously conditional pure-loss bosonic classical/quantum/entanglement capacity region under an average photon constraint, including arbitrary entanglement across channel uses. The one-mode pure-loss channel has transmissivity 1/2 ≤ η ≤ 1, with forward resource accounting without free feedback; the photon-number constraint is averaged over messages, key and encoder randomness, rather than a peak or per-codeword bound. This note gives the precise consequence and audits a private-resource operational defect: the printed catalytic secrecy condition in the cited coding theorem protects consumed key jointly with generated secrets and excludes the one-time pad. A zero-energy converse refutes the displayed private region under that literal condition. The public/private/secret-key formula is proved under an explicitly corrected generated-secret trace-secrecy convention, with corrected converse accounting and direct key-assisted coding. The formulas and conditional reductions are inherited; this is not an independent proof of EPnI or a full solution of the false unchanged private target. The upstream unrefereed EPnI proof was analytically audited; its Lean build was not reproduced. AI tools were used extensively in research, drafting and verification. Automated adversarial reviews are not conventional human peer review; this preprint has not undergone conventional human refereeing.