# Bosonic entropy and channel-bound calculator

Family 273: The entropy photon-number inequality. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Optical communication researchers can calculate the claimed entropy photon-number lower bound and compare thermal-input equality cases.

## Applicability and commercial boundary

Independence between the two finite-energy inputs matters even when each is internally entangled. The selected formal scope does not cover the thermal-attenuator or broadcast-capacity corollaries.

## Initial business decision

Conditional engineering. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Implement the thermal entropy inverse with stable endpoint handling and isolate the inequality from unverified corollary applications.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstract passages and available family scope notes were also inspected; paper-level theorem and algorithm details still require deeper review. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[The entropy photon-number inequality](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-photon-number-inequality-September-24-2026/paper.pdf).