# Source and theorem interfaces

**Hellinger contraction with arbitrary Boolean output bias**, OpenAI, September 24, 2026.

Selected scientific pin: `c61bc00b45b94b47131e6ddb293d4ddede9ffa2f`, source family `results/hellinger-noise-contraction/build`. Original sources remain preserved. The complete analytic proof, ten sections, profile data, six arithmetic programs, runner and requirements are retained. The working entry was renamed from `paper.tex` to `main.tex` for the existing portable helper.

The release adds historical and methodological credit, a complete local ordinary Courtade–Kumar corollary following ABCJN Proposition 1, an editable proof diagram, and explicit calibrated-edge domains, retained calibration loss, and repeated-node concavity interfaces. No polynomial, coefficient, subdivision depth, theorem hypothesis or proof mechanism was weakened. Mathematical programs, fixed data and runner retain their bytes. Certificate README wording removes an absent historical run-directory reference.

The theorem has no interarticle dependency. Analytic machinery is proved locally and finite arithmetic is supplied as part of the proof. The bibliography credits original problem statements, antecedent inequalities, the information implication and methods. The Boolean information consequence supplies no asserted implication to the companion soft-channel theorem.

Source reading, literature evidence, debate, arithmetic execution and final reviews are separate evidence records. Historical archive and review status is not a proof premise.