What was already known
Earlier work posed this inequality and proved restricted cases or weaker mean-dependent bounds. Separate 2026 results address the weaker Courtade–Kumar information inequality.
AI involvement
OpenAI attributes the Hellinger manuscript to its internal model. The proof draws on earlier human methods for Boolean-noise inequalities.
OpenAI authorship and the cited release's model-production account support AI-led mathematical work; autonomous session provenance is absent.
- Supporting source (github.com) — Companion information-contraction formalization scope
- Supporting source (github.com) — How the results were produced and verification caveat
Importance
The sharp arbitrary-bias inequality resolves the full Hellinger conjecture and implies the information bound.
Limitations
The supplied exact-arithmetic programs have instructions but no recorded successful run; no completed check of the analytic reductions is documented. A companion Lean theorem proves a different information statement.
Technical verification
The manuscript supplies a computer-assisted analytic proof and exact-arithmetic programs, but the available release gives instructions for running the programs without a recorded successful run or a completed check of the full theorem. Reported is the evidence default. The Lean scope for result 119 concerns binary information contraction, not this Hellinger inequality.
Human understanding
No human account of the new asymmetric induction, calibrated energy continuation and certificate interfaces is documented. Few is the evidence default, not a claim that people cannot understand them.
Correction and publication history
If correct, the sharp arbitrary-bias inequality resolves the full Hellinger conjecture and implies the information bound.
Read this published revision