# Hamiltonian fixed-point lower-bound limitation library

Family 347: Counterexamples to stable-Morse and strong Arnold fixed-point bounds. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Symplectic researchers can flag stable-Morse and strong Arnold bounds contradicted by the specified finite-dimensional examples.

## Applicability and commercial boundary

The counterexamples concern particular manifolds and nondegenerate Hamiltonian maps; other proven fixed-point bounds remain applicable.

## Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

## Next verification action

Extract the exact manifold, fixed-point data and violated inequality.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Hamiltonian Fixed Points Below the Stable Morse Number in Dimension Twenty-Two](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two-October-5-2026/hamiltonian-fixed-points-below-stable-morse-number.pdf).