Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 347. Counterexamples to strong forms of Arnold's fixed-point conjecture
Family claims › Differential geometry · lines 2254–2259
OpenAI@2026-10-07#rem:oai-347
Disproves stable-Morse lower bounds for nondegenerate Hamiltonian fixed points: on simply connected closed Kähler manifolds of real dimension , the deficit below the stable Morse number is unbounded. A separate Hamiltonian diffeomorphism of the complex quadric threefold has exactly three fixed points, fewer than the four critical points required of every smooth function.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 333. Smooth isometric immersions of surfaces into R 4
- remark: Remark: Family 334. A smooth surface metric with no local immersion in R 3
- remark: Remark: Family 335. Gromov's integral scalar-curvature inequality
- remark: Remark: Family 336. Spectral scalar curvature and codimension-two width
- remark: Remark: Family 337. Cartan–Hadamard isoperimetry and CAT (0) fillings
- remark: Remark: Family 338. Yau's uniformization conjecture
- remark: Remark: Family 339. Katok's entropy rigidity conjecture
- remark: Remark: Family 340. A counterexample to the nearby Lagrangian conjecture