Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 143-01. Uniform bounds for planar polynomial limit cycles
Manuscript map · lines 5175–5184
OpenAI@2026-10-07#rem:oai-p-143-01
Authors: OpenAI. Family 143.
Title: Uniform bounds for planar polynomial limit cycles.
Abstract: For every degree, we prove that the number of isolated periodic orbits of a real planar polynomial vector field is bounded by a finite constant depending only on that degree. This establishes the uniform boundedness assertion in the second part of Hilbert's sixteenth problem. The proof uses separation of asymptotic expansions on nested complex domains and a finite-dimensional counting argument.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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