Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 350-03. Power-law violations of Yau's nodal upper bound
Manuscript map · lines 9155–9164
OpenAI@2026-10-07#rem:oai-p-350-03
Authors: OpenAI. Family 350.
Title: Power-law violations of Yau's nodal upper bound.
Abstract: We construct a smooth Riemannian metric on $S{}4{}times S{}1$ and a sequence of real Laplace eigenfunctions whose nodal four-volume grows faster than ${}lambda{}{1/2+{}epsilon_0}$ for one fixed ${}epsilon_0{}gt 0$. This disproves the smooth upper-bound assertion in Yau's nodal-set conjecture and the proposed bound with an arbitrarily small positive power loss.
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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