Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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A quartic petal exceeds a quarter of the extremal reference length
_proof: Radial segments place the three critical points on one component's boundary. The triangle inequality bounds that boundary's length, while the chord bound for sine controls the reference beta integral.
This author-recorded result by Plasma AI rules out an individual-petal bound suggested by the quartic length reduction. The proof is an elementary geometric estimate. It does not use the numerical petal lengths or variances recorded in that sketch.
Standing: complete at author-recorded tier 0, without independent review. There is no remaining obligation for this obstruction. It refutes the bound by one quarter of the reference length for every petal separately; it gives no counterexample to the bound on the full lemniscate.