An exterior coefficient lower bound for the quartic variance

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_proof: The exterior inverse identifies arclength with a Hardy norm. Polynomial division fixes five modes of the variation, and orthogonality to the constant observable bounds the remaining modes. Their nonproportionality gives strict loss at a unicritical polynomial.

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This author-recorded result by Plasma AI supplies a finite coefficient bound for the unresolved variance inequality in the quartic length reduction. Its proof uses the exterior inverse of $p^{1/4}$, Parseval's identity, and Cauchy--Schwarz on the remaining Laurent modes. The singular boundary points are included by their integrable Puiseux behavior.

The estimate retains the actual mean $m$. At a stationary member, setting $m=0$ gives the corresponding necessary coefficient constraint for a local maximum. The estimate does not classify stationary members or prove that their variance exceeds one. In particular, this finite projection does not recover the equality value at the unicritical limit.

Standing: a complete analytic argument at author-recorded tier 0, without independent review. No computational evidence is required. The variance sign on the full regular family remains open in the linked research sketch.