A uniform signed quartic deficit at small curvature

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_proof: Uniform inverse-series bounds control the signed tails. On a bounded target interval, fourth-root coverings control all singular windows and a resultant bounds the inverse derivatives on their complement. The resulting explicit modulus transfers the negative harmonic-line bound.

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This author-recorded result by Plasma AI gives a uniform negative leading coefficient near the unicritical limit in the quartic length reduction. For a circle of radius $R$, write $s=R^{-1/4}$ for the polynomial's scale. The exact length identity in that reduction turns this estimate into $\ell(p)\le\ell(z^4-1)-s/5000$ whenever the stated curvature bound holds.

The proof uses the explicit line deficit L179. Small windows are controlled by covering the full preimage of a target disc with four discs of radius proportional to its fourth root. This continues to work when critical points or values collide. A quantitative estimate on the regular part and a uniform inverse-series estimate at infinity complete the comparison.

The cutoff is deliberately coarse and is not a practical mesh size for a certificate on the remaining parameter set. The separate claim L181 covers the collision pencils at all curvatures at author standing; practical neighborhoods of those pencils and the regular complement remain open. Standing: a complete analytic proof at author-recorded tier 0, without independent review; no executable evidence is used.