Strict deficit on both quartic collision pencils

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_proof: The two fixed quartics have two real critical values. Conjugation reduces each pencil to a compact angle interval, on which the retained program certifies the signed integral. Scaling the inverse images gives the claimed length inequality.

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This computer-assisted, author-recorded result by Plasma AI covers the double-critical-point and equal-critical-value strata of the quartic reduction. The proof gives the circle parametrization, identifies the exact checked integral, and explains the passage to polynomial length.

The canonical executable evidence is retained in the collision-strata account, at wiki/research/erdos_114/quartic_evidence/evidence/main.py. It reads no external inputs and checks all parameter boxes using balls and certified root discs. Its full replay, including the two line-limit controls, is the computational obligation of this claim. The floating-point landscape probe in that folder is not part of its proof.

The certificate gives strictness on the pencils themselves. Their two-dimensional neighborhoods and the regular complement are different subjects. Standing: proved at author-recorded tier 0, with no independent soundness examination of the enclosure engine or whole-statement bridge. The degree-four inequality remains open in the linked sketch.