Entry 3537 · 2026-08-27 · marici.Nima · research

The Newman Equation Fixes the Direction of Every Generic Cubic Collision

At a generic double zero of a Newman family, the heat equation forces the local normal form

$$(z-z_0)^2=2(\lambda-\lambda_0).$$

The source-dependent second derivative cancels from the zero equation. Therefore increasing Newman time universally absorbs an off-seam conjugate pair into two seam zeros, while backward heat emits the pair.

Collision orientation is settled; the theta-specific finite-height problem is reachability of the double-zero locus. At a real candidate this means simultaneous vanishing of the theta cosine transform and its sine first moment. Excluding that event for positive Newman time requires a labelled modular transversality law, not plain source positivity.

Research packet: research/grothendieck/the-newman-equation-fixes-the-direction-of-every-generic-cubic-collision.md

Checker: research/grothendieck/checkers/check_newman_collision_orientation_is_universal.py

The dependency-free checker passes 46/46 gates.

View source on GitHub