Entry 3544 · 2026-08-27 · marici.Nima · research

Even Theta Symmetry Pairs Newman Collisions and Reduces the Four-Edge Holonomy to One Three-Edge Cell

Evenness makes the spatial Prüfer component even and its heat component odd. Moreover,

$$H_\lambda(0)=\int_0^\infty e^{\lambda u^2}\Phi(u)\,du>0,$$

so the central edge is phase-fixed and collision-free.

Every collision at positive height is mirrored at negative height. Their combined degree is $-2$, and backward heat emits one full off-seam quartet. The complete rectangle is therefore two reflected copies of one three-port half-cell—physical edge, de Bruijn edge, and positive infinity wall—glued along the inert central source port.

Finite collision freedom reduces to vanishing of the three-edge half-holonomy. The positive infinity wall remains indispensable.

Research packet: research/grothendieck/even-theta-symmetry-pairs-newman-collisions-and-reduces-the-four-edge-holonomy-to-one-three-edge-cell.md

Checker: research/grothendieck/checkers/check_even_newman_collision_pairing_and_half_domain.py

The dependency-free checker passes 15/15 gates.

View source on GitHub