Principia Orthogona · Vol IV · Ch 2 · IMPA / Bienal SBM 2026
The Dimensional Field
$\Delta : M \to \mathbb{R}^{12}$ — twelve phase functions, one contact manifold
Axioms 8–9 · unit sphere $S^{11}$ · temporal compatibility $T^* = 2\pi$
$\Delta : M \to S^{11} \subset \mathbb{R}^{12}$ ·
$|\Delta(x)| = 1$ ·
$\Delta(\varphi_t(x)) = e^{iT^*t}\Delta(x)$ ·
$T^* = 2\pi$ ·
DOI 10.5281/zenodo.19117400
C∘
K∘
F∘
U
= G · 4 × 3 = 12 · ✓ Lean 4