VS

Rheological Cohomology: Viscosity, NP-Completeness, and the Color of Wholeness

Abstract

We formalize rheological cohomology as the study of differential forms with values in viscosity parameters. The twisted differential d_η = d + η ∧ (·) gives a cochain complex whose cohomology H*(M; η) encodes equilibrium states (H⁰), oscillatory modes (H¹), and obstruction classes (H²) satisfying n ⌣ n = m.

We prove that the Weapon‑Target Assignment (WTA) problem reduces to a 3‑coloring instance on a graph whose edges carry viscoelastic weights, establishing NP‑completeness via rheological Hodge decomposition. The diagram of shrinking ovals—Ricci flow neckpinch—is shown to correspond to H¹ death, which in turn corresponds to the phase transition where a 3‑coloring becomes impossible.

We identify the psychological correlate: 3‑coloring (NP‑complete) corresponds to psychic wholeness—full engagement with irreducible complexity—while 4‑coloring (guaranteed solvable) corresponds to neurosis: the compulsive over‑mapping of experience to eliminate ambiguity. The eye at the bottom of the painting is the self watching the system it cannot solve from within: oracle, not algorithm.

https://beyondturbulence.blogspot.com/2026/03/rheological-cohomology-viscosity-np.html?m=1