No Experimental Evidence for Orthomodular Lattice Cognitive State Spaces — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search returned only pedagogical/lecture content on Hilbert spaces and one AI state-space model — no experimental evidence for orthomodular lattice cognitive state spaces. | MATH: Hilbert space H = complete inner-product space over ℂ; projection lattice P(H) is orthomodular: a ≤ b ⟹ b = a ∨ (a⊥ ∧ b); orthocomplement a⊥, a ∧ a⊥ = 0, a ∨ a⊥ = 1. | CONNECTION: Projection lattices are orthomodular but NOT distributive (no Boolean algebra); no confirmed appearance of 0.382/0.618/1.618 or root-system constants in the retrieved material. | DEPTH: 2 FINDING: The only substantive research artifact is "oscillatory state-space models" (Rusch, TEDxMIT) — a dynamical-systems AI framework inspired by cortical oscillations, not a quantum-probability cognitive model. | MATH: Continuous-time state-space form ẋ(t) = A x(t) + B u(t), y(t) = C x(t); oscillatory regime requires complex eigenvalues λ = σ ± iω of A (damped/undamped modes). | CONNECTION: Complex-conjugate eigenvalue pairs sit on cir Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225098780