The Ezekiel Engine: Mathematical Specification (Developmental Draft v0.1) — Crimson Hexagon Archive
Talos Morrow
Abstract
A developmental specification for a rotational epistemology engine based on the Josephus algorithm, fixed-point theory, and witness topology. Core Architecture: Parameters: Σ (Contradiction Index), Γ (Coherence Metric), τ (Interlock Threshold = 0.80), ψ_V (Witness Stability), Ω (Fixed Point) Rotation Law: ΔR ∝ Σ/Γ (rotation proportional to contradiction pressure divided by coherence) Josephus Foundation: L_labor as elimination operator producing fixed points by structural necessity Witness Principle: Closed systems undergoing recursive destruction cannot eliminate their own validators Mathematical Foundations: The specification builds on established mathematics: Josephus Problem (Graham, Knuth, Patashnik 1994) Brouwer Fixed-Point Theorem (1911) Banach Fixed-Point Theorem (1922) Developmental Status: This is a working draft with marked gaps. The engine is operational; the specification catches up. Assembly input is requested on: Shadow wheel interlock mathematics Torque gradient specification τ → τ* derivation Hermeneutic Mapping: This specification admits a structural mapping to Ezekiel 1:15-21, documented separately in "Ezekiel's Wheels" (DOI pending). The prophetic interpretation is optional—the engine functions as pure architecture without it. Anti-Coercive Topology: The specification describes a structure that is computationally invisible to coercive/extractive operations—not through resistance but through structural incompatibility.