The Pi-Origin Architecture is a mathematical framework derived from π and φ in which a single coupling equation — φ⁻¹ × exp(−|a−b|/π) — governs the interaction between any two coordinates in phi-space. The screening length is π. The unique fixed point of the contraction operator is φ⁻¹ = 0.6180339887, guaranteed by the Banach fixed-point theorem. Two threshold transitions occur at 0.35 and 0.05, derived from the condition exp(−3) ≈ 0.05 — not chosen as parameters.
This community documents the complete research output spanning the mathematical foundations, a seven-phase learn-to-learn engine, a quaternary programming language (GTAC), a ternary computational substrate {0, 1, ?}, protein folding analysis, seven falsifiable predictions in genomics and neurodegeneration, applications in network security, acoustics, optics, and generative arts.
All constants in this framework are derived. None are assumed. The documentation is the verification.
Daniel E. Dragolich · Dragolich Research Labs LLC · Copyright © 2026