ψ-Spiral Retention: A Universal Variational Principle of Difference Preservation from Biology to Cosmology

This article introduces the ψ-Spiral Retention framework, a unified variational principle describing how natural systems preserve distinguishability (Δψ) under growth, motion, noise, and cosmic expansion. Across biological signalling, fluid vortices, morphological spirals, and late-time cosmological structure, we show that systems converge toward configurations that minimize the rate of distinguishability loss. The ψ-retentive functional, its Euler–Lagrange equation, the ψ-Safety (C-term) constraint, and the curvature–difference coupling together define three canonical extremal classes: logarithmic spirals (static retention), oscillatory trajectories (dynamic retention), and vortices (retention in flow). We demonstrate that the same invariant governing biological and fluidic systems also produces correlation plateaus, suppressed structure growth, and a retentive floor Δψ̇ → 0 in cosmology. ψ-Architecture thus establishes retention as a scale-independent structural principle, linking local biological patterns with the large-scale Universe through a single law of difference preservation.