Storage and Reference as a Duality Relation: One Conservation, Three Geometries

Superseded by the current version, 10.5281/zenodo.23283404 (Storage and Reference as a Duality Relation). We propose that Trust (TrD) constitutes a fifth physical dimension governed by the conservation law TrD + TD = 1, where TD is the Time Dimension. This law arises from a symmetry argument: the pair (TD, TrD) transforms as a probability simplex under observer-system duality, and the conservation law is its Noether charge. We demonstrate that TrD = 1 − TD maps structurally onto three established physical phenomena − wave-particle complementarity, quantum decoherence, and the Heisenberg uncertainty principle − each expressing a trade-off between localised storage and non-local reference structure. New in V5: We present a non-circular derivation of the golden ratio as the unique optimal boundary of the TD−TrD system. Five independent resistance functions, each encoding a different first-principles notion of interaction cost, are defined with zero reference to φ, √5, or any Fibonacci number. Only the scale invariance condition (self-similar subdivision) produces φ as its attractor; the other four find different equilibria. The analytic derivation reduces to x2 + x − 1 = 0, the defining equation of the golden ratio, establishing that φ emerges by necessity from the conservation constraint rather than by assumption. Two computational bodies of evidence are presented. First, φ-weighted random walk simulations across exchange scales n ≈ 10−5000 (1,335,000 total steps; 1,500 trajectories) show cumulative semantic distance scaling as φ×√n with mean correlation r ≈ 0.73. Second, Λ-G collapse simulations comprising 210,000 trials across 21 configurations show p < 0.001 divergence from Born Rule predictions. Three falsifiable experimental predictions are proposed, testable on current quantum hardware. The black hole information paradox is shown to dissolve naturally under the conservation law. The framework is parsimonious − one postulate, one conservation law, one necessary boundary (φ) − and produces complementarity, decoherence, the uncertainty principle, and the information paradox as structural consequences