Ridge Geometry is a canonical framework for determining admissibility in symbolic systems subject to constraint. Rather than describing states, trajectories, or optimization objectives, it specifies the structural conditions under which transformation, transmission, or evolution can occur without violating the invariants that sustain coherence. These conditions define narrow corridors of persistence—ridges—along which symbolic entities may diffuse, drift, bifurcate, or stabilize while remaining structurally tenable. The framework operates prior to representation, dynamics, metrics, or learning. It introduces no distance function, no global ordering, and no optimality criterion. Instead, it determines where coherence can persist at all. Structural failure is not treated as error, noise, or insufficient modeling, but as an admissibility boundary that precedes description. Ridge geometry distinguishes transformations that preserve invariants, transitions that induce irreversible deformation, and passages that remain undecidable without collapsing the structure that carries them. In these latter regimes, refusal and non-closure are not exceptional outcomes, but structurally stable results. Persistence, rather than optimization, becomes the primary organizing principle. A central contribution of ridge geometry is the explicit separation between the canonical structure of admissibility and the surfaces constructed upon it. Visualizations, graphs, simulations, audits, and AI-driven instruments are treated as surface-level projections constrained by ridge geometry, not as expressions of the canon itself. Such surfaces are disposable by design: when subjected to forced unification or totalization, they are expected to fail, while the canonical structure remains invariant. Ridge geometry further introduces the notion of symbolic fingerprints: structural characterizations of symbolic fields that are independent of semantic content, representation, or implementation. These fingerprints function as living keys. They evolve under constraint as invariants and regimes shift, while preserving structural memory without storing states, histories, or trajectories. Temporal ordering, when present, is treated as an index over admissibility regimes rather than as a dynamical law. Ridge geometry does not subsume existing theories in dynamics, logic, optimization, or learning. Instead, it establishes a prior art canon governing when such frameworks may be legitimately applied, and when their use constitutes an inadmissible reduction. © 2026 ΔR7 / KoRVersion: V1License: CC BY-NC 4.0Status: Canonical admissibility frameworkDistribution: PDF / Zenodo / IPFS / TraceLockTraceLock ID: 622d5a4f3aaf01f52e842a4ad386ab5c33c5233d91b21e92aa6bc25b2b374547
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