The Davis Manifold: Geometry-First Detection with Compositional Error Budgets Conceptual Framework Paper This manuscript introduces Davis manifolds and Davis systems as a unified mathematical framework for safety-critical detection in domains with identity-preserving temporal structure. The framework is designed for applications where an underlying configuration (e.g., viral antigenic state, human identity, physical pose) evolves along continuous paths while only indirect, noisy observations are available. Core Contributions Geometric Foundation: Defines Davis manifolds as Riemannian state spaces with bounded geodesic–Euclidean distortion profiles ε(L) along benign path families, soft/hard configuration margins (κ_hard, κ_soft), and explicit ambiguity bands triggering abstention. Existence Theory: Proves that contrastive training (InfoNCE) with smoothness regularization yields Davis manifolds with explicit distortion bounds ε(L) ≤ K(λ)L, establishing a tunable trade-off between geometric fidelity and representation flexibility. Detection Guarantees: Derives finite-variance Cantelli bounds mapping separation in a scalar detection statistic to misclassification risk, with a compositional error budget decomposing failure into geometry error (E_geom), feature linkage error (E_link), calibration error (ξ), and abstention failure (ζ). Path-Horizon Optimization: Formalizes the trade-off between path length (detection coverage) and distortion (geometric stability), providing operational guidelines for selecting the horizon L*. Operational Protocols: Supplies complete validation workflows including distortion audits, margin estimation, error-budget estimation, calibration methods, and deployment monitoring procedures. Scope and Instantiations This is a conceptual and theoretical manuscript. It presents definitions, assumptions, theorems, and empirical protocols but does not report performance metrics. The framework is instantiated through two worked examples: HERALD: Viral antigenic drift surveillance using pullback Riemannian geometry on sequence space VIDAR: Deepfake detection via identity trajectories on the hypersphere Keywords Riemannian geometry, metric learning, contrastive learning, temporal detection, safety-critical AI, abstention, error budgets, calibration, viral surveillance, deepfake detection, explainable AI Document Type Theoretical framework paper with operational protocols Author Bee Rosa Davis, NASA Mission Systems Engineer & IBM X-Force Red Principal Adversarial Intelligence Engineer Note: This work provides a reusable theoretical foundation for geometry-first detection systems across domains including biosurveillance, media forensics, robotics, and medical monitoring. Related Work HERALD (one of the two instantiating systems discussed in this framework) is patent-pending: Davis, B. R. (2025). HERALD: High-resolution Early Recognition of Antigenic Landscape Divergence. Zenodo. https://doi.org/10.5281/zenodo.17640400 U.S. Provisional Patent Application No. 63/919,595, filed November 18, 2025.