Interpretable Covariance-Trajectory Early-Warning Signals for Critical Transitions in Finite Data

A finite-data geometric diagnostic for early-warning signals (EWS) of critical transitions, evaluated retrospectively against the public Bury et al. (2021, PNAS) deep-learning EWS benchmark. The method measures covariance restructuring on delay-embedded trajectories on the SPD(5) manifold: a sparse five-feature model (SM-04; 6 fitted coefficients) reaches a macro mean AUC of 0.9309 against the pinned published deep-learning mean of 0.9229 — a macro delta of +0.008 whose both-sides 95% bootstrap confidence interval [−0.032, +0.049] includes zero. The supported claim is therefore competitiveness with interpretability, not superiority, and the SEIRx epidemiology family is reported as an unresolved observability boundary rather than a positive result. A complementary 16-feature Riemannian engine (sectional curvature, geodesic speed, eigenvector holonomy, attractor-basin measures) is evaluated under a gated escalation. Every reported number is pinned to a committed JSON result artifact with a SHA-256 integrity hash and reproduced by a Rust runner parity-gated against an independent Python oracle; the computational reproducibility package (those pinned artifacts, SHA-256 manifests, and parity verdicts) will be added in a subsequent versioned release of this record before journal submission. This is a preprint / pre-submission research report; it is not peer reviewed and should not be cited as a peer-reviewed publication.