Epistemic Curvature

Riemannian Curvature of the Fisher-Rao Statistical Manifold

Phases 1–4 Complete

Normal + NIG + Mixture

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Key Metrics

Current R(t)

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Scalar curvature

GBM Null

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−d(d+1)(d−1)/8

Deviation

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R(t) − R₀

Max |κ|

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Principal Ricci eigenvalue

Falsification

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Tests passed / 5

Ablation Rate

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Specs passing ≥3/5

Phase 1 — Curvature Dynamics

Scalar Curvature R(t) vs VIX — Stress Event OverlayDiscovery

Computing curvature field…

Curvature Spectrum κ(t) — Ricci Eigenvalue DecompositionEigendecomposition

Decomposing Ricci tensor…

Curvature–VIX Lead-Lag Cross-CorrelationEvidence

Computing cross-correlation…

Phase 2 — Multi-Family Comparison & Phase 4 — Ablation

Multi-Family Curvature: Normal vs NIG vs MixturePhase 2

Comparing manifold families…

Ablation Matrix — Cross-Specification RobustnessPhase 4

Running ablation suite…

Phase 3 — Directional Analysis & Integrity

Directional Fragility MapRisk Factors

Projecting eigenvectors…

R(t) Distribution vs GBM NullStatistical Test

Building distribution…

Fisher Metric Condition NumberIntegrity

Monitoring conditioning…

Pre-Registered Falsification Tests

Loading manifest…