Kappa-FIN: Topological Early Warning System for Financial Market Crises

David Ohio requests your endorsement to submit an article to the stat.APsection of arXiv. To tell us that you would (or would not) like toendorse this person, please visit the following URL:https://arxiv.org/auth/endorse?x=XZKYR7--Version 4 of Kappa-FIN introduces engine_v4 with Structural Phase Speed (SPS), extends the validated scenario corpus from 17 to 22 crises (1985–2026 including live contemporary analysis), and documents a negative experimental result (FR vs OR curvature redundancy). What's new in v4: ENGINE v4:- Structural Phase Speed (SPS) replaces static viscosity as the primary dynamical observable- tau_K_max: maximum rigidity persistence duration — measures how long a network sustains crystallized structure- Cross-universe comparability caveat formalized: tau_K_max measures duration of rigidity, NOT progress toward rupture. Qualitative pattern similarity across universes is informative but not predictive. 5 NEW SCENARIOS (22 total):- AI Full Ecosystem (NVDA, MSFT, GOOGL, META, AMD, AVGO, TSM, SMCI, ARM, PLTR, SNOW, AI): ν_s = 886.8, CRITICAL structural alert- AI Infrastructure (NVDA, AMD, AVGO, TSM, SMCI, ARM, MRVL): ν_s = 2.1, HEALTHY- Iran War Energy (XOM, CVX, COP, SLB, HAL, OXY, DVN, PXD): PR = 0.822, 82% pre-existing damage from Jun 2025 12-Day War- Iran War Global Macro (SPY, TLT, GLD, USO, UUP, EEM, VIX, DXY): Monitoring regime- AI Bubble Deep (extended AI ecosystem analysis with temporal archaeology) IRAN WAR ARCHAEOLOGICAL ANALYSIS:- Jun 12, 2025: Oh = 0.106, Phi = 0.000 — eve of 12-Day War, NORMAL- Jun 27, 2025: Oh = 1.161 — ALERT crystallizes 3 days post-ceasefire (not during war)- Jun 30, 2025: Phi = 0.220 — crosses detection threshold (Phi_c = 0.120)- Jul 3, 2025: Phi = 0.527 — MAXIMUM structural damage- Sep 15, 2025: Phi returns below threshold (3-month recovery)- Dec 19, 2025: Energy/Defense network Phi crossing — 71 days before Feb 2026 war- Feb 28, 2026: Iran War begins — system re-shocked before full recovery RESILIENCE HYPOTHESIS (Eurozone evidence):- Wave 1 (Jan 2010): Drive 0.081, Duration 2d, Phi peak 0.159 — Greek crisis, no defenses- Wave 2 (Sep 2010): Drive 0.081, Duration 4d, Phi peak 0.294 — Irish contagion- Wave 3 (May 2014): Drive 0.242, Duration 1d, Phi peak 0.241 — 3x stronger drive, LESS damage- 3.5 years between Wave 2 and Wave 3: EFSF, ESM, "whatever it takes" (Jul 2012), banking union- Preemptive strategic framework documented (Field state × Policy state → Action matrix) FR vs OR EXPERIMENT (negative result):- Hypothesis: Ollivier-Ricci curvature captures complementary information to Forman-Ricci- Result: Per-edge Spearman ρ = 0.952 ± 0.018 — OR is redundant with FR in kNN networks (n=13, k=5)- FR leads OR by 39 days in first low-curvature crossing- Conclusion: FR alone is sufficient for Kappa-FIN. Documented as honest negative result. PAPER v4:- Cross-universe comparability caveats added (Sections 5.6, 8, 9)- All DOIs updated for HUGO ecosystem references Repository: https://github.com/aprimora-ai/Kappa-FINPart of the Kappa Method ecosystem: Kappa-LLM (hallucination detection), Kappa-Radiante (structural navigation), Kappa-Education (student dropout prediction).HUGO AGI Framework: HUGO, ECHO, REMIND, RHEO, ANIMA. David Ohio | Independent Researcher | odavidohio@gmail.com | CC BY 4.0