Dimensional Collapse and Anomalous Scaling in Multi-Asset Financial Markets: Real-Time Early Warning via Topological Phase Space Manifolds

Manuscript v2 (September 2026) of Paper 4 in the author’s econophysics / quantitative-finance series. This deposit archives the full preprint PDF, LaTeX source, embedded TikZ figures, and licensing files for a dual-reading phase-space framework built on the information functional I(T, D) = A − p·log₂(T) + ½·log₂(D) with master exponent p = 2H + 1. The same coordinates (p, D_eff) are used in two complementary ways: (1) a systemic early-warning reading when p rises toward the Chirikov numerical landmark (~2.34) and the covariance participation-ratio dimension D_eff collapses; (2) a market-health / all-clear reading when D_eff stays elevated (~5) and p remains moderate (~2.22), indicating a diversified return manifold. Empirical case study: 40 leading S&P 500 stocks across Technology, Financials, Energy, and Health Care (Yahoo Finance), contrasting calm 2019 (250 trading days) with the Feb–Mar 2020 liquidity crash (49 trading days). Headline contrast: H 0.609→0.680, p 2.218→2.360, D_eff 5.09→1.83 (−64%). Builds on the methodological release Pirolo (2026a), doi:10.5281/zenodo.22287190. Related companion (shared projective–informational lineage, different domain): Projective-Relational KV-Cache, doi:10.5281/zenodo.22326711. License: CC BY-NC-ND 4.0 (manuscript text and figures). PolyForm Noncommercial License 1.0.0 (all algorithms and code). Author: Andrés Sebastián Pirolo (ORCID 0009-0004-3899-1222). **Keywords** econophysics; Hurst exponent; dimensional collapse; participation ratio; covariance spectrum; early-warning signals; market-health indicator; anomalous diffusion; multi-asset markets; Chirikov map; random matrix theory; topological phase space; systemic risk; COVID-19 crash