README.md

Topological Data Analysis Research Vault

An industrial-grade computational research archive implementing Topological Data Analysis (TDA) and Persistent Homology for systemic risk, market phase transitions, and liquidity crash early warning signals.

Developed by At1uri as part of the Institutional Quantitative AI Suite.

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Vault Contents

1. 01_takens_embedding_and_rips_filtration.py: Optimal delay selection via Average Mutual Information (AMI), False Nearest Neighbors (FNN), and Vietoris-Rips filtration.
2. 02_matrix_reduction_persistent_homology.py: Boundary matrix reduction over field $\mathbb{F}_2$ with persistence pairing and elder rule.
3. 03_persistent_landscapes_and_wasserstein_distance.py: Bubenik (2015) persistence landscapes and 1-Wasserstein / bottleneck distance metrics.
4. 04_topological_crash_early_warning_system.py: Real-time topological condensation monitor generating rolling entropy and dynamic crash alert signals.
5. 05_multivariate_correlation_clique_complexes.py: Flag complexes / clique complexes on cross-asset correlation networks.
6. 06_tda_market_pipeline.ipynb: Master Jupyter Notebook integrating 3D phase space plots and empirical backtests.
7. topological_data_analysis_suite.zip: Complete packaged archive with cryptographic SHA-256 verification.

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Linked Hub Repositories

• Interactive Space: Topological Market Dynamics Studio
• Model Card: Topological Phase Transition Detector
• Dataset: Topological Market Persistence Benchmarks
• Curated Collection: Institutional Quantitative AI Suite