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# 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](https://huggingface.co/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](https://huggingface.co/spaces/At1uri/topological-data-analysis-market-dynamics-studio)
- **Model Card**: [Topological Phase Transition Detector](https://huggingface.co/At1uri/topological-phase-transition-detector)
- **Dataset**: [Topological Market Persistence Benchmarks](https://huggingface.co/datasets/At1uri/topological-market-persistence-benchmarks)
- **Curated Collection**: [Institutional Quantitative AI Suite](https://huggingface.co/collections/At1uri/institutional-quantitative-ai-suite-6aeeaed0365774ae33b9621e)

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	# 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](https://huggingface.co/At1uri) as part of the Institutional Quantitative AI Suite.

	---

	## 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.

	---

	## Linked Hub Repositories
	- Interactive Space: [Topological Market Dynamics Studio](https://huggingface.co/spaces/At1uri/topological-data-analysis-market-dynamics-studio)
	- Model Card: [Topological Phase Transition Detector](https://huggingface.co/At1uri/topological-phase-transition-detector)
	- Dataset: [Topological Market Persistence Benchmarks](https://huggingface.co/datasets/At1uri/topological-market-persistence-benchmarks)
	- Curated Collection: [Institutional Quantitative AI Suite](https://huggingface.co/collections/At1uri/institutional-quantitative-ai-suite-6aeeaed0365774ae33b9621e)