Hankel-Geometric Matrix Completion for Limit Order Book State Estimation

A Riemannian ADMM Framework with Information Geometry Analysis

Authors: Ritesh Roshan Sahoo, Arushi Uppal, Rudru Mahima, Arnav Sharma
Affiliation: School of Artificial Intelligence, Amrita Vishwa Vidyapeetham, Delhi NCR
Data: Binance aggTrades — BTC, ETH, SOL, ADA — April 3–6, 2026 — 100 ms bars

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Package Structure

FINAL_PACKAGE/
├── README.md                        ← This file
│
├── paper/
│   ├── final_v5.tex                 ← LaTeX source (equation-15 spacing fixed)
│   ├── references.bib               ← BibTeX bibliography
│   └── hankel_lob_FINAL.pdf         ← Compiled research paper (final)
│
├── code/
│   ├── main.py                      ← Entry point — runs full pipeline
│   ├── pipeline.py                  ← Top-level orchestration
│   ├── core/
│   │   └── hankel_engine.py         ← R-ADMM, Hankel lift, MP rank, IGI, Kyle-λ
│   ├── data/
│   │   └── pipeline.py              ← Binance aggTrades ingestion & bar construction
│   └── visualization/
│       └── visualize.py             ← All figure generation
│
├── figures/                         ← All 21 publication-ready figures (PNG)
│   ├── figA_multi_asset_returns.png
│   ├── figBC_recon_OFI.png
│   ├── figD1_hankel_btc.png  …  figD4_hankel_ada.png
│   ├── figD_hankel_combined.png
│   ├── figE1–E3  sv_spectrum (BTC/ETH/SOL)
│   ├── figF_admm_convergence.png
│   ├── figG_recon_error_conformal.png
│   ├── figH_conformal_anomaly.png
│   ├── figI_IGI_rolling.png
│   ├── figJ_IGI_RV_leadlag.png
│   ├── figK_kyle_lambda_rolling.png
│   ├── figL_IGI_crossasset_corr.png
│   ├── figM_allasset_recon_error.png
│   ├── figN_quant_performance_table.png
│   ├── figO_RIP_verification.png
│   ├── figP_missingness_mask.png
│   └── lob_research_figure.png
│
└── outputs/
    └── results_summary.txt          ← Full per-asset metrics (MSE, R², Pearson r, etc.)

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Key Results

Asset	MSE	R²	Pearson r	Dir. Acc	Kyle λ	RIP δ₂ᵣ
BTC	0.103	0.894	0.956	88.9%	0.001365	0.300 ✓
ETH	0.096	0.900	0.958	88.5%	0.002373	0.300 ✓
SOL	0.117	0.872	0.951	86.4%	0.003613	0.300 ✓
ADA	0.088	0.910	0.964	83.0%	0.000218	0.300 ✓

RIP threshold: √2 − 1 ≈ 0.414. All assets pass (δ₂ᵣ ≈ 0.300 < 0.414).

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LaTeX Fix Applied

Equation 15 (augmented Lagrangian) was corrected from a broken two-line align + \notag construct (which caused a vertical spacing gap in the two-column layout) to a clean single-line equation environment.

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Compiling the Paper (Overleaf / local)

1. Upload contents of paper/ to Overleaf as the project root.
2. Set compiler to pdfLaTeX.
3. Place all figures/fig*.png in the same root directory.
4. Compile final_v5.tex.

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Phase Roadmap

• Phase 1 (complete): R-ADMM proof of concept on 4-day crypto data.
• Phase 2 (ICAIF 2026): IGI as leading volatility indicator; 1s bars, n≥5000; Kalman/GP/SAITS/TimesNet baselines.
• Phase 3 (QF Journal): Formal proofs for Conjecture 3.1 and Proposition 3.4.
• Phase 4 (JFE/RFS/JF): Systemic risk, COVID/FTX/Crypto Winter stress tests, IGI-informed execution.