My Projects
AI-powered semantic search and Q&A over 700,000+ arXiv mathematics papers. Ask natural language questions like "What did Tao prove about prime gaps?" and get relevant papers with AI-synthesized answers. Hybrid search combines BGE embeddings with full-text search. Multi-LLM support (DeepSeek, GPT-5.2, Claude).
GitHub template that creates Python packages which maintain themselves. Monthly CI workflow tests with latest dependencies, and when tests fail, Claude AI automatically diagnoses and fixes compatibility issues, then creates a PR. No more bitrot - your packages essentially maintain themselves for pennies per year. A "Djinn" that fixes your code while you sleep.
Comprehensive benchmark comparing Mathpix against LLM-based OCR (Gemini, GPT-5.2, Claude) for mathematical PDF content. Surprising finding: Gemini 3 Flash is 6x cheaper than Mathpix AND more accurate. Mathpix produced critical semantic errors (reading "5" as "$\overline{0}$") that would break mathematical datasets.
Comprehensive evaluation of frontier LLMs on 320 classical analysis problems from Polya-Szego (1925). Key finding: 95.4% informal reasoning accuracy but only 2.8% complete Lean4 proofs. The 30x gap reveals that formal verification—not understanding—is the bottleneck in AI mathematics. Also verified the book contains no mathematical errors.
Follow-up to our benchmark: using Aristotle to automatically verify LLM-generated Lean proofs. 80/80 submissions verified successfully (100% success rate). Aristotle corrects formalization errors and synthesizes complete, machine-checkable proofs. The "30x gap" can be bridged with the right tools.
Revolutionary platform for human-AI design collaboration featuring reference image intelligence, auto-refinement with multimodal verification, and multi-provider ecosystem (OmniGen, FLUX, OpenAI, Stability AI). Proprietary verification engine ensures quality through iterative improvement and provides comprehensive analytics for continuous learning. Perfect for research, commercial applications, and technology licensing.
Revolutionary AI-powered system that automatically audits mathematical proofs in arXiv papers. Analyzed over 31,000 papers from math.DS and math.GT categories, identifying ~380 papers with critical errors or counterexamples. Features advanced search by author, verdict, journal tier, and provides detailed AI analysis with referee-style recommendations. 70% of wrong papers contain explicit counterexamples to their main claims.
Software suite for analyzing ideal convex polyhedra in hyperbolic 3-space. Using Rivin's variational characterization, we develop efficient algorithms for checking combinatorial realizability and finding volume-maximizing configurations. Our study reveals that maximal volume polyhedra exhibit dihedral angles that are rational multiples of Ο, and volume distributions follow a Beta distribution with mean converging to ln(2) β 0.69. Complete data provided for small vertex counts with verified rational angle structures.
FinData AI
Real-time sentiment analysis platform for stocks and politics. Features AI-powered sentiment scoring, interactive visualizations with EMA smoothing, and smart data downsampling for optimal performance. Built with modern web technologies and deployed on scalable cloud infrastructure.
DiRe-JAX
Advanced dimension reduction software suite that improves upon UMAP with enhanced performance and accuracy. Provides state-of-the-art algorithms for high-dimensional data visualization and analysis, enabling researchers and data scientists to better understand complex datasets through intelligent dimensionality reduction.
GraphEm
Comprehensive graph embedding software that maps complex network structures into low-dimensional spaces while preserving essential topological properties. Features automated centrality detection to identify key nodes and relationships, making it invaluable for social network analysis, biological networks, and knowledge graphs.
Modernized Python library for solving hard counting problems (#SAT, vertex covers) using tensor network contractions. Originally by Kourtis & Meichanetzidis, we updated it with NetworkX/opt_einsum, added Jones polynomial computation for knot theory, and made it self-maintaining with Claude-powered auto-fixes. Physics meets CS.
tl-tensor-examples
Fast Jones polynomial computation and knot identification using tensor networks. Hybrid engine auto-selects between tl-tensor (Rust) for wide braids and classical algorithms for narrow ones. Includes knot database up to 12 crossings, notation converters, and CLI tools. Self-maintaining with Claude-powered auto-fixes.
