[{"id": "AGeneralizedTrace", "title": "A Generalized Trace Reconstruction Problem: Recovering a String of Probabilities", "authors": "Joey Rivkin, Gregory Valiant, Paul Valiant", "venue": "STOC 2025", "blurb": "Formalizes the lower bound for the generalized trace reconstruction problem of recovering a string of probabilities from random traces.", "pdf_url": "/files/AGeneralizedTrace/A_Generalized_Trace_Reconstruction_Problem_Recovering_a_String_of_Probabilities.pdf", "counts": {"envs": 140, "decls": 1228, "links": 1228}}, {"id": "ASharp", "title": "A Sharp Version of Talagrand's Selector Process Conjecture and an Application to Rounding Fractional Covers", "authors": "Huy Tuan Pham", "venue": "STOC 2025", "blurb": "Formalizes a sharp version of Talagrand's selector process conjecture and its consequence for rounding fractional covers to integral ones.", "pdf_url": "/files/ASharp/A_sharp_version_of_Talagrands_selector_process_conjecture_and_an_application_to_rounding_fractional_covers.pdf", "counts": {"envs": 120, "decls": 150, "links": 150}}, {"id": "ApproximantionMedian", "title": "Approximation Guarantees of the Median Mechanism in \u211d\u1d48", "authors": "Nick Gravin, Jianhao Jia", "venue": "STOC 2025", "blurb": "Formalizes the dimension-independent approximation ratio of the coordinate-wise median mechanism in \u211d\u1d48.", "pdf_url": "/files/ApproximantionMedian/Approximation_guarantees_of_Median_Mechanism_in_\u211dd.pdf", "counts": {"envs": 162, "decls": 255, "links": 255}}, {"id": "EfficientlyLeanringMixtures", "title": "Efficiently Learning Mixtures of Two Gaussians", "authors": "Adam Tauman Kalai, Ankur Moitra, Gregory Valiant", "venue": "STOC 2010", "blurb": "Formalizes that the first six moments of a one-dimensional mixture of two Gaussians suffice to robustly recover its parameters.", "pdf_url": "/files/EfficientlyLeanringMixtures/Efficiently_Learning_Mixtures_of_Two_Gaussians.pdf", "counts": {"envs": 489, "decls": 652, "links": 624}}, {"id": "Refuting", "title": "Refuting the Direct Sum Conjecture for Total Functions in Deterministic Communication Complexity", "authors": "Simon Mackenzie, Abdallah Saffidine", "venue": "STOC 2025", "blurb": "Formalizes a counterexample refuting the direct sum conjecture for total functions in deterministic communication complexity.", "pdf_url": "/files/Refuting/Refuting_the_Direct_Sum_Conjecture_for_Total_Functions_in_Deterministic_Communication_Complexity.pdf", "counts": {"envs": 640, "decls": 294, "links": 290}}, {"id": "cdc", "title": "A Proof of the Cycle Double Cover Conjecture", "authors": "OpenAI", "venue": "OpenAI note (2025)", "blurb": "Formalizes a proof of the cycle double cover conjecture \u2014 every finite bridgeless graph has a collection of cycles covering each edge exactly twice \u2014 reducing it to an elementary linear-algebra argument over \ud835\udd3d\u2082\u00b3.", "pdf_url": "/files/cdc/cdc_proof.pdf", "counts": {"envs": 14, "decls": 497, "links": 497}}, {"id": "unitdistance", "title": "Planar Point Sets with Many Unit Distances", "authors": "OpenAI", "venue": "OpenAI note (2026)", "blurb": "Formalizes the disproof of Erd\u0151s's unit-distance conjecture: an infinite unramified 3-tower of totally real fields yields n-point planar sets with \u03bd(n) \u2265 n^{1+\u03b4} unit distances for infinitely many n.", "pdf_url": "/files/unitdistance/unit-distance-proof.pdf", "counts": {"envs": 0, "decls": 464, "links": 461}}, {"id": "StrongPerfectGraphTheorem", "title": "The Strong Perfect Graph Theorem", "authors": "Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas", "venue": "Annals of Mathematics 164 (2006)", "blurb": "Formalizes the strong perfect graph theorem \u2014 a graph is perfect if and only if it is Berge \u2014 through the paper's structure theorem: every Berge graph is basic, or one of it and its complement admits a proper 2-join, or it admits a proper homogeneous pair or a balanced skew partition. The main theorem is sorry-free with only Lean's three foundational axioms.", "pdf_url": "/files/StrongPerfectGraphTheorem/perfect.pdf", "counts": {"envs": 65, "decls": 6855, "links": 5343}}]