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2512.12960/corollary-separation | Strict separation of 3-query RLDCs and LDCs | # Research Challenge: Strict separation of 3-query RLDCs and LDCs
> **Source paper:** 3-Query RLDCs are Strictly Stronger than 3-Query LDCs
> **Reference:** [arXiv:2512.12960](https://arxiv.org/abs/2512.12960) — Corollary separation
> **Task:** Prove the theorem stated below. This document is self-contained: all d... | 3-Query RLDCs are Strictly Stronger than 3-Query LDCs | 2512.12960 | https://arxiv.org/abs/2512.12960 | CC0 1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | 3-query-rldcs-are-strictly-stronger-than-3-query-ldcs/corollary-separation.md |
2512.12960/thm-RLDC-intro | Near-quadratic 3-query RLDC construction | # Research Challenge: Near-quadratic 3-query RLDC construction
> **Source paper:** 3-Query RLDCs are Strictly Stronger than 3-Query LDCs
> **Reference:** [arXiv:2512.12960](https://arxiv.org/abs/2512.12960) — Thm RLDC.intro
> **Task:** Prove the theorem stated below. This document is self-contained: all definition... | 3-Query RLDCs are Strictly Stronger than 3-Query LDCs | 2512.12960 | https://arxiv.org/abs/2512.12960 | CC0 1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | 3-query-rldcs-are-strictly-stronger-than-3-query-ldcs/thm-RLDC-intro.md |
2512.12960/thm-ldc-lb | Cubic lower bound for 3-query LDCs | # Research Challenge: Cubic lower bound for 3-query LDCs
> **Source paper:** 3-Query RLDCs are Strictly Stronger than 3-Query LDCs
> **Reference:** [arXiv:2512.12960](https://arxiv.org/abs/2512.12960) — Thm ldc.lb
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and nota... | 3-Query RLDCs are Strictly Stronger than 3-Query LDCs | 2512.12960 | https://arxiv.org/abs/2512.12960 | CC0 1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | 3-query-rldcs-are-strictly-stronger-than-3-query-ldcs/thm-ldc-lb.md |
2509.11399/theorem-hardness | Streaming hardness above the LP threshold | # Research Challenge: Streaming hardness above the LP threshold
> **Source paper:** A Dichotomy Theorem for Multi-Pass Streaming CSPs
> **Reference:** [arXiv:2509.11399](https://arxiv.org/abs/2509.11399) — Theorem hardness
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions... | A Dichotomy Theorem for Multi-Pass Streaming CSPs | 2509.11399 | https://arxiv.org/abs/2509.11399 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-dichotomy-theorem-for-multi-pass-streaming-csps/theorem-hardness.md |
2509.11399/theorem-main | Dichotomy for multi-pass streaming CSPs | # Research Challenge: Dichotomy for multi-pass streaming CSPs
> **Source paper:** A Dichotomy Theorem for Multi-Pass Streaming CSPs
> **Reference:** [arXiv:2509.11399](https://arxiv.org/abs/2509.11399) — Theorem main
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and n... | A Dichotomy Theorem for Multi-Pass Streaming CSPs | 2509.11399 | https://arxiv.org/abs/2509.11399 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-dichotomy-theorem-for-multi-pass-streaming-csps/theorem-main.md |
2509.11399/theorem-streaming-solve-lp | Streaming algorithm approximating the LP value | # Research Challenge: Streaming algorithm approximating the LP value
> **Source paper:** A Dichotomy Theorem for Multi-Pass Streaming CSPs
> **Reference:** [arXiv:2509.11399](https://arxiv.org/abs/2509.11399) — Theorem streaming.solve.lp
> **Task:** Prove the theorem stated below. This document is self-contained: ... | A Dichotomy Theorem for Multi-Pass Streaming CSPs | 2509.11399 | https://arxiv.org/abs/2509.11399 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-dichotomy-theorem-for-multi-pass-streaming-csps/theorem-streaming-solve-lp.md |
2510.08542/rapid | Rapid mixing of the Gibbs sampler at high temperature | # Research Challenge: Rapid mixing of the Gibbs sampler at high temperature
> **Source paper:** A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature
> **Reference:** [arXiv:2510.08542](https://arxiv.org/abs/2510.08542) — Rapid
> **Task:** Prove the th... | A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature | 2510.08542 | https://arxiv.org/abs/2510.08542 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-dobrushin-condition-for-quantum-markov-chains-rapid-mixing-and-conditional-mutual-information-at-high-temperature/rapid.md |
2510.08542/thm-cmi-main | Decay of conditional mutual information for high-temperature Gibbs states | # Research Challenge: Decay of conditional mutual information for high-temperature Gibbs states
> **Source paper:** A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature
> **Reference:** [arXiv:2510.08542](https://arxiv.org/abs/2510.08542) — Thm cmi.main... | A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature | 2510.08542 | https://arxiv.org/abs/2510.08542 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-dobrushin-condition-for-quantum-markov-chains-rapid-mixing-and-conditional-mutual-information-at-high-temperature/thm-cmi-main.md |
2510.08542/thm-dobrushin-implies-mixing | Quantum Dobrushin condition implies rapid mixing | # Research Challenge: Quantum Dobrushin condition implies rapid mixing
> **Source paper:** A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature
> **Reference:** [arXiv:2510.08542](https://arxiv.org/abs/2510.08542) — Thm dobrushin.implies.mixing
> **Ta... | A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature | 2510.08542 | https://arxiv.org/abs/2510.08542 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-dobrushin-condition-for-quantum-markov-chains-rapid-mixing-and-conditional-mutual-information-at-high-temperature/thm-dobrushin-implies-mixing.md |
2605.00797/theorem-main | Deterministic fully dynamic maximal matching in n^{1/2+o(1)} time | # Research Challenge: Deterministic fully dynamic maximal matching in n^{1/2+o(1)} time
> **Source paper:** A Faster Deterministic Algorithm for Fully Dynamic Maximal Matching
> **Reference:** [arXiv:2605.00797](https://arxiv.org/abs/2605.00797) — Theorem main
> **Task:** Prove the theorem stated below. This docum... | A Faster Deterministic Algorithm for Fully Dynamic Maximal Matching | 2605.00797 | https://arxiv.org/abs/2605.00797 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-faster-deterministic-algorithm-for-fully-dynamic-maximal-matching/theorem-main.md |
2603.00770/thm-gaussian-general | Lower bound for sparse Gaussian mean detection | # Research Challenge: Lower bound for sparse Gaussian mean detection
> **Source paper:** A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures
> **Reference:** [arXiv:2603.00770](https://arxiv.org/abs/2603.00770) — Thm gaussian.general
> **Task:** Prove the theorem stated below. This docum... | A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures | 2603.00770 | https://arxiv.org/abs/2603.00770 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-unified-approach-to-memory-sample-tradeoffs-for-detecting-planted-structures/thm-gaussian-general.md |
2603.00770/thm-main | Lower bound for planted biclique streaming detection | # Research Challenge: Lower bound for planted biclique streaming detection
> **Source paper:** A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures
> **Reference:** [arXiv:2603.00770](https://arxiv.org/abs/2603.00770) — Thm main
> **Task:** Prove the theorem stated below. This document is... | A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures | 2603.00770 | https://arxiv.org/abs/2603.00770 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-unified-approach-to-memory-sample-tradeoffs-for-detecting-planted-structures/thm-main.md |
2603.00770/thm-micgeneral | General memory-sample lower bound framework | # Research Challenge: General memory-sample lower bound framework
> **Source paper:** A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures
> **Reference:** [arXiv:2603.00770](https://arxiv.org/abs/2603.00770) — Thm micgeneral
> **Task:** Prove the theorem stated below. This document is se... | A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures | 2603.00770 | https://arxiv.org/abs/2603.00770 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-unified-approach-to-memory-sample-tradeoffs-for-detecting-planted-structures/thm-micgeneral.md |
2603.00770/thm-pca-general | Lower bound for sparse PCA detection | # Research Challenge: Lower bound for sparse PCA detection
> **Source paper:** A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures
> **Reference:** [arXiv:2603.00770](https://arxiv.org/abs/2603.00770) — Thm pca.general
> **Task:** Prove the theorem stated below. This document is self-con... | A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures | 2603.00770 | https://arxiv.org/abs/2603.00770 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | a-unified-approach-to-memory-sample-tradeoffs-for-detecting-planted-structures/thm-pca-general.md |
2606.17260/theorem-1 | Linear convergence of HFopt-avg under quadratic growth | # Research Challenge: Linear convergence of HFopt-avg under quadratic growth
> **Source paper:** Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time
> **Reference:** [arXiv:2606.17260](https://arxiv.org/abs/2606.17260) — Theorem 1
> **Task:** Prove the theorem stated below.... | Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time | 2606.17260 | https://arxiv.org/abs/2606.17260 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | accelerated-convex-optimization-via-hamiltonian-dynamics-with-deterministic-integration-time/theorem-1.md |
2606.17260/theorem-2 | Accelerated convergence of HFopt-avg for convex f | # Research Challenge: Accelerated convergence of HFopt-avg for convex f
> **Source paper:** Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time
> **Reference:** [arXiv:2606.17260](https://arxiv.org/abs/2606.17260) — Theorem 2
> **Task:** Prove the theorem stated below. This... | Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time | 2606.17260 | https://arxiv.org/abs/2606.17260 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | accelerated-convex-optimization-via-hamiltonian-dynamics-with-deterministic-integration-time/theorem-2.md |
2606.17260/theorem-3 | Linear convergence of discretized dHFA under quadratic growth | # Research Challenge: Linear convergence of discretized dHFA under quadratic growth
> **Source paper:** Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time
> **Reference:** [arXiv:2606.17260](https://arxiv.org/abs/2606.17260) — Theorem 3
> **Task:** Prove the theorem stated... | Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time | 2606.17260 | https://arxiv.org/abs/2606.17260 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | accelerated-convex-optimization-via-hamiltonian-dynamics-with-deterministic-integration-time/theorem-3.md |
2606.17260/theorem-4 | Accelerated convergence of discretized dHFA for convex f | # Research Challenge: Accelerated convergence of discretized dHFA for convex f
> **Source paper:** Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time
> **Reference:** [arXiv:2606.17260](https://arxiv.org/abs/2606.17260) — Theorem 4
> **Task:** Prove the theorem stated belo... | Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time | 2606.17260 | https://arxiv.org/abs/2606.17260 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | accelerated-convex-optimization-via-hamiltonian-dynamics-with-deterministic-integration-time/theorem-4.md |
2509.20848/theorem-3 | Query complexity of learning decision stumps | # Research Challenge: Query complexity of learning decision stumps
> **Source paper:** Actively Learning Halfspaces without Synthetic Data
> **Reference:** [arXiv:2509.20848](https://arxiv.org/abs/2509.20848) — Theorem 3
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions a... | Actively Learning Halfspaces without Synthetic Data | 2509.20848 | https://arxiv.org/abs/2509.20848 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | actively-learning-halfspaces-without-synthetic-data/theorem-3.md |
2509.20848/theorem-agnostic-formal | Tolerant agnostic learner for known-direction halfspaces | # Research Challenge: Tolerant agnostic learner for known-direction halfspaces
> **Source paper:** Actively Learning Halfspaces without Synthetic Data
> **Reference:** [arXiv:2509.20848](https://arxiv.org/abs/2509.20848) — Theorem agnostic.formal
> **Task:** Prove the theorem stated below. This document is self-co... | Actively Learning Halfspaces without Synthetic Data | 2509.20848 | https://arxiv.org/abs/2509.20848 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | actively-learning-halfspaces-without-synthetic-data/theorem-agnostic-formal.md |
2509.20848/theorem-d-direction-hs | Active learning halfspaces with known directions | # Research Challenge: Active learning halfspaces with known directions
> **Source paper:** Actively Learning Halfspaces without Synthetic Data
> **Reference:** [arXiv:2509.20848](https://arxiv.org/abs/2509.20848) — Theorem d.direction.hs
> **Task:** Prove the theorem stated below. This document is self-contained: ... | Actively Learning Halfspaces without Synthetic Data | 2509.20848 | https://arxiv.org/abs/2509.20848 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | actively-learning-halfspaces-without-synthetic-data/theorem-d-direction-hs.md |
2602.23448/lemma-subroutine-main | Fast augmenting-chain subroutine for degree reduction | # Research Challenge: Fast augmenting-chain subroutine for degree reduction
> **Source paper:** Additive One Approximation for Minimum Degree Spanning Tree: Breaking the $O(mn)$ Time Barrier
> **Reference:** [arXiv:2602.23448](https://arxiv.org/abs/2602.23448) — Lemma subroutine.main
> **Task:** Prove the theorem ... | Additive One Approximation for Minimum Degree Spanning Tree: Breaking the $O(mn)$ Time Barrier | 2602.23448 | https://arxiv.org/abs/2602.23448 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | additive-one-approximation-for-minimum-degree-spanning-tree-breaking-the-o-mn-time-barrier/lemma-subroutine-main.md |
2505.21892/theorem-4-1 | Almost-linear convergence of quantized transition diffusion | # Research Challenge: Almost-linear convergence of quantized transition diffusion
> **Source paper:** Almost Linear Convergence under Minimal Score Assumptions: Quantized Transition Diffusion
> **Reference:** [arXiv:2505.21892](https://arxiv.org/abs/2505.21892) — Theorem 4.1
> **Task:** Prove the theorem stated be... | Almost Linear Convergence under Minimal Score Assumptions: Quantized Transition Diffusion | 2505.21892 | https://arxiv.org/abs/2505.21892 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | almost-linear-convergence-under-minimal-score-assumptions-quantized-transition-diffusion/theorem-4-1.md |
2603.27795/theorem-1 | Optimal (1+ε)-approximation for stochastic vertex cover | # Research Challenge: Optimal (1+ε)-approximation for stochastic vertex cover
> **Source paper:** An Optimal Algorithm for Stochastic Vertex Cover
> **Reference:** [arXiv:2603.27795](https://arxiv.org/abs/2603.27795) — Theorem 1
> **Task:** Prove the theorem stated below. This document is self-contained: all defin... | An Optimal Algorithm for Stochastic Vertex Cover | 2603.27795 | https://arxiv.org/abs/2603.27795 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | an-optimal-algorithm-for-stochastic-vertex-cover/theorem-1.md |
2603.29702/theorem-lcs-main | Subquadratic (1-eps)-approximation for LCS | # Research Challenge: Subquadratic (1-eps)-approximation for LCS
> **Source paper:** Approximation Schemes for Edit Distance and LCS in Quasi-Strongly Subquadratic Time
> **Reference:** [arXiv:2603.29702](https://arxiv.org/abs/2603.29702) — Theorem lcs.main
> **Task:** Prove the theorem stated below. This document... | Approximation Schemes for Edit Distance and LCS in Quasi-Strongly Subquadratic Time | 2603.29702 | https://arxiv.org/abs/2603.29702 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | approximation-schemes-for-edit-distance-and-lcs-in-quasi-strongly-subquadratic-time/theorem-lcs-main.md |
2603.29702/theorem-main | Subquadratic (1+eps)-approximation for edit distance | # Research Challenge: Subquadratic (1+eps)-approximation for edit distance
> **Source paper:** Approximation Schemes for Edit Distance and LCS in Quasi-Strongly Subquadratic Time
> **Reference:** [arXiv:2603.29702](https://arxiv.org/abs/2603.29702) — Theorem main
> **Task:** Prove the theorem stated below. This do... | Approximation Schemes for Edit Distance and LCS in Quasi-Strongly Subquadratic Time | 2603.29702 | https://arxiv.org/abs/2603.29702 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | approximation-schemes-for-edit-distance-and-lcs-in-quasi-strongly-subquadratic-time/theorem-main.md |
2511.13659/thm-informal-hecke | Hecke equidistribution for rank-r module lattices | # Research Challenge: Hecke equidistribution for rank-r module lattices
> **Source paper:** Average hardness of SIVP for module lattices of fixed rank
> **Reference:** [arXiv:2511.13659](https://arxiv.org/abs/2511.13659) — Thm informal.hecke
> **Task:** Prove the theorem stated below. This document is self-contain... | Average hardness of SIVP for module lattices of fixed rank | 2511.13659 | https://arxiv.org/abs/2511.13659 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | average-hardness-of-sivp-for-module-lattices-of-fixed-rank/thm-informal-hecke.md |
2511.13659/thm-main | Average-case hardness of fixed-rank module SIVP | # Research Challenge: Average-case hardness of fixed-rank module SIVP
> **Source paper:** Average hardness of SIVP for module lattices of fixed rank
> **Reference:** [arXiv:2511.13659](https://arxiv.org/abs/2511.13659) — Thm main
> **Task:** Prove the theorem stated below. This document is self-contained: all defi... | Average hardness of SIVP for module lattices of fixed rank | 2511.13659 | https://arxiv.org/abs/2511.13659 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | average-hardness-of-sivp-for-module-lattices-of-fixed-rank/thm-main.md |
2509.20697/thm-Search_sqncp-qsdp_equivalence | Search QNCP and QSDP are equivalent | # Research Challenge: Search QNCP and QSDP are equivalent
> **Source paper:** Average-Case Complexity of Quantum Stabilizer Decoding
> **Reference:** [arXiv:2509.20697](https://arxiv.org/abs/2509.20697) — Thm Search_sqncp.qsdp_equivalence
> **Task:** Prove the theorem stated below. This document is self-contained:... | Average-Case Complexity of Quantum Stabilizer Decoding | 2509.20697 | https://arxiv.org/abs/2509.20697 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | average-case-complexity-of-quantum-stabilizer-decoding/thm-Search_sqncp-qsdp_equivalence.md |
2509.20697/thm-classical-representation-equivalent | Quantum LSN equivalent to classical LSN | # Research Challenge: Quantum LSN equivalent to classical LSN
> **Source paper:** Average-Case Complexity of Quantum Stabilizer Decoding
> **Reference:** [arXiv:2509.20697](https://arxiv.org/abs/2509.20697) — Thm classical.representation.equivalent
> **Task:** Prove the theorem stated below. This document is self-... | Average-Case Complexity of Quantum Stabilizer Decoding | 2509.20697 | https://arxiv.org/abs/2509.20697 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | average-case-complexity-of-quantum-stabilizer-decoding/thm-classical-representation-equivalent.md |
2509.20697/thm-decision-to-search-lsn | Search-to-decision reduction for LSN | # Research Challenge: Search-to-decision reduction for LSN
> **Source paper:** Average-Case Complexity of Quantum Stabilizer Decoding
> **Reference:** [arXiv:2509.20697](https://arxiv.org/abs/2509.20697) — Thm decision.to.search.lsn
> **Task:** Prove the theorem stated below. This document is self-contained: all d... | Average-Case Complexity of Quantum Stabilizer Decoding | 2509.20697 | https://arxiv.org/abs/2509.20697 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | average-case-complexity-of-quantum-stabilizer-decoding/thm-decision-to-search-lsn.md |
2507.15173/thm-alg-main | Recovering dense edges from Markov dynamics | # Research Challenge: Recovering dense edges from Markov dynamics
> **Source paper:** Better Models and Algorithms for Learning Ising Models from Dynamics
> **Reference:** [arXiv:2507.15173](https://arxiv.org/abs/2507.15173) — Thm alg.main
> **Task:** Prove the theorem stated below. This document is self-contained... | Better Models and Algorithms for Learning Ising Models from Dynamics | 2507.15173 | https://arxiv.org/abs/2507.15173 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | better-models-and-algorithms-for-learning-ising-models-from-dynamics/thm-alg-main.md |
2507.15173/thm-main-match | Recovering the residual matching of edges | # Research Challenge: Recovering the residual matching of edges
> **Source paper:** Better Models and Algorithms for Learning Ising Models from Dynamics
> **Reference:** [arXiv:2507.15173](https://arxiv.org/abs/2507.15173) — Thm main.match
> **Task:** Prove the theorem stated below. This document is self-contained... | Better Models and Algorithms for Learning Ising Models from Dynamics | 2507.15173 | https://arxiv.org/abs/2507.15173 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | better-models-and-algorithms-for-learning-ising-models-from-dynamics/thm-main-match.md |
2507.15173/thm-main-paramter | Estimating Ising coupling parameters from dynamics | # Research Challenge: Estimating Ising coupling parameters from dynamics
> **Source paper:** Better Models and Algorithms for Learning Ising Models from Dynamics
> **Reference:** [arXiv:2507.15173](https://arxiv.org/abs/2507.15173) — Thm main.paramter
> **Task:** Prove the theorem stated below. This document is se... | Better Models and Algorithms for Learning Ising Models from Dynamics | 2507.15173 | https://arxiv.org/abs/2507.15173 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | better-models-and-algorithms-for-learning-ising-models-from-dynamics/thm-main-paramter.md |
2510.21613/cor-easytouse | Explicit shadow path length bound | # Research Challenge: Explicit shadow path length bound
> **Source paper:** Beyond Smoothed Analysis: Analyzing the Simplex Method by the Book
> **Reference:** [arXiv:2510.21613](https://arxiv.org/abs/2510.21613) — Cor easytouse
> **Task:** Prove the theorem stated below. This document is self-contained: all defin... | Beyond Smoothed Analysis: Analyzing the Simplex Method by the Book | 2510.21613 | https://arxiv.org/abs/2510.21613 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | beyond-smoothed-analysis-analyzing-the-simplex-method-by-the-book/cor-easytouse.md |
2510.21613/thm-bound_p_slack-epoch | Expected shadow path length bound for simplex | # Research Challenge: Expected shadow path length bound for simplex
> **Source paper:** Beyond Smoothed Analysis: Analyzing the Simplex Method by the Book
> **Reference:** [arXiv:2510.21613](https://arxiv.org/abs/2510.21613) — Thm bound_p_slack.epoch
> **Task:** Prove the theorem stated below. This document is sel... | Beyond Smoothed Analysis: Analyzing the Simplex Method by the Book | 2510.21613 | https://arxiv.org/abs/2510.21613 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | beyond-smoothed-analysis-analyzing-the-simplex-method-by-the-book/thm-bound_p_slack-epoch.md |
2505.15652/theorem-1 | Faster MIS in high-girth graphs | # Research Challenge: Faster MIS in high-girth graphs
> **Source paper:** Breaking Barriers for Distributed MIS by Faster Degree Reduction
> **Reference:** [arXiv:2505.15652](https://arxiv.org/abs/2505.15652) — Theorem 1
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions a... | Breaking Barriers for Distributed MIS by Faster Degree Reduction | 2505.15652 | https://arxiv.org/abs/2505.15652 | CC0 1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | breaking-barriers-for-distributed-mis-by-faster-degree-reduction/theorem-1.md |
2505.15652/theorem-2 | Faster MIS in trees | # Research Challenge: Faster MIS in trees
> **Source paper:** Breaking Barriers for Distributed MIS by Faster Degree Reduction
> **Reference:** [arXiv:2505.15652](https://arxiv.org/abs/2505.15652) — Theorem 2
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation ... | Breaking Barriers for Distributed MIS by Faster Degree Reduction | 2505.15652 | https://arxiv.org/abs/2505.15652 | CC0 1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | breaking-barriers-for-distributed-mis-by-faster-degree-reduction/theorem-2.md |
2505.15652/theorem-7-2 | Fast degree reduction for bounded arboricity | # Research Challenge: Fast degree reduction for bounded arboricity
> **Source paper:** Breaking Barriers for Distributed MIS by Faster Degree Reduction
> **Reference:** [arXiv:2505.15652](https://arxiv.org/abs/2505.15652) — Theorem 7.2
> **Task:** Prove the theorem stated below. This document is self-contained: al... | Breaking Barriers for Distributed MIS by Faster Degree Reduction | 2505.15652 | https://arxiv.org/abs/2505.15652 | CC0 1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | breaking-barriers-for-distributed-mis-by-faster-degree-reduction/theorem-7-2.md |
2505.15652/theorem-lb | Lower bound on one-round independent set | # Research Challenge: Lower bound on one-round independent set
> **Source paper:** Breaking Barriers for Distributed MIS by Faster Degree Reduction
> **Reference:** [arXiv:2505.15652](https://arxiv.org/abs/2505.15652) — Theorem lb
> **Task:** Prove the theorem stated below. This document is self-contained: all def... | Breaking Barriers for Distributed MIS by Faster Degree Reduction | 2505.15652 | https://arxiv.org/abs/2505.15652 | CC0 1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | breaking-barriers-for-distributed-mis-by-faster-degree-reduction/theorem-lb.md |
2603.22167/theorem-calibeating-calibration | Simultaneous calibeating and calibration tradeoff | # Research Challenge: Simultaneous calibeating and calibration tradeoff
> **Source paper:** Calibeating Made Simple
> **Reference:** [arXiv:2603.22167](https://arxiv.org/abs/2603.22167) — Theorem calibeating.calibration
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions an... | Calibeating Made Simple | 2603.22167 | https://arxiv.org/abs/2603.22167 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | calibeating-made-simple/theorem-calibeating-calibration.md |
2603.22167/theorem-lower-bound | Lower bound on calibeating rate | # Research Challenge: Lower bound on calibeating rate
> **Source paper:** Calibeating Made Simple
> **Reference:** [arXiv:2603.22167](https://arxiv.org/abs/2603.22167) — Theorem lower.bound
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation needed to understan... | Calibeating Made Simple | 2603.22167 | https://arxiv.org/abs/2603.22167 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | calibeating-made-simple/theorem-lower-bound.md |
2603.22167/theorem-upper-bound-multi-calibeating | Multi-calibeating from calibeating plus experts | # Research Challenge: Multi-calibeating from calibeating plus experts
> **Source paper:** Calibeating Made Simple
> **Reference:** [arXiv:2603.22167](https://arxiv.org/abs/2603.22167) — Theorem upper.bound.multi.calibeating
> **Task:** Prove the theorem stated below. This document is self-contained: all definition... | Calibeating Made Simple | 2603.22167 | https://arxiv.org/abs/2603.22167 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | calibeating-made-simple/theorem-upper-bound-multi-calibeating.md |
2603.22167/theorem-upper-bound | Calibeating from online regret bounds | # Research Challenge: Calibeating from online regret bounds
> **Source paper:** Calibeating Made Simple
> **Reference:** [arXiv:2603.22167](https://arxiv.org/abs/2603.22167) — Theorem upper.bound
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation needed to und... | Calibeating Made Simple | 2603.22167 | https://arxiv.org/abs/2603.22167 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | calibeating-made-simple/theorem-upper-bound.md |
2511.15142/theorem-boolean-linear-optimization | Combinatorial linear optimization with comparison queries | # Research Challenge: Combinatorial linear optimization with comparison queries
> **Source paper:** Combinatorial Optimization using Comparison Oracles
> **Reference:** [arXiv:2511.15142](https://arxiv.org/abs/2511.15142) — Theorem boolean.linear.optimization
> **Task:** Prove the theorem stated below. This docume... | Combinatorial Optimization using Comparison Oracles | 2511.15142 | https://arxiv.org/abs/2511.15142 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | combinatorial-optimization-using-comparison-oracles/theorem-boolean-linear-optimization.md |
2511.15142/theorem-general-linear-optimization | Linear optimization via comparisons and conic dimension | # Research Challenge: Linear optimization via comparisons and conic dimension
> **Source paper:** Combinatorial Optimization using Comparison Oracles
> **Reference:** [arXiv:2511.15142](https://arxiv.org/abs/2511.15142) — Theorem general.linear.optimization
> **Task:** Prove the theorem stated below. This document... | Combinatorial Optimization using Comparison Oracles | 2511.15142 | https://arxiv.org/abs/2511.15142 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | combinatorial-optimization-using-comparison-oracles/theorem-general-linear-optimization.md |
2511.15142/theorem-matroids-matchings-paths | Matroids, intersections, and paths via comparisons | # Research Challenge: Matroids, intersections, and paths via comparisons
> **Source paper:** Combinatorial Optimization using Comparison Oracles
> **Reference:** [arXiv:2511.15142](https://arxiv.org/abs/2511.15142) — Theorem matroids.matchings.paths
> **Task:** Prove the theorem stated below. This document is self... | Combinatorial Optimization using Comparison Oracles | 2511.15142 | https://arxiv.org/abs/2511.15142 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | combinatorial-optimization-using-comparison-oracles/theorem-matroids-matchings-paths.md |
2511.15142/theorem-min-cut | Exact minimum cut via cut comparison queries | # Research Challenge: Exact minimum cut via cut comparison queries
> **Source paper:** Combinatorial Optimization using Comparison Oracles
> **Reference:** [arXiv:2511.15142](https://arxiv.org/abs/2511.15142) — Theorem min.cut
> **Task:** Prove the theorem stated below. This document is self-contained: all definit... | Combinatorial Optimization using Comparison Oracles | 2511.15142 | https://arxiv.org/abs/2511.15142 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | combinatorial-optimization-using-comparison-oracles/theorem-min-cut.md |
2602.21390/theorem-OI | Online Outcome Indistinguishability via Defensive Generation | # Research Challenge: Online Outcome Indistinguishability via Defensive Generation
> **Source paper:** Defensive Generation
> **Reference:** [arXiv:2602.21390](https://arxiv.org/abs/2602.21390) — Theorem OI
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation ne... | Defensive Generation | 2602.21390 | https://arxiv.org/abs/2602.21390 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | defensive-generation/theorem-OI.md |
2510.16991/theorem-main-reduction | Deterministic reduction from 3COL to GapSVP | # Research Challenge: Deterministic reduction from 3COL to GapSVP
> **Source paper:** Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$
> **Reference:** [arXiv:2510.16991](https://arxiv.org/abs/2510.16991) — Theorem main.reduction
> **Task:** Prove the theorem stated belo... | Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$ | 2510.16991 | https://arxiv.org/abs/2510.16991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-hardness-of-approximation-of-unique-svp-and-gapsvp-in-lp-norms-for-p-2/theorem-main-reduction.md |
2510.16991/theorem-svp-high-p | Stronger GapSVP hardness for large p | # Research Challenge: Stronger GapSVP hardness for large p
> **Source paper:** Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$
> **Reference:** [arXiv:2510.16991](https://arxiv.org/abs/2510.16991) — Theorem svp.high.p
> **Task:** Prove the theorem stated below. This doc... | Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$ | 2510.16991 | https://arxiv.org/abs/2510.16991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-hardness-of-approximation-of-unique-svp-and-gapsvp-in-lp-norms-for-p-2/theorem-svp-high-p.md |
2510.16991/theorem-svp-p-gt-2 | Deterministic hardness of GapSVP in l_p, p>2 | # Research Challenge: Deterministic hardness of GapSVP in l_p, p>2
> **Source paper:** Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$
> **Reference:** [arXiv:2510.16991](https://arxiv.org/abs/2510.16991) — Theorem svp.p.gt.2
> **Task:** Prove the theorem stated below. ... | Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$ | 2510.16991 | https://arxiv.org/abs/2510.16991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-hardness-of-approximation-of-unique-svp-and-gapsvp-in-lp-norms-for-p-2/theorem-svp-p-gt-2.md |
2510.16991/theorem-usvp-high-p | Stronger uSVP hardness for large p | # Research Challenge: Stronger uSVP hardness for large p
> **Source paper:** Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$
> **Reference:** [arXiv:2510.16991](https://arxiv.org/abs/2510.16991) — Theorem usvp.high.p
> **Task:** Prove the theorem stated below. This docu... | Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$ | 2510.16991 | https://arxiv.org/abs/2510.16991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-hardness-of-approximation-of-unique-svp-and-gapsvp-in-lp-norms-for-p-2/theorem-usvp-high-p.md |
2510.16991/theorem-usvp-p-gt-2 | Deterministic hardness of unique-SVP in l_p, p>2 | # Research Challenge: Deterministic hardness of unique-SVP in l_p, p>2
> **Source paper:** Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$
> **Reference:** [arXiv:2510.16991](https://arxiv.org/abs/2510.16991) — Theorem usvp.p.gt.2
> **Task:** Prove the theorem stated be... | Deterministic Hardness of Approximation of Unique-SVP and GapSVP in $\ell_p$ norms for $p>2$ | 2510.16991 | https://arxiv.org/abs/2510.16991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-hardness-of-approximation-of-unique-svp-and-gapsvp-in-lp-norms-for-p-2/theorem-usvp-p-gt-2.md |
2511.05176/theorem-det-gs | Deterministic Guruswami-Sudan list decoding of Reed-Solomon codes | # Research Challenge: Deterministic Guruswami-Sudan list decoding of Reed-Solomon codes
> **Source paper:** Deterministic list decoding of Reed-Solomon codes
> **Reference:** [arXiv:2511.05176](https://arxiv.org/abs/2511.05176) — Theorem det.gs
> **Task:** Prove the theorem stated below. This document is self-cont... | Deterministic list decoding of Reed-Solomon codes | 2511.05176 | https://arxiv.org/abs/2511.05176 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-list-decoding-of-reed-solomon-codes/theorem-det-gs.md |
2511.05176/theorem-sudan-technical | Deterministic Sudan list decoding of Reed-Solomon codes | # Research Challenge: Deterministic Sudan list decoding of Reed-Solomon codes
> **Source paper:** Deterministic list decoding of Reed-Solomon codes
> **Reference:** [arXiv:2511.05176](https://arxiv.org/abs/2511.05176) — Theorem sudan.technical
> **Task:** Prove the theorem stated below. This document is self-conta... | Deterministic list decoding of Reed-Solomon codes | 2511.05176 | https://arxiv.org/abs/2511.05176 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-list-decoding-of-reed-solomon-codes/theorem-sudan-technical.md |
2511.08551/theorem-pathcover | Deterministic path cover via clustered DAGs | # Research Challenge: Deterministic path cover via clustered DAGs
> **Source paper:** Deterministic Negative-Weight Shortest Paths in Nearly Linear Time via Path Covers
> **Reference:** [arXiv:2511.08551](https://arxiv.org/abs/2511.08551) — Theorem pathcover
> **Task:** Prove the theorem stated below. This documen... | Deterministic Negative-Weight Shortest Paths in Nearly Linear Time via Path Covers | 2511.08551 | https://arxiv.org/abs/2511.08551 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-negative-weight-shortest-paths-in-nearly-linear-time-via-path-covers/theorem-pathcover.md |
2511.08551/thm-main | Deterministic near-linear negative-weight SSSP | # Research Challenge: Deterministic near-linear negative-weight SSSP
> **Source paper:** Deterministic Negative-Weight Shortest Paths in Nearly Linear Time via Path Covers
> **Reference:** [arXiv:2511.08551](https://arxiv.org/abs/2511.08551) — Thm main
> **Task:** Prove the theorem stated below. This document is s... | Deterministic Negative-Weight Shortest Paths in Nearly Linear Time via Path Covers | 2511.08551 | https://arxiv.org/abs/2511.08551 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-negative-weight-shortest-paths-in-nearly-linear-time-via-path-covers/thm-main.md |
2511.08551/thm-path-cover-intro | Covering d-paths with clustered projection | # Research Challenge: Covering d-paths with clustered projection
> **Source paper:** Deterministic Negative-Weight Shortest Paths in Nearly Linear Time via Path Covers
> **Reference:** [arXiv:2511.08551](https://arxiv.org/abs/2511.08551) — Thm path.cover.intro
> **Task:** Prove the theorem stated below. This docum... | Deterministic Negative-Weight Shortest Paths in Nearly Linear Time via Path Covers | 2511.08551 | https://arxiv.org/abs/2511.08551 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | deterministic-negative-weight-shortest-paths-in-nearly-linear-time-via-path-covers/thm-path-cover-intro.md |
2606.12879/theorem-1 | Exact vertex matching guarantee for diffusion-network alignment | # Research Challenge: Exact vertex matching guarantee for diffusion-network alignment
> **Source paper:** Diffusion-Network Alignment: An Efficient Algorithm and Explicit Probability Bounds
> **Reference:** [arXiv:2606.12879](https://arxiv.org/abs/2606.12879) — Theorem 1
> **Task:** Prove the theorem stated below.... | Diffusion-Network Alignment: An Efficient Algorithm and Explicit Probability Bounds | 2606.12879 | https://arxiv.org/abs/2606.12879 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | diffusion-network-alignment-an-efficient-algorithm-and-explicit-probability-bounds/theorem-1.md |
2606.12879/theorem-tree-test | Tree correlation detection threshold via order statistic | # Research Challenge: Tree correlation detection threshold via order statistic
> **Source paper:** Diffusion-Network Alignment: An Efficient Algorithm and Explicit Probability Bounds
> **Reference:** [arXiv:2606.12879](https://arxiv.org/abs/2606.12879) — Theorem tree.test
> **Task:** Prove the theorem stated below... | Diffusion-Network Alignment: An Efficient Algorithm and Explicit Probability Bounds | 2606.12879 | https://arxiv.org/abs/2606.12879 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | diffusion-network-alignment-an-efficient-algorithm-and-explicit-probability-bounds/theorem-tree-test.md |
2510.04929/theorem-factorization | QHO Evolution Operator Factorization | # Research Challenge: QHO Evolution Operator Factorization
> **Source paper:** Efficient Quantum Hermite Transform
> **Reference:** [arXiv:2510.04929](https://arxiv.org/abs/2510.04929) — Theorem factorization
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation ... | Efficient Quantum Hermite Transform | 2510.04929 | https://arxiv.org/abs/2510.04929 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-quantum-hermite-transform/theorem-factorization.md |
2510.04929/theorem-fastforwarding | Fast-Forwarding Discrete QHO Simulation | # Research Challenge: Fast-Forwarding Discrete QHO Simulation
> **Source paper:** Efficient Quantum Hermite Transform
> **Reference:** [arXiv:2510.04929](https://arxiv.org/abs/2510.04929) — Theorem fastforwarding
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notat... | Efficient Quantum Hermite Transform | 2510.04929 | https://arxiv.org/abs/2510.04929 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-quantum-hermite-transform/theorem-fastforwarding.md |
2510.04929/theorem-quantumhermitetransform | Efficient Quantum Hermite Transform | # Research Challenge: Efficient Quantum Hermite Transform
> **Source paper:** Efficient Quantum Hermite Transform
> **Reference:** [arXiv:2510.04929](https://arxiv.org/abs/2510.04929) — Theorem quantumhermitetransform
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and ... | Efficient Quantum Hermite Transform | 2510.04929 | https://arxiv.org/abs/2510.04929 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-quantum-hermite-transform/theorem-quantumhermitetransform.md |
2510.04929/thm-apx-hermite | Fast Hermite Coefficient Sampling | # Research Challenge: Fast Hermite Coefficient Sampling
> **Source paper:** Efficient Quantum Hermite Transform
> **Reference:** [arXiv:2510.04929](https://arxiv.org/abs/2510.04929) — Thm apx.hermite
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation needed to... | Efficient Quantum Hermite Transform | 2510.04929 | https://arxiv.org/abs/2510.04929 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-quantum-hermite-transform/thm-apx-hermite.md |
2601.14906/corollary-main-structural | Characterization of structurally bounded expansion | # Research Challenge: Characterization of structurally bounded expansion
> **Source paper:** Efficient reversal of transductions of sparse graph classes
> **Reference:** [arXiv:2601.14906](https://arxiv.org/abs/2601.14906) — Corollary main.structural
> **Task:** Prove the theorem stated below. This document is sel... | Efficient reversal of transductions of sparse graph classes | 2601.14906 | https://arxiv.org/abs/2601.14906 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-reversal-of-transductions-of-sparse-graph-classes/corollary-main-structural.md |
2601.14906/theorem-almost-nowhere-dense-sparsification | Efficient almost-nowhere-dense sparsification of stable classes | # Research Challenge: Efficient almost-nowhere-dense sparsification of stable classes
> **Source paper:** Efficient reversal of transductions of sparse graph classes
> **Reference:** [arXiv:2601.14906](https://arxiv.org/abs/2601.14906) — Theorem almost.nowhere.dense.sparsification
> **Task:** Prove the theorem sta... | Efficient reversal of transductions of sparse graph classes | 2601.14906 | https://arxiv.org/abs/2601.14906 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-reversal-of-transductions-of-sparse-graph-classes/theorem-almost-nowhere-dense-sparsification.md |
2601.14906/theorem-main | Efficient sparsification of stable classes with linear neighborhood complexity | # Research Challenge: Efficient sparsification of stable classes with linear neighborhood complexity
> **Source paper:** Efficient reversal of transductions of sparse graph classes
> **Reference:** [arXiv:2601.14906](https://arxiv.org/abs/2601.14906) — Theorem main
> **Task:** Prove the theorem stated below. This ... | Efficient reversal of transductions of sparse graph classes | 2601.14906 | https://arxiv.org/abs/2601.14906 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-reversal-of-transductions-of-sparse-graph-classes/theorem-main.md |
2602.15008/theorem-masking-main | KL convergence for masking discrete diffusion | # Research Challenge: KL convergence for masking discrete diffusion
> **Source paper:** Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
> **Reference:** [arXiv:2602.15008](https://arxiv.org/abs/2602.15008) — Theorem masking.main
> **Task:** Prove the theorem stated below. This docu... | Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees | 2602.15008 | https://arxiv.org/abs/2602.15008 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-sampling-with-discrete-diffusion-models-sharp-and-adaptive-guarantees/theorem-masking-main.md |
2602.15008/theorem-uniform-lower | Lower bound on iterations for uniform sampler | # Research Challenge: Lower bound on iterations for uniform sampler
> **Source paper:** Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
> **Reference:** [arXiv:2602.15008](https://arxiv.org/abs/2602.15008) — Theorem uniform.lower
> **Task:** Prove the theorem stated below. This doc... | Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees | 2602.15008 | https://arxiv.org/abs/2602.15008 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-sampling-with-discrete-diffusion-models-sharp-and-adaptive-guarantees/theorem-uniform-lower.md |
2602.15008/theorem-uniform | KL convergence of uniform-noise discrete diffusion sampler | # Research Challenge: KL convergence of uniform-noise discrete diffusion sampler
> **Source paper:** Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
> **Reference:** [arXiv:2602.15008](https://arxiv.org/abs/2602.15008) — Theorem uniform
> **Task:** Prove the theorem stated below. T... | Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees | 2602.15008 | https://arxiv.org/abs/2602.15008 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-sampling-with-discrete-diffusion-models-sharp-and-adaptive-guarantees/theorem-uniform.md |
2511.04907/theorem-smcal-general-introduction | Oracle-efficient swap multicalibration for elicitable properties | # Research Challenge: Oracle-efficient swap multicalibration for elicitable properties
> **Source paper:** Efficient Swap Multicalibration of Elicitable Properties
> **Reference:** [arXiv:2511.04907](https://arxiv.org/abs/2511.04907) — Theorem smcal.general.introduction
> **Task:** Prove the theorem stated below. ... | Efficient Swap Multicalibration of Elicitable Properties | 2511.04907 | https://arxiv.org/abs/2511.04907 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-swap-multicalibration-of-elicitable-properties/theorem-smcal-general-introduction.md |
2511.04907/theorem-smcal-general-result | General regret-dependent swap multicalibration bound | # Research Challenge: General regret-dependent swap multicalibration bound
> **Source paper:** Efficient Swap Multicalibration of Elicitable Properties
> **Reference:** [arXiv:2511.04907](https://arxiv.org/abs/2511.04907) — Theorem smcal.general.result
> **Task:** Prove the theorem stated below. This document is s... | Efficient Swap Multicalibration of Elicitable Properties | 2511.04907 | https://arxiv.org/abs/2511.04907 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | efficient-swap-multicalibration-of-elicitable-properties/theorem-smcal-general-result.md |
2512.24152/theorem-logarithmic-reduction-to-slc-black-box-sampling | Logarithmic reduction of SLC sampling to well-conditioned subproblems | # Research Challenge: Logarithmic reduction of SLC sampling to well-conditioned subproblems
> **Source paper:** Score-based sampling without diffusions: Guidance from a simple and modular scheme
> **Reference:** [arXiv:2512.24152](https://arxiv.org/abs/2512.24152) — Theorem logarithmic.reduction.to.slc.black.box.sam... | Fast Score-Based Sampling via Log-Concave Reductions | 2512.24152 | https://arxiv.org/abs/2512.24152 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fast-score-based-sampling-via-log-concave-reductions/theorem-logarithmic-reduction-to-slc-black-box-sampling.md |
2512.24152/theorem-slc-reduction-for-multi-modal-case | SLC reduction for multi-modal targets | # Research Challenge: SLC reduction for multi-modal targets
> **Source paper:** Score-based sampling without diffusions: Guidance from a simple and modular scheme
> **Reference:** [arXiv:2512.24152](https://arxiv.org/abs/2512.24152) — Theorem slc.reduction.for.multi.modal.case
> **Task:** Prove the theorem stated ... | Fast Score-Based Sampling via Log-Concave Reductions | 2512.24152 | https://arxiv.org/abs/2512.24152 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fast-score-based-sampling-via-log-concave-reductions/theorem-slc-reduction-for-multi-modal-case.md |
2506.11355/maintheorem | Certifying any pure state with single-qubit measurements | # Research Challenge: Certifying any pure state with single-qubit measurements
> **Source paper:** Few Single-Qubit Measurements Suffice to Certify Any Quantum State
> **Reference:** [arXiv:2506.11355](https://arxiv.org/abs/2506.11355) — Maintheorem
> **Task:** Prove the theorem stated below. This document is self... | Few Single-Qubit Measurements Suffice to Certify Any Quantum State | 2506.11355 | https://arxiv.org/abs/2506.11355 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | few-single-qubit-measurements-suffice-to-certify-any-quantum-state/maintheorem.md |
2506.11355/thm-main | Single-copy fidelity certification via single-qubit measurements | # Research Challenge: Single-copy fidelity certification via single-qubit measurements
> **Source paper:** Few Single-Qubit Measurements Suffice to Certify Any Quantum State
> **Reference:** [arXiv:2506.11355](https://arxiv.org/abs/2506.11355) — Thm main
> **Task:** Prove the theorem stated below. This document is... | Few Single-Qubit Measurements Suffice to Certify Any Quantum State | 2506.11355 | https://arxiv.org/abs/2506.11355 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | few-single-qubit-measurements-suffice-to-certify-any-quantum-state/thm-main.md |
2603.28265/theorem-2-center | 3-SUM lower bound for Euclidean 2-center in R^3 | # Research Challenge: 3-SUM lower bound for Euclidean 2-center in R^3
> **Source paper:** Fine-Grained Complexity of Continuous Euclidean k-Center
> **Reference:** [arXiv:2603.28265](https://arxiv.org/abs/2603.28265) — Theorem 2.center
> **Task:** Prove the theorem stated below. This document is self-contained: al... | Fine-Grained Complexity of Continuous Euclidean k-Center | 2603.28265 | https://arxiv.org/abs/2603.28265 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fine-grained-complexity-of-continuous-euclidean-k-center/theorem-2-center.md |
2603.28265/theorem-6-center | 3-SUM lower bound for Euclidean 6-center in the plane | # Research Challenge: 3-SUM lower bound for Euclidean 6-center in the plane
> **Source paper:** Fine-Grained Complexity of Continuous Euclidean k-Center
> **Reference:** [arXiv:2603.28265](https://arxiv.org/abs/2603.28265) — Theorem 6.center
> **Task:** Prove the theorem stated below. This document is self-contain... | Fine-Grained Complexity of Continuous Euclidean k-Center | 2603.28265 | https://arxiv.org/abs/2603.28265 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fine-grained-complexity-of-continuous-euclidean-k-center/theorem-6-center.md |
2603.28265/theorem-k-center-approx | ETH hardness of approximate Euclidean k-center | # Research Challenge: ETH hardness of approximate Euclidean k-center
> **Source paper:** Fine-Grained Complexity of Continuous Euclidean k-Center
> **Reference:** [arXiv:2603.28265](https://arxiv.org/abs/2603.28265) — Theorem k.center.approx
> **Task:** Prove the theorem stated below. This document is self-contain... | Fine-Grained Complexity of Continuous Euclidean k-Center | 2603.28265 | https://arxiv.org/abs/2603.28265 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fine-grained-complexity-of-continuous-euclidean-k-center/theorem-k-center-approx.md |
2603.28265/theorem-k-center | Tight ETH lower bound for Euclidean k-center | # Research Challenge: Tight ETH lower bound for Euclidean k-center
> **Source paper:** Fine-Grained Complexity of Continuous Euclidean k-Center
> **Reference:** [arXiv:2603.28265](https://arxiv.org/abs/2603.28265) — Theorem k.center
> **Task:** Prove the theorem stated below. This document is self-contained: all d... | Fine-Grained Complexity of Continuous Euclidean k-Center | 2603.28265 | https://arxiv.org/abs/2603.28265 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fine-grained-complexity-of-continuous-euclidean-k-center/theorem-k-center.md |
2606.11283/theorem-dp-synth-data-noisy-lp | FPT private synthetic data via treewidth | # Research Challenge: FPT private synthetic data via treewidth
> **Source paper:** Fixed-Parameter Tractability of Private Synthetic Data Generation
> **Reference:** [arXiv:2606.11283](https://arxiv.org/abs/2606.11283) — Theorem dp.synth.data.noisy.lp
> **Task:** Prove the theorem stated below. This document is se... | Fixed-Parameter Tractability of Private Synthetic Data Generation | 2606.11283 | https://arxiv.org/abs/2606.11283 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fixed-parameter-tractability-of-private-synthetic-data-generation/theorem-dp-synth-data-noisy-lp.md |
2606.11283/theorem-hierarchical | Efficient private synthetic data for hierarchical queries | # Research Challenge: Efficient private synthetic data for hierarchical queries
> **Source paper:** Fixed-Parameter Tractability of Private Synthetic Data Generation
> **Reference:** [arXiv:2606.11283](https://arxiv.org/abs/2606.11283) — Theorem hierarchical
> **Task:** Prove the theorem stated below. This documen... | Fixed-Parameter Tractability of Private Synthetic Data Generation | 2606.11283 | https://arxiv.org/abs/2606.11283 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fixed-parameter-tractability-of-private-synthetic-data-generation/theorem-hierarchical.md |
2606.11283/theorem-implicit-pmwu-accuracy | Accuracy of implicit private MWU | # Research Challenge: Accuracy of implicit private MWU
> **Source paper:** Fixed-Parameter Tractability of Private Synthetic Data Generation
> **Reference:** [arXiv:2606.11283](https://arxiv.org/abs/2606.11283) — Theorem implicit.pmwu.accuracy
> **Task:** Prove the theorem stated below. This document is self-conta... | Fixed-Parameter Tractability of Private Synthetic Data Generation | 2606.11283 | https://arxiv.org/abs/2606.11283 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fixed-parameter-tractability-of-private-synthetic-data-generation/theorem-implicit-pmwu-accuracy.md |
2606.11283/theorem-ipmwu-run-time-accuracy | Running time of implicit private MWU | # Research Challenge: Running time of implicit private MWU
> **Source paper:** Fixed-Parameter Tractability of Private Synthetic Data Generation
> **Reference:** [arXiv:2606.11283](https://arxiv.org/abs/2606.11283) — Theorem ipmwu.run.time.accuracy
> **Task:** Prove the theorem stated below. This document is self-... | Fixed-Parameter Tractability of Private Synthetic Data Generation | 2606.11283 | https://arxiv.org/abs/2606.11283 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | fixed-parameter-tractability-of-private-synthetic-data-generation/theorem-ipmwu-run-time-accuracy.md |
2601.22535/theorem-constant-rate-aLLDCs | Constant-rate binary local list decoding near 1/2 | # Research Challenge: Constant-rate binary local list decoding near 1/2
> **Source paper:** High Rate Efficient Local List Decoding from HDX
> **Reference:** [arXiv:2601.22535](https://arxiv.org/abs/2601.22535) — Theorem constant.rate.aLLDCs
> **Task:** Prove the theorem stated below. This document is self-contain... | High Rate Efficient Local List Decoding from HDX | 2601.22535 | https://arxiv.org/abs/2601.22535 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | high-rate-efficient-local-list-decoding-from-hdx/theorem-constant-rate-aLLDCs.md |
2601.22535/theorem-list-recovery | Local list recovery from expanding hypergraph systems | # Research Challenge: Local list recovery from expanding hypergraph systems
> **Source paper:** High Rate Efficient Local List Decoding from HDX
> **Reference:** [arXiv:2601.22535](https://arxiv.org/abs/2601.22535) — Theorem list.recovery
> **Task:** Prove the theorem stated below. This document is self-contained:... | High Rate Efficient Local List Decoding from HDX | 2601.22535 | https://arxiv.org/abs/2601.22535 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | high-rate-efficient-local-list-decoding-from-hdx/theorem-list-recovery.md |
2601.22535/theorem-polylog-rate-aLLDCs | Polylog-rate binary local list decoding near 1/2 | # Research Challenge: Polylog-rate binary local list decoding near 1/2
> **Source paper:** High Rate Efficient Local List Decoding from HDX
> **Reference:** [arXiv:2601.22535](https://arxiv.org/abs/2601.22535) — Theorem polylog.rate.aLLDCs
> **Task:** Prove the theorem stated below. This document is self-contained... | High Rate Efficient Local List Decoding from HDX | 2601.22535 | https://arxiv.org/abs/2601.22535 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | high-rate-efficient-local-list-decoding-from-hdx/theorem-polylog-rate-aLLDCs.md |
2601.22535/theorem-uniform-complexity-preserving-hardness-amplification | Complexity-preserving uniform hardness amplification | # Research Challenge: Complexity-preserving uniform hardness amplification
> **Source paper:** High Rate Efficient Local List Decoding from HDX
> **Reference:** [arXiv:2601.22535](https://arxiv.org/abs/2601.22535) — Theorem uniform.complexity.preserving.hardness.amplification
> **Task:** Prove the theorem stated b... | High Rate Efficient Local List Decoding from HDX | 2601.22535 | https://arxiv.org/abs/2601.22535 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | high-rate-efficient-local-list-decoding-from-hdx/theorem-uniform-complexity-preserving-hardness-amplification.md |
2504.01856/thm-construct-protocol | Improved multi-round coin flipping protocol | # Research Challenge: Improved multi-round coin flipping protocol
> **Source paper:** Improved Bounds for Coin Flipping, Leader Election, and Random Selection
> **Reference:** [arXiv:2504.01856](https://arxiv.org/abs/2504.01856) — Thm construct.protocol
> **Task:** Prove the theorem stated below. This document is ... | Improved Bounds for Coin Flipping, Leader Election, and Random Selection | 2504.01856 | https://arxiv.org/abs/2504.01856 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | improved-bounds-for-coin-flipping-leader-election-and-random-selection/thm-construct-protocol.md |
2504.01856/thm-multioutput-coin-flipping-protocol-general | One-round multi-output coin flipping protocol | # Research Challenge: One-round multi-output coin flipping protocol
> **Source paper:** Improved Bounds for Coin Flipping, Leader Election, and Random Selection
> **Reference:** [arXiv:2504.01856](https://arxiv.org/abs/2504.01856) — Thm multioutput.coin.flipping.protocol.general
> **Task:** Prove the theorem state... | Improved Bounds for Coin Flipping, Leader Election, and Random Selection | 2504.01856 | https://arxiv.org/abs/2504.01856 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | improved-bounds-for-coin-flipping-leader-election-and-random-selection/thm-multioutput-coin-flipping-protocol-general.md |
2504.01856/thm-protocol-lb-longer-messages | Lower bound for longer-message protocols | # Research Challenge: Lower bound for longer-message protocols
> **Source paper:** Improved Bounds for Coin Flipping, Leader Election, and Random Selection
> **Reference:** [arXiv:2504.01856](https://arxiv.org/abs/2504.01856) — Thm protocol.lb.longer.messages
> **Task:** Prove the theorem stated below. This docume... | Improved Bounds for Coin Flipping, Leader Election, and Random Selection | 2504.01856 | https://arxiv.org/abs/2504.01856 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | improved-bounds-for-coin-flipping-leader-election-and-random-selection/thm-protocol-lb-longer-messages.md |
2504.01856/thm-protocol-lb | Round lower bound for coin flipping | # Research Challenge: Round lower bound for coin flipping
> **Source paper:** Improved Bounds for Coin Flipping, Leader Election, and Random Selection
> **Reference:** [arXiv:2504.01856](https://arxiv.org/abs/2504.01856) — Thm protocol.lb
> **Task:** Prove the theorem stated below. This document is self-contained:... | Improved Bounds for Coin Flipping, Leader Election, and Random Selection | 2504.01856 | https://arxiv.org/abs/2504.01856 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | improved-bounds-for-coin-flipping-leader-election-and-random-selection/thm-protocol-lb.md |
2602.17894/theorem-avg-risk-lb | Prediction risk lower bound under budget | # Research Challenge: Prediction risk lower bound under budget
> **Source paper:** Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget
> **Reference:** [arXiv:2602.17894](https://arxiv.org/abs/2602.17894) — Theorem avg.risk.lb
> **Task:** Prove the theorem stated below. Thi... | Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget | 2602.17894 | https://arxiv.org/abs/2602.17894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | learning-from-biased-and-costly-data-sources-minimax-optimal-data-collection-under-a-budget/theorem-avg-risk-lb.md |
2602.17894/theorem-avg-risk-ub | Prediction risk upper bound via reweighted ERM | # Research Challenge: Prediction risk upper bound via reweighted ERM
> **Source paper:** Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget
> **Reference:** [arXiv:2602.17894](https://arxiv.org/abs/2602.17894) — Theorem avg.risk.ub
> **Task:** Prove the theorem stated belo... | Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget | 2602.17894 | https://arxiv.org/abs/2602.17894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | learning-from-biased-and-costly-data-sources-minimax-optimal-data-collection-under-a-budget/theorem-avg-risk-ub.md |
2602.17894/theorem-me-lb | Minimax lower bound for mean estimation under budget | # Research Challenge: Minimax lower bound for mean estimation under budget
> **Source paper:** Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget
> **Reference:** [arXiv:2602.17894](https://arxiv.org/abs/2602.17894) — Theorem me.lb
> **Task:** Prove the theorem stated belo... | Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget | 2602.17894 | https://arxiv.org/abs/2602.17894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | learning-from-biased-and-costly-data-sources-minimax-optimal-data-collection-under-a-budget/theorem-me-lb.md |
2602.17894/theorem-me-strat-ub | Minimax-optimal mean estimation policies | # Research Challenge: Minimax-optimal mean estimation policies
> **Source paper:** Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget
> **Reference:** [arXiv:2602.17894](https://arxiv.org/abs/2602.17894) — Theorem me.strat.ub
> **Task:** Prove the theorem stated below. Thi... | Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget | 2602.17894 | https://arxiv.org/abs/2602.17894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | learning-from-biased-and-costly-data-sources-minimax-optimal-data-collection-under-a-budget/theorem-me-strat-ub.md |
2602.05704/theorem-main | SGD fails to align with target subspace | # Research Challenge: SGD fails to align with target subspace
> **Source paper:** Limitations of SGD for Multi-Index Models Beyond Statistical Queries
> **Reference:** [arXiv:2602.05704](https://arxiv.org/abs/2602.05704) — Theorem main
> **Task:** Prove the theorem stated below. This document is self-contained: al... | Limitations of SGD for Multi-Index Models Beyond Statistical Queries | 2602.05704 | https://arxiv.org/abs/2602.05704 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | limitations-of-sgd-for-multi-index-models-beyond-statistical-queries/theorem-main.md |
2602.05704/theorem-migeneral | SGD lower bound for multi-index models | # Research Challenge: SGD lower bound for multi-index models
> **Source paper:** Limitations of SGD for Multi-Index Models Beyond Statistical Queries
> **Reference:** [arXiv:2602.05704](https://arxiv.org/abs/2602.05704) — Theorem migeneral
> **Task:** Prove the theorem stated below. This document is self-contained... | Limitations of SGD for Multi-Index Models Beyond Statistical Queries | 2602.05704 | https://arxiv.org/abs/2602.05704 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | limitations-of-sgd-for-multi-index-models-beyond-statistical-queries/theorem-migeneral.md |
2602.05704/theorem-periodic | SGD stuck on sine target | # Research Challenge: SGD stuck on sine target
> **Source paper:** Limitations of SGD for Multi-Index Models Beyond Statistical Queries
> **Reference:** [arXiv:2602.05704](https://arxiv.org/abs/2602.05704) — Theorem periodic
> **Task:** Prove the theorem stated below. This document is self-contained: all definitio... | Limitations of SGD for Multi-Index Models Beyond Statistical Queries | 2602.05704 | https://arxiv.org/abs/2602.05704 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | limitations-of-sgd-for-multi-index-models-beyond-statistical-queries/theorem-periodic.md |
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