id stringlengths 16 71 | title stringlengths 19 78 | text stringlengths 1.44k 10.9k | paper_title stringlengths 20 121 | arxiv_id stringlengths 10 10 | arxiv_url stringlengths 32 32 | source_license stringclasses 2
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2602.05704/theorem-sqbad | SQ lower bound for the function class | # Research Challenge: SQ lower bound for the function class
> **Source paper:** Limitations of SGD for Multi-Index Models Beyond Statistical Queries
> **Reference:** [arXiv:2602.05704](https://arxiv.org/abs/2602.05704) — Theorem sqbad
> **Task:** Prove the theorem stated below. This document is self-contained: all... | 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-sqbad.md |
2606.14095/theorem-thm-heteWCMDP | Sample complexity for heterogeneous weakly-coupled MDPs | # Research Challenge: Sample complexity for heterogeneous weakly-coupled MDPs
> **Source paper:** Lyapunov-Based Sample Complexity Analysis for Weakly-Coupled MDPs
> **Reference:** [arXiv:2606.14095](https://arxiv.org/abs/2606.14095) — Theorem thm.heteWCMDP
> **Task:** Prove the theorem stated below. This document... | Lyapunov-Based Sample Complexity Analysis for Weakly-Coupled MDPs | 2606.14095 | https://arxiv.org/abs/2606.14095 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | lyapunov-based-sample-complexity-analysis-for-weakly-coupled-mdps/theorem-thm-heteWCMDP.md |
2606.14095/theorem-thm-homoRB | Sample complexity for homogeneous restless bandits | # Research Challenge: Sample complexity for homogeneous restless bandits
> **Source paper:** Lyapunov-Based Sample Complexity Analysis for Weakly-Coupled MDPs
> **Reference:** [arXiv:2606.14095](https://arxiv.org/abs/2606.14095) — Theorem thm.homoRB
> **Task:** Prove the theorem stated below. This document is self... | Lyapunov-Based Sample Complexity Analysis for Weakly-Coupled MDPs | 2606.14095 | https://arxiv.org/abs/2606.14095 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | lyapunov-based-sample-complexity-analysis-for-weakly-coupled-mdps/theorem-thm-homoRB.md |
2510.23991/thm-k-dim-matching | Hardness of k-Dimensional Matching | # Research Challenge: Hardness of k-Dimensional Matching
> **Source paper:** Near Optimal Hardness of Approximating $k$-CSP
> **Reference:** [arXiv:2510.23991](https://arxiv.org/abs/2510.23991) — Thm k.dim.matching
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and not... | Near Optimal Hardness of Approximating $k$-CSP | 2510.23991 | https://arxiv.org/abs/2510.23991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | near-optimal-hardness-of-approximating-k-csp/thm-k-dim-matching.md |
2510.23991/thm-main | Near-optimal hardness of approximating k-CSP | # Research Challenge: Near-optimal hardness of approximating k-CSP
> **Source paper:** Near Optimal Hardness of Approximating $k$-CSP
> **Reference:** [arXiv:2510.23991](https://arxiv.org/abs/2510.23991) — Thm main
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and not... | Near Optimal Hardness of Approximating $k$-CSP | 2510.23991 | https://arxiv.org/abs/2510.23991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | near-optimal-hardness-of-approximating-k-csp/thm-main.md |
2510.23991/thm-other-problems | Hardness of packing and matroid problems | # Research Challenge: Hardness of packing and matroid problems
> **Source paper:** Near Optimal Hardness of Approximating $k$-CSP
> **Reference:** [arXiv:2510.23991](https://arxiv.org/abs/2510.23991) — Thm other.problems
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions a... | Near Optimal Hardness of Approximating $k$-CSP | 2510.23991 | https://arxiv.org/abs/2510.23991 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | near-optimal-hardness-of-approximating-k-csp/thm-other-problems.md |
2511.21659/theorem-1 | Length lower bound for non-adaptive relaxed LDCs | # Research Challenge: Length lower bound for non-adaptive relaxed LDCs
> **Source paper:** 2511.21659
> **Reference:** [arXiv:2511.21659](https://arxiv.org/abs/2511.21659) — Theorem 1
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation needed to understand the ... | Nearly Tight Lower Bounds for Relaxed Locally Decodable Codes via Robust Daisies | 2511.21659 | https://arxiv.org/abs/2511.21659 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | nearly-tight-lower-bounds-for-relaxed-locally-decodable-codes-via-robust-daisies/theorem-1.md |
2505.00894/theorem-concentration-read-k-bijections | Concentration for read-k function families over bijections | # Research Challenge: Concentration for read-k function families over bijections
> **Source paper:** Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations
> **Reference:** [arXiv:2505.00894](https://arxiv.org/abs/2505.00894) — Theorem concentration.read.k.bijections
> **... | Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations | 2505.00894 | https://arxiv.org/abs/2505.00894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | non-adaptive-cryptanalytic-time-space-lower-bounds-via-a-shearer-like-inequality-for-permutations/theorem-concentration-read-k-bijections.md |
2505.00894/theorem-dl-nonadaptive-intro | Non-adaptive time-space lower bound for discrete log | # Research Challenge: Non-adaptive time-space lower bound for discrete log
> **Source paper:** Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations
> **Reference:** [arXiv:2505.00894](https://arxiv.org/abs/2505.00894) — Theorem dl.nonadaptive.intro
> **Task:** Prove the... | Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations | 2505.00894 | https://arxiv.org/abs/2505.00894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | non-adaptive-cryptanalytic-time-space-lower-bounds-via-a-shearer-like-inequality-for-permutations/theorem-dl-nonadaptive-intro.md |
2505.00894/theorem-g-nonadaptive | Time-space lower bound for non-adaptive permutation challenge games | # Research Challenge: Time-space lower bound for non-adaptive permutation challenge games
> **Source paper:** Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations
> **Reference:** [arXiv:2505.00894](https://arxiv.org/abs/2505.00894) — Theorem g.nonadaptive
> **Task:** P... | Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations | 2505.00894 | https://arxiv.org/abs/2505.00894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | non-adaptive-cryptanalytic-time-space-lower-bounds-via-a-shearer-like-inequality-for-permutations/theorem-g-nonadaptive.md |
2505.00894/theorem-variant-shearer-bijections | Shearer-like KL inequality for permutations | # Research Challenge: Shearer-like KL inequality for permutations
> **Source paper:** Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations
> **Reference:** [arXiv:2505.00894](https://arxiv.org/abs/2505.00894) — Theorem variant.shearer.bijections
> **Task:** Prove the th... | Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations | 2505.00894 | https://arxiv.org/abs/2505.00894 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | non-adaptive-cryptanalytic-time-space-lower-bounds-via-a-shearer-like-inequality-for-permutations/theorem-variant-shearer-bijections.md |
2602.06257/thm-agnostic-lower-bound | Lower bound for proper agnostic learners | # Research Challenge: Lower bound for proper agnostic learners
> **Source paper:** On Randomized Algorithms in Online Strategic Classification
> **Reference:** [arXiv:2602.06257](https://arxiv.org/abs/2602.06257) — Thm:agnostic lower.bound
> **Task:** Prove the theorem stated below. This document is self-contained... | On Randomized Algorithms in Online Strategic Classification | 2602.06257 | https://arxiv.org/abs/2602.06257 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-randomized-algorithms-in-online-strategic-classification/thm-agnostic-lower-bound.md |
2602.06257/thm-finite-realizable-upper-bound | Realizable upper bound for finite classes | # Research Challenge: Realizable upper bound for finite classes
> **Source paper:** On Randomized Algorithms in Online Strategic Classification
> **Reference:** [arXiv:2602.06257](https://arxiv.org/abs/2602.06257) — Thm:finite realizable.upper.bound
> **Task:** Prove the theorem stated below. This document is self... | On Randomized Algorithms in Online Strategic Classification | 2602.06257 | https://arxiv.org/abs/2602.06257 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-randomized-algorithms-in-online-strategic-classification/thm-finite-realizable-upper-bound.md |
2602.06257/thm-improper-upper-bound | Agnostic improper regret bound | # Research Challenge: Agnostic improper regret bound
> **Source paper:** On Randomized Algorithms in Online Strategic Classification
> **Reference:** [arXiv:2602.06257](https://arxiv.org/abs/2602.06257) — Thm:improper upper.bound
> **Task:** Prove the theorem stated below. This document is self-contained: all defi... | On Randomized Algorithms in Online Strategic Classification | 2602.06257 | https://arxiv.org/abs/2602.06257 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-randomized-algorithms-in-online-strategic-classification/thm-improper-upper-bound.md |
2602.06257/thm-infinite-realizable-upper-bound | Realizable upper bound via Littlestone dimension | # Research Challenge: Realizable upper bound via Littlestone dimension
> **Source paper:** On Randomized Algorithms in Online Strategic Classification
> **Reference:** [arXiv:2602.06257](https://arxiv.org/abs/2602.06257) — Thm:infinite realizable.upper.bound
> **Task:** Prove the theorem stated below. This documen... | On Randomized Algorithms in Online Strategic Classification | 2602.06257 | https://arxiv.org/abs/2602.06257 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-randomized-algorithms-in-online-strategic-classification/thm-infinite-realizable-upper-bound.md |
2602.06257/thm-realizable-LB | Realizable lower bound for randomized learners | # Research Challenge: Realizable lower bound for randomized learners
> **Source paper:** On Randomized Algorithms in Online Strategic Classification
> **Reference:** [arXiv:2602.06257](https://arxiv.org/abs/2602.06257) — Thm:realizable LB
> **Task:** Prove the theorem stated below. This document is self-contained:... | On Randomized Algorithms in Online Strategic Classification | 2602.06257 | https://arxiv.org/abs/2602.06257 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-randomized-algorithms-in-online-strategic-classification/thm-realizable-LB.md |
2606.21951/theorem-priv-sparse-cov-est-lower-bound | Lower bound for private sparse covariance estimation | # Research Challenge: Lower bound for private sparse covariance estimation
> **Source paper:** On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA
> **Reference:** [arXiv:2606.21951](https://arxiv.org/abs/2606.21951) — Theorem priv.sparse.cov.est.lower.bound
> **Task:** Prove the theorem... | On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA | 2606.21951 | https://arxiv.org/abs/2606.21951 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-curse-of-dimensionality-in-private-sparse-covariance-estimation-and-pca/theorem-priv-sparse-cov-est-lower-bound.md |
2606.21951/theorem-priv-sparse-cov-est-upper-bound | Upper bound for private sparse covariance estimation | # Research Challenge: Upper bound for private sparse covariance estimation
> **Source paper:** On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA
> **Reference:** [arXiv:2606.21951](https://arxiv.org/abs/2606.21951) — Theorem priv.sparse.cov.est.upper.bound
> **Task:** Prove the theorem... | On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA | 2606.21951 | https://arxiv.org/abs/2606.21951 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-curse-of-dimensionality-in-private-sparse-covariance-estimation-and-pca/theorem-priv-sparse-cov-est-upper-bound.md |
2606.21951/theorem-priv-sparse-pca-approx-dp-lower-bound | Approximate-DP lower bound for sparse PCA | # Research Challenge: Approximate-DP lower bound for sparse PCA
> **Source paper:** On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA
> **Reference:** [arXiv:2606.21951](https://arxiv.org/abs/2606.21951) — Theorem priv.sparse.pca.approx.dp.lower.bound
> **Task:** Prove the theorem stat... | On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA | 2606.21951 | https://arxiv.org/abs/2606.21951 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-curse-of-dimensionality-in-private-sparse-covariance-estimation-and-pca/theorem-priv-sparse-pca-approx-dp-lower-bound.md |
2606.21951/theorem-priv-sparse-pca-upper-bound-gamma | Upper bound for private sparse PCA | # Research Challenge: Upper bound for private sparse PCA
> **Source paper:** On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA
> **Reference:** [arXiv:2606.21951](https://arxiv.org/abs/2606.21951) — Theorem priv.sparse.pca.upper.bound.gamma
> **Task:** Prove the theorem stated below. T... | On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA | 2606.21951 | https://arxiv.org/abs/2606.21951 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-curse-of-dimensionality-in-private-sparse-covariance-estimation-and-pca/theorem-priv-sparse-pca-upper-bound-gamma.md |
2511.13999/theorem-info-cap-oracle-lb | Lower bound via oracle information capacity | # Research Challenge: Lower bound via oracle information capacity
> **Source paper:** On the Gradient Complexity of Private Optimization with Private Oracles
> **Reference:** [arXiv:2511.13999](https://arxiv.org/abs/2511.13999) — Theorem info.cap.oracle.lb
> **Task:** Prove the theorem stated below. This document ... | On the Gradient Complexity of Private Optimization with Private Oracles | 2511.13999 | https://arxiv.org/abs/2511.13999 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-gradient-complexity-of-private-optimization-with-private-oracles/theorem-info-cap-oracle-lb.md |
2511.13999/theorem-main-lb | Gradient complexity lower bound for private proxy oracles | # Research Challenge: Gradient complexity lower bound for private proxy oracles
> **Source paper:** On the Gradient Complexity of Private Optimization with Private Oracles
> **Reference:** [arXiv:2511.13999](https://arxiv.org/abs/2511.13999) — Theorem main.lb
> **Task:** Prove the theorem stated below. This docume... | On the Gradient Complexity of Private Optimization with Private Oracles | 2511.13999 | https://arxiv.org/abs/2511.13999 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-gradient-complexity-of-private-optimization-with-private-oracles/theorem-main-lb.md |
2511.13999/theorem-main-ub | Upper bound with private proxy oracle | # Research Challenge: Upper bound with private proxy oracle
> **Source paper:** On the Gradient Complexity of Private Optimization with Private Oracles
> **Reference:** [arXiv:2511.13999](https://arxiv.org/abs/2511.13999) — Theorem main.ub
> **Task:** Prove the theorem stated below. This document is self-contained... | On the Gradient Complexity of Private Optimization with Private Oracles | 2511.13999 | https://arxiv.org/abs/2511.13999 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-gradient-complexity-of-private-optimization-with-private-oracles/theorem-main-ub.md |
2602.23763/theorem-classical-separation | Classical memory-query separation for 2-nested collision finding | # Research Challenge: Classical memory-query separation for 2-nested collision finding
> **Source paper:** On the Need for (Quantum) Memory with Short Outputs
> **Reference:** [arXiv:2602.23763](https://arxiv.org/abs/2602.23763) — Theorem classical.separation
> **Task:** Prove the theorem stated below. This docume... | On the Need for (Quantum) Memory with Short Outputs | 2602.23763 | https://arxiv.org/abs/2602.23763 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-need-for-quantum-memory-with-short-outputs/theorem-classical-separation.md |
2602.23763/theorem-main-classical | Classical time-space lower bound for nested collision finding | # Research Challenge: Classical time-space lower bound for nested collision finding
> **Source paper:** On the Need for (Quantum) Memory with Short Outputs
> **Reference:** [arXiv:2602.23763](https://arxiv.org/abs/2602.23763) — Theorem main.classical
> **Task:** Prove the theorem stated below. This document is sel... | On the Need for (Quantum) Memory with Short Outputs | 2602.23763 | https://arxiv.org/abs/2602.23763 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-need-for-quantum-memory-with-short-outputs/theorem-main-classical.md |
2602.23763/theorem-main-quantum | Quantum time-space lower bound for nested collision finding | # Research Challenge: Quantum time-space lower bound for nested collision finding
> **Source paper:** On the Need for (Quantum) Memory with Short Outputs
> **Reference:** [arXiv:2602.23763](https://arxiv.org/abs/2602.23763) — Theorem main.quantum
> **Task:** Prove the theorem stated below. This document is self-co... | On the Need for (Quantum) Memory with Short Outputs | 2602.23763 | https://arxiv.org/abs/2602.23763 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-need-for-quantum-memory-with-short-outputs/theorem-main-quantum.md |
2602.23763/theorem-quantum-separation | Quantum memory-query separation for 4-nested collision finding | # Research Challenge: Quantum memory-query separation for 4-nested collision finding
> **Source paper:** On the Need for (Quantum) Memory with Short Outputs
> **Reference:** [arXiv:2602.23763](https://arxiv.org/abs/2602.23763) — Theorem quantum.separation
> **Task:** Prove the theorem stated below. This document i... | On the Need for (Quantum) Memory with Short Outputs | 2602.23763 | https://arxiv.org/abs/2602.23763 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-need-for-quantum-memory-with-short-outputs/theorem-quantum-separation.md |
2510.04115/theorem-dfa_hard | SQ hardness of learning semiautomata | # Research Challenge: SQ hardness of learning semiautomata
> **Source paper:** On the Statistical Query Complexity of Learning Semiautomata: a Random Walk Approach
> **Reference:** [arXiv:2510.04115](https://arxiv.org/abs/2510.04115) — Theorem dfa_hard
> **Task:** Prove the theorem stated below. This document is s... | On the Statistical Query Complexity of Learning Semiautomata: a Random Walk Approach | 2510.04115 | https://arxiv.org/abs/2510.04115 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-statistical-query-complexity-of-learning-semiautomata-a-random-walk-approach/theorem-dfa_hard.md |
2510.04115/theorem-p_agree | Agreement probability via random walk | # Research Challenge: Agreement probability via random walk
> **Source paper:** On the Statistical Query Complexity of Learning Semiautomata: a Random Walk Approach
> **Reference:** [arXiv:2510.04115](https://arxiv.org/abs/2510.04115) — Theorem p_agree
> **Task:** Prove the theorem stated below. This document is s... | On the Statistical Query Complexity of Learning Semiautomata: a Random Walk Approach | 2510.04115 | https://arxiv.org/abs/2510.04115 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | on-the-statistical-query-complexity-of-learning-semiautomata-a-random-walk-approach/theorem-p_agree.md |
2606.14640/theorem-experts-regret | Regret for expert advice with noisy probes | # Research Challenge: Regret for expert advice with noisy probes
> **Source paper:** Online Convex Optimization with Sublinear Noisy Probes
> **Reference:** [arXiv:2606.14640](https://arxiv.org/abs/2606.14640) — Theorem experts.regret
> **Task:** Prove the theorem stated below. This document is self-contained: all... | Online Convex Optimization with Sublinear Noisy Probes | 2606.14640 | https://arxiv.org/abs/2606.14640 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | online-convex-optimization-with-sublinear-noisy-probes/theorem-experts-regret.md |
2606.14640/theorem-noise-oco | Regret for OCO with noisy comparison probes | # Research Challenge: Regret for OCO with noisy comparison probes
> **Source paper:** Online Convex Optimization with Sublinear Noisy Probes
> **Reference:** [arXiv:2606.14640](https://arxiv.org/abs/2606.14640) — Theorem noise.oco
> **Task:** Prove the theorem stated below. This document is self-contained: all def... | Online Convex Optimization with Sublinear Noisy Probes | 2606.14640 | https://arxiv.org/abs/2606.14640 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | online-convex-optimization-with-sublinear-noisy-probes/theorem-noise-oco.md |
2606.14640/theorem-thmlbcvx | Matching lower bounds for probe-based regret | # Research Challenge: Matching lower bounds for probe-based regret
> **Source paper:** Online Convex Optimization with Sublinear Noisy Probes
> **Reference:** [arXiv:2606.14640](https://arxiv.org/abs/2606.14640) — Theorem thmlbcvx
> **Task:** Prove the theorem stated below. This document is self-contained: all def... | Online Convex Optimization with Sublinear Noisy Probes | 2606.14640 | https://arxiv.org/abs/2606.14640 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | online-convex-optimization-with-sublinear-noisy-probes/theorem-thmlbcvx.md |
2602.06797/theorem-optimal-fractional-lrs | Optimal fractional LRS scaling | # Research Challenge: Optimal fractional LRS scaling
> **Source paper:** Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay
> **Reference:** [arXiv:2602.06797](https://arxiv.org/abs/2602.06797) — Theorem optimal.fractional.lrs
> **Task:** Prove the theorem stated bel... | Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay | 2602.06797 | https://arxiv.org/abs/2602.06797 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | optimal-learning-rate-schedules-under-functional-scaling-laws-power-decay-and-warmup-stable-decay/theorem-optimal-fractional-lrs.md |
2602.06797/theorem-optimal_lrs | Optimal LRS: power decay vs WSD | # Research Challenge: Optimal LRS: power decay vs WSD
> **Source paper:** Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay
> **Reference:** [arXiv:2602.06797](https://arxiv.org/abs/2602.06797) — Theorem optimal_lrs
> **Task:** Prove the theorem stated below. This d... | Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay | 2602.06797 | https://arxiv.org/abs/2602.06797 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | optimal-learning-rate-schedules-under-functional-scaling-laws-power-decay-and-warmup-stable-decay/theorem-optimal_lrs.md |
2602.06797/theorem-power-rate | Power-decay LRS achieves optimal risk | # Research Challenge: Power-decay LRS achieves optimal risk
> **Source paper:** Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay
> **Reference:** [arXiv:2602.06797](https://arxiv.org/abs/2602.06797) — Theorem power.rate
> **Task:** Prove the theorem stated below. T... | Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay | 2602.06797 | https://arxiv.org/abs/2602.06797 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | optimal-learning-rate-schedules-under-functional-scaling-laws-power-decay-and-warmup-stable-decay/theorem-power-rate.md |
2605.19625/maintheorem-asymptotic | Asymptotic optimal reconstruction error | # Research Challenge: Asymptotic optimal reconstruction error
> **Source paper:** Optimal Reconstruction from Linear Queries
> **Reference:** [arXiv:2605.19625](https://arxiv.org/abs/2605.19625) — Maintheorem asymptotic
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions an... | Optimal Reconstruction from Linear Queries | 2605.19625 | https://arxiv.org/abs/2605.19625 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | optimal-reconstruction-from-linear-queries/maintheorem-asymptotic.md |
2605.19625/maintheorem-dim-bounds | Dimension threshold for vanishing excess error | # Research Challenge: Dimension threshold for vanishing excess error
> **Source paper:** Optimal Reconstruction from Linear Queries
> **Reference:** [arXiv:2605.19625](https://arxiv.org/abs/2605.19625) — Maintheorem dim.bounds
> **Task:** Prove the theorem stated below. This document is self-contained: all definit... | Optimal Reconstruction from Linear Queries | 2605.19625 | https://arxiv.org/abs/2605.19625 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | optimal-reconstruction-from-linear-queries/maintheorem-dim-bounds.md |
2605.19625/maintheorem-excess-bounds | Doubly-exponential convergence of excess error | # Research Challenge: Doubly-exponential convergence of excess error
> **Source paper:** Optimal Reconstruction from Linear Queries
> **Reference:** [arXiv:2605.19625](https://arxiv.org/abs/2605.19625) — Maintheorem excess.bounds
> **Task:** Prove the theorem stated below. This document is self-contained: all defi... | Optimal Reconstruction from Linear Queries | 2605.19625 | https://arxiv.org/abs/2605.19625 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | optimal-reconstruction-from-linear-queries/maintheorem-excess-bounds.md |
2602.03827/maintheorem-algo | Efficient algorithms for perfect resilience | # Research Challenge: Efficient algorithms for perfect resilience
> **Source paper:** 2602.03827
> **Reference:** [arXiv:2602.03827](https://arxiv.org/abs/2602.03827) — Maintheorem algo
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation needed to understand th... | Perfect Network Resilience in Polynomial Time | 2602.03827 | https://arxiv.org/abs/2602.03827 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | perfect-network-resilience-in-polynomial-time/maintheorem-algo.md |
2602.03827/theorem-structure | Structural characterization of perfect resilience | # Research Challenge: Structural characterization of perfect resilience
> **Source paper:** 2602.03827
> **Reference:** [arXiv:2602.03827](https://arxiv.org/abs/2602.03827) — Theorem structure
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notation needed to unders... | Perfect Network Resilience in Polynomial Time | 2602.03827 | https://arxiv.org/abs/2602.03827 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | perfect-network-resilience-in-polynomial-time/theorem-structure.md |
2510.00076/theorem-DP-ERM-littlestone | Private empirical risk minimization for Littlestone classes | # Research Challenge: Private empirical risk minimization for Littlestone classes
> **Source paper:** Private Learning of Littlestone Classes, Revisited
> **Reference:** [arXiv:2510.00076](https://arxiv.org/abs/2510.00076) — Theorem DP.ERM.littlestone
> **Task:** Prove the theorem stated below. This document is se... | Private Learning of Littlestone Classes, Revisited | 2510.00076 | https://arxiv.org/abs/2510.00076 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | private-learning-of-littlestone-classes-revisited/theorem-DP-ERM-littlestone.md |
2510.00076/theorem-unnumbered-1 | Private online learning of Littlestone classes | # Research Challenge: Private online learning of Littlestone classes
> **Source paper:** Private Learning of Littlestone Classes, Revisited
> **Reference:** [arXiv:2510.00076](https://arxiv.org/abs/2510.00076) — Theorem unnumbered.1
> **Task:** Prove the theorem stated below. This document is self-contained: all d... | Private Learning of Littlestone Classes, Revisited | 2510.00076 | https://arxiv.org/abs/2510.00076 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | private-learning-of-littlestone-classes-revisited/theorem-unnumbered-1.md |
2510.00076/theorem-unnumbered-2 | Private PAC learning of Littlestone classes | # Research Challenge: Private PAC learning of Littlestone classes
> **Source paper:** Private Learning of Littlestone Classes, Revisited
> **Reference:** [arXiv:2510.00076](https://arxiv.org/abs/2510.00076) — Theorem unnumbered.2
> **Task:** Prove the theorem stated below. This document is self-contained: all defi... | Private Learning of Littlestone Classes, Revisited | 2510.00076 | https://arxiv.org/abs/2510.00076 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | private-learning-of-littlestone-classes-revisited/theorem-unnumbered-2.md |
2510.00322/thm-lower-general | Query lower bound for private black-box estimation | # Research Challenge: Query lower bound for private black-box estimation
> **Source paper:** Privately Estimating Black-Box Statistics
> **Reference:** [arXiv:2510.00322](https://arxiv.org/abs/2510.00322) — Thm:lower general
> **Task:** Prove the theorem stated below. This document is self-contained: all definitio... | Privately Estimating Black-Box Statistics | 2510.00322 | https://arxiv.org/abs/2510.00322 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | privately-estimating-black-box-statistics/thm-lower-general.md |
2510.00322/thm-main | Private black-box statistic estimation via oracle queries | # Research Challenge: Private black-box statistic estimation via oracle queries
> **Source paper:** Privately Estimating Black-Box Statistics
> **Reference:** [arXiv:2510.00322](https://arxiv.org/abs/2510.00322) — Thm:main
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions... | Privately Estimating Black-Box Statistics | 2510.00322 | https://arxiv.org/abs/2510.00322 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | privately-estimating-black-box-statistics/thm-main.md |
2507.19290/corollary-linear | Learning linearly parameterized matrix families | # Research Challenge: Learning linearly parameterized matrix families
> **Source paper:** Query Efficient Structured Matrix Learning
> **Reference:** [arXiv:2507.19290](https://arxiv.org/abs/2507.19290) — Corollary linear
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions ... | Query Efficient Structured Matrix Learning | 2507.19290 | https://arxiv.org/abs/2507.19290 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | query-efficient-structured-matrix-learning/corollary-linear.md |
2507.19290/theorem-covering-number-approximation | Approximation via covering number | # Research Challenge: Approximation via covering number
> **Source paper:** Query Efficient Structured Matrix Learning
> **Reference:** [arXiv:2507.19290](https://arxiv.org/abs/2507.19290) — Theorem covering.number.approximation
> **Task:** Prove the theorem stated below. This document is self-contained: all defin... | Query Efficient Structured Matrix Learning | 2507.19290 | https://arxiv.org/abs/2507.19290 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | query-efficient-structured-matrix-learning/theorem-covering-number-approximation.md |
2507.19290/theorem-robust | Query-efficient learning for finite matrix families | # Research Challenge: Query-efficient learning for finite matrix families
> **Source paper:** Query Efficient Structured Matrix Learning
> **Reference:** [arXiv:2507.19290](https://arxiv.org/abs/2507.19290) — Theorem robust
> **Task:** Prove the theorem stated below. This document is self-contained: all definition... | Query Efficient Structured Matrix Learning | 2507.19290 | https://arxiv.org/abs/2507.19290 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | query-efficient-structured-matrix-learning/theorem-robust.md |
2507.19290/theorem-two-sided-lower-bound | Lower bound for structured matrix learning | # Research Challenge: Lower bound for structured matrix learning
> **Source paper:** Query Efficient Structured Matrix Learning
> **Reference:** [arXiv:2507.19290](https://arxiv.org/abs/2507.19290) — Theorem two.sided.lower.bound
> **Task:** Prove the theorem stated below. This document is self-contained: all defi... | Query Efficient Structured Matrix Learning | 2507.19290 | https://arxiv.org/abs/2507.19290 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | query-efficient-structured-matrix-learning/theorem-two-sided-lower-bound.md |
2603.01346/thm-no-learner-m2-smart | No learner beats quadratic sample overhead | # Research Challenge: No learner beats quadratic sample overhead
> **Source paper:** Relatively Smart: A New Approach for Instance-Optimal Learning
> **Reference:** [arXiv:2603.01346](https://arxiv.org/abs/2603.01346) — Thm no.learner.m2.smart
> **Task:** Prove the theorem stated below. This document is self-conta... | Relatively Smart: A New Approach for Instance-Optimal Learning | 2603.01346 | https://arxiv.org/abs/2603.01346 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | relatively-smart-a-new-approach-for-instance-optimal-learning/thm-no-learner-m2-smart.md |
2603.01346/thm-oig-erm-fail | ERM and OIG need quadratic sample blow-up | # Research Challenge: ERM and OIG need quadratic sample blow-up
> **Source paper:** Relatively Smart: A New Approach for Instance-Optimal Learning
> **Reference:** [arXiv:2603.01346](https://arxiv.org/abs/2603.01346) — Thm oig.erm.fail
> **Task:** Prove the theorem stated below. This document is self-contained: al... | Relatively Smart: A New Approach for Instance-Optimal Learning | 2603.01346 | https://arxiv.org/abs/2603.01346 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | relatively-smart-a-new-approach-for-instance-optimal-learning/thm-oig-erm-fail.md |
2603.01346/thm-oig-square-smart | OIG learner is relatively smart | # Research Challenge: OIG learner is relatively smart
> **Source paper:** Relatively Smart: A New Approach for Instance-Optimal Learning
> **Reference:** [arXiv:2603.01346](https://arxiv.org/abs/2603.01346) — Thm oig.square.smart
> **Task:** Prove the theorem stated below. This document is self-contained: all defi... | Relatively Smart: A New Approach for Instance-Optimal Learning | 2603.01346 | https://arxiv.org/abs/2603.01346 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | relatively-smart-a-new-approach-for-instance-optimal-learning/thm-oig-square-smart.md |
2604.01307/theorem-function-inversion-all | Space-efficient function inversion data structure | # Research Challenge: Space-efficient function inversion data structure
> **Source paper:** Space-Efficient Text Indexing with Mismatches using Function Inversion
> **Reference:** [arXiv:2604.01307](https://arxiv.org/abs/2604.01307) — Theorem function.inversion.all
> **Task:** Prove the theorem stated below. This ... | Space-Efficient Text Indexing with Mismatches using Function Inversion | 2604.01307 | https://arxiv.org/abs/2604.01307 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | space-efficient-text-indexing-with-mismatches-using-function-inversion/theorem-function-inversion-all.md |
2604.01307/theorem-result-improved-cgl | Improved text index with k mismatches | # Research Challenge: Improved text index with k mismatches
> **Source paper:** Space-Efficient Text Indexing with Mismatches using Function Inversion
> **Reference:** [arXiv:2604.01307](https://arxiv.org/abs/2604.01307) — Theorem result.improved.cgl
> **Task:** Prove the theorem stated below. This document is sel... | Space-Efficient Text Indexing with Mismatches using Function Inversion | 2604.01307 | https://arxiv.org/abs/2604.01307 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | space-efficient-text-indexing-with-mismatches-using-function-inversion/theorem-result-improved-cgl.md |
2604.01307/theorem-result-small-space | Space-efficient k-mismatch index via function inversion | # Research Challenge: Space-efficient k-mismatch index via function inversion
> **Source paper:** Space-Efficient Text Indexing with Mismatches using Function Inversion
> **Reference:** [arXiv:2604.01307](https://arxiv.org/abs/2604.01307) — Theorem result.small.space
> **Task:** Prove the theorem stated below. Thi... | Space-Efficient Text Indexing with Mismatches using Function Inversion | 2604.01307 | https://arxiv.org/abs/2604.01307 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | space-efficient-text-indexing-with-mismatches-using-function-inversion/theorem-result-small-space.md |
2601.23229/thm-main1 | Near-linear bound on dyadic scales of signed subset sums | # Research Challenge: Near-linear bound on dyadic scales of signed subset sums
> **Source paper:** Strongly Polynomial Time Complexity of Policy Iteration for $L_\infty$ Robust MDPs
> **Reference:** [arXiv:2601.23229](https://arxiv.org/abs/2601.23229) — Thm main1
> **Task:** Prove the theorem stated below. This do... | Strongly Polynomial Time Complexity of Policy Iteration for $L_\infty$ Robust MDPs | 2601.23229 | https://arxiv.org/abs/2601.23229 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | strongly-polynomial-time-complexity-of-policy-iteration-for-linfty-robust-mdps/thm-main1.md |
2601.23229/thm-rmc-iterations | Strongly polynomial iteration bound for RMC policy iteration | # Research Challenge: Strongly polynomial iteration bound for RMC policy iteration
> **Source paper:** Strongly Polynomial Time Complexity of Policy Iteration for $L_\infty$ Robust MDPs
> **Reference:** [arXiv:2601.23229](https://arxiv.org/abs/2601.23229) — Thm rmc.iterations
> **Task:** Prove the theorem stated b... | Strongly Polynomial Time Complexity of Policy Iteration for $L_\infty$ Robust MDPs | 2601.23229 | https://arxiv.org/abs/2601.23229 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | strongly-polynomial-time-complexity-of-policy-iteration-for-linfty-robust-mdps/thm-rmc-iterations.md |
2601.23229/thm-rmdp-iterations | Strongly polynomial iteration bound for RMDP policy iteration | # Research Challenge: Strongly polynomial iteration bound for RMDP policy iteration
> **Source paper:** Strongly Polynomial Time Complexity of Policy Iteration for $L_\infty$ Robust MDPs
> **Reference:** [arXiv:2601.23229](https://arxiv.org/abs/2601.23229) — Thm rmdp.iterations
> **Task:** Prove the theorem stated... | Strongly Polynomial Time Complexity of Policy Iteration for $L_\infty$ Robust MDPs | 2601.23229 | https://arxiv.org/abs/2601.23229 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | strongly-polynomial-time-complexity-of-policy-iteration-for-linfty-robust-mdps/thm-rmdp-iterations.md |
2511.04125/corollary-nphard | SVP_p NP-hard to approximate within 2^{log^{1-ε}n} | # Research Challenge: SVP_p NP-hard to approximate within 2^{log^{1-ε}n}
> **Source paper:** SVP$_p$ is Deterministically NP-Hard for all $p > 2$, Even to Approximate Within a Factor of $2^{\log^{1-\varepsilon} n}$
> **Reference:** [arXiv:2511.04125](https://arxiv.org/abs/2511.04125) — Corollary nphard
> **Task:**... | SVP$_p$ is Deterministically NP-Hard for all $p > 2$, Even to Approximate Within a Factor of $2^{\log^{1-\varepsilon} n}$ | 2511.04125 | https://arxiv.org/abs/2511.04125 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | svpp-is-deterministically-np-hard-for-all-p-2-even-to-approximate-within-a-factor-of-2log1-varepsilon-n/corollary-nphard.md |
2511.04125/theorem-mainresultformal | PCP to GapSVP_p hardness reduction | # Research Challenge: PCP to GapSVP_p hardness reduction
> **Source paper:** SVP$_p$ is Deterministically NP-Hard for all $p > 2$, Even to Approximate Within a Factor of $2^{\log^{1-\varepsilon} n}$
> **Reference:** [arXiv:2511.04125](https://arxiv.org/abs/2511.04125) — Theorem mainresultformal
> **Task:** Prove t... | SVP$_p$ is Deterministically NP-Hard for all $p > 2$, Even to Approximate Within a Factor of $2^{\log^{1-\varepsilon} n}$ | 2511.04125 | https://arxiv.org/abs/2511.04125 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | svpp-is-deterministically-np-hard-for-all-p-2-even-to-approximate-within-a-factor-of-2log1-varepsilon-n/theorem-mainresultformal.md |
2511.07835/thm-DFKO-informal | Constant-sample tester with explicit gap | # Research Challenge: Constant-sample tester with explicit gap
> **Source paper:** Testing noisy low-degree polynomials for sparsity
> **Reference:** [arXiv:2511.07835](https://arxiv.org/abs/2511.07835) — Thm DFKO.informal
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions... | Testing noisy low-degree polynomials for sparsity | 2511.07835 | https://arxiv.org/abs/2511.07835 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | testing-noisy-low-degree-polynomials-for-sparsity/thm-DFKO-informal.md |
2511.07835/thm-alg-for-f | Computing the maximum sparsity gap | # Research Challenge: Computing the maximum sparsity gap
> **Source paper:** Testing noisy low-degree polynomials for sparsity
> **Reference:** [arXiv:2511.07835](https://arxiv.org/abs/2511.07835) — Thm alg.for.f
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and notat... | Testing noisy low-degree polynomials for sparsity | 2511.07835 | https://arxiv.org/abs/2511.07835 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | testing-noisy-low-degree-polynomials-for-sparsity/thm-alg-for-f.md |
2511.07835/thm-sharp-lower | Logarithmic lower bound below the gap | # Research Challenge: Logarithmic lower bound below the gap
> **Source paper:** Testing noisy low-degree polynomials for sparsity
> **Reference:** [arXiv:2511.07835](https://arxiv.org/abs/2511.07835) — Thm sharp.lower
> **Task:** Prove the theorem stated below. This document is self-contained: all definitions and ... | Testing noisy low-degree polynomials for sparsity | 2511.07835 | https://arxiv.org/abs/2511.07835 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | testing-noisy-low-degree-polynomials-for-sparsity/thm-sharp-lower.md |
2511.07835/thm-sharp-upper | Sample-efficient sparsity tester above the gap | # Research Challenge: Sample-efficient sparsity tester above the gap
> **Source paper:** Testing noisy low-degree polynomials for sparsity
> **Reference:** [arXiv:2511.07835](https://arxiv.org/abs/2511.07835) — Thm sharp.upper
> **Task:** Prove the theorem stated below. This document is self-contained: all definit... | Testing noisy low-degree polynomials for sparsity | 2511.07835 | https://arxiv.org/abs/2511.07835 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | testing-noisy-low-degree-polynomials-for-sparsity/thm-sharp-upper.md |
2603.24493/theorem-characterization | Finite linear VC characterizes uniform estimability | # Research Challenge: Finite linear VC characterizes uniform estimability
> **Source paper:** Uniform Laws of Large Numbers in Product Spaces
> **Reference:** [arXiv:2603.24493](https://arxiv.org/abs/2603.24493) — Theorem characterization
> **Task:** Prove the theorem stated below. This document is self-contained:... | Uniform Laws of Large Numbers in Product Spaces | 2603.24493 | https://arxiv.org/abs/2603.24493 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | uniform-laws-of-large-numbers-in-product-spaces/theorem-characterization.md |
2603.24493/theorem-vc-aggregation | VC bound for aggregations of a base class | # Research Challenge: VC bound for aggregations of a base class
> **Source paper:** Uniform Laws of Large Numbers in Product Spaces
> **Reference:** [arXiv:2603.24493](https://arxiv.org/abs/2603.24493) — Theorem vc.aggregation
> **Task:** Prove the theorem stated below. This document is self-contained: all definit... | Uniform Laws of Large Numbers in Product Spaces | 2603.24493 | https://arxiv.org/abs/2603.24493 | CC BY 4.0 | http://creativecommons.org/licenses/by/4.0/ | uniform-laws-of-large-numbers-in-product-spaces/theorem-vc-aggregation.md |
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