PƒPPrompts for Progress

Problems index

One question.
Every attempt.

A problem's status is separate from any attempt's outcome. Counts below describe this archive, not the totality of research activity.

23problems and collections
24record-to-problem links
1explicitly open problems

Canonical targets

Browse the research questions.

Collections remain aggregated when a campaign spans many problems without enough statement-level evidence for individual pages.

research question · astrobiology and analytical chemistryAstrobiology hypotheses from mass-spectrometry data

Generating plausible and novel hypotheses about meteorite and soil chemistry from mass-spectrometry data and the astrobiology literature.

Hypotheses awaiting validationAs of 2025-03-29
1 Partial progress
1attempt
benchmark · atomic force microscopy and laboratory automationAutonomous atomic-force-microscopy workflows

Designing, executing, and analyzing atomic-force-microscopy experiments while measuring tool-coordination, code-generation, and instruction-adherence failures.

Benchmark campaignAs of 2025-10-14
1 Mixed campaign
1attempt
problem · geometric analysis and general relativityBartnik admissible-extension conjecture

Whether every Bartnik body possesses a smooth admissible asymptotically flat extension satisfying the boundary, curvature, topology, and horizon conditions.

OpenAs of 2026-07-15
1 Documented attempt
1attempt
research question · drug repurposingBreast-cancer drug-combination discovery

Finding drug combinations with useful synergy against breast-cancer models while retaining biological plausibility and safety.

Active researchAs of 2025
1 Mixed campaign
1attempt
problem · graph theoryCycle Double Cover Conjecture

Whether every finite bridgeless loopless multigraph has a cycle double cover.

Resolution claimedAs of 2026-07-16
1 Complete result
1attempt
benchmark · classical, wave, and quantum dynamicsDiscovery of physical models from simulated observations

Recovering equations of motion, Hamiltonians, and other model structure by designing and analyzing experiments in initially unknown simulated systems.

Benchmark campaignAs of 2026-07-08
1 Mixed campaign
1attempt
research question · ophthalmology and drug repurposingDrug-repurposing directions for dry AMD

Identifying mechanistically plausible existing drugs that could improve retinal pigment epithelium function in dry age-related macular degeneration.

Active researchAs of 2026
1 Partial progress
1attempt
research question · ocean-atmosphere variability and seasonal forecastingEight-month Atlantic Niño forecasting

Identifying physically meaningful precursors that can extend June-August Atlantic Niño forecast skill to an eight-month lead.

Active researchAs of 2025-07-23
1 Documented attempt
1attempt
collection · discrete geometry, number theory, and extremal optimizationEinsteinArena mathematical optimization problems

A live collection of verifier-backed mathematical optimization problems where independently operated agents submit constructions and share research notes.

Live problem collectionAs of 2026-07-17
1 Partial progress
1attempt
collection · machine-learning research and meta-scienceEnd-to-end autonomous machine-learning research

Taking machine-learning research ideas through hypothesis formation, implementation, evaluation, and paper preparation while preserving failed attempts.

Research-attempt collectionAs of 2026-01-06
1 Mixed campaign
1attempt
collection · number theory and combinatoricsErdős open problems

A collection of open-labeled problems associated with Paul Erdős, used in several large AI proof-search campaigns.

Problem collectionAs of 2026-07-16
2 Mixed campaign
2attempts
problem · combinatorial number theoryErdős problem 848

A canonical Erdős problem in combinatorial number theory for which an AI-assisted solution was reported.

Resolution claimedAs of 2025-11-20
1 Complete result
1attempt
benchmark · research mathematicsFirst Proof research problems

Ten research-level mathematics problems used to assess AI-generated proof attempts with problem-author feedback.

Benchmark setAs of 2026-04
1 Mixed campaign
1attempt
research question · combinatoricsImproved cap-set constructions

Constructing larger subsets of finite vector spaces containing no nontrivial three-term arithmetic progressions.

Active researchAs of 2023-12-14
1 Partial progress
1attempt
research question · solid-state chemistry and battery materialsLithium-halide spinel electrolyte optimization

Optimizing air-sensitive chloride spinel solid electrolytes for both phase purity and ionic conductivity.

Active researchAs of 2026-04-13
1 Mixed campaign
1attempt
collection · integer sequencesOEIS conjectures and open questions

Conjectures and open questions arising from integer sequences catalogued by the OEIS.

Problem collectionAs of 2026-05-21
1 Mixed campaign
1attempt
benchmark · computational biology and bioinformaticsOpen-ended bioinformatics research questions

Research-like bioinformatics questions derived from published notebooks, requiring data exploration, code execution, interpretation, and hypothesis generation.

Benchmark collectionAs of 2025-02-28
1 Mixed campaign
1attempt
problem · discrete geometryPlanar unit-distance conjecture

An Erdős conjecture concerning the asymptotic upper-bound behavior of unit-distance pairs among planar point sets.

Disproof claimedAs of 2026-05-20
1 Complete result
1attempt
problem · optimizationPoint convergence of Nesterov accelerated gradient

Establishing pointwise convergence behavior for Nesterov's accelerated gradient method under the studied convex optimization conditions.

Resolution claimedAs of 2025-10-27
1 Complete result
1attempt
research question · synthetic chemistry and laboratory automationReproducibility of published chemical synthesis procedures

Translating published synthesis prose into executable procedures while detecting ambiguity and identifying procedures that cannot be reproduced.

Active researchAs of 2026-04-03
1 Mixed campaign
1attempt
research question · protein engineeringSARS-CoV-2 nanobody variant design

Designing nanobody variants with improved expression and binding against evolving SARS-CoV-2 variants.

Active researchAs of 2025
1 Partial progress
1attempt
problem · analysis and differential equationsUniqueness for a weighted difference-quotient differential equation

Whether zero initial data force uniqueness for a difference-quotient differential equation with a positive smooth weight.

Counterexample claimedAs of 2026-05-06
1 Complete result
1attempt
problem · convex optimizationZeroth-order convex-optimization lower bound

Closing a lower-bound gap for zeroth-order convex optimization, including a stronger refinement and formal verification.

Gap claimed closedAs of 2026-07-16
1 Complete result
1attempt

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