claims depot

Topics

Every reviewed claim, written or formalized in Lean, shelved by the problem it attacks. Assignment is deterministic (phrase match over the claim graph, plus paper metadata signals) and recomputed nightly, so each shelf stays current as the corpus grows. The same data, typed, at /api/topics.

A shelf collects what has been claimed. The Frontier is the layer above it: for the major open problems, which claims assert that something would settle the problem, and what those assertions imply once chained.

Dark Matter 7394 claims
The dominant matter component inferred gravitationally but not directly detected. formal 569 6825 papers
Dark Energy 2900 claims
The accelerating expansion of the universe and the cosmological constant problem. formal 506 2394 papers
Quantum Gravity 1740 claims
Reconciling general relativity with quantum mechanics. formal 404 1337 papers
Navier-Stokes Regularity 1031 claims
Whether smooth initial data for the 3D Navier-Stokes equations can develop singularities in finite time. formal 397 634 papers
The Hubble Tension 715 claims
The disagreement between early- and late-universe measurements of the expansion rate. formal 114 601 papers
The Measurement Problem 652 claims
What happens when a quantum superposition becomes a definite outcome. formal 237 415 papers
Matter-Antimatter Asymmetry 651 claims
Why the observable universe contains much more matter than antimatter. formal 45 606 papers
Yang-Mills Mass Gap 552 claims
Proving that quantum Yang-Mills theory exists rigorously and has a positive mass gap. formal 178 374 papers
P versus NP 518 claims
Whether every problem whose solution can be checked quickly can also be solved quickly. formal 142 357 papers
The Riemann Hypothesis 453 claims
All nontrivial zeros of the Riemann zeta function lie on the critical line. formal 160 293 papers
The Collatz Conjecture 261 claims
Iterate n to n/2 or 3n+1; does every starting value reach 1? formal 107 154 papers
The Twin Prime Conjecture 256 claims
Are there infinitely many primes p with p + 2 also prime? formal 108 148 papers
The Hodge Conjecture 231 claims
Whether certain de Rham cohomology classes on projective varieties are algebraic. formal 85 146 papers
The Strong CP Problem 217 claims
Why quantum chromodynamics conserves CP symmetry. formal 29 188 papers
The Hierarchy Problem 157 claims
Why the Higgs mass is far below the Planck scale. formal 16 141 papers
Birch and Swinnerton-Dyer 128 claims
The rank of an elliptic curve equals the order of vanishing of its L-function at s = 1. formal 52 76 papers
High-Temperature Superconductivity 112 claims
Explaining high-temperature superconductivity and finding higher-temperature materials. formal 3 109 papers
Goldbach's Conjecture 106 claims
Every even integer greater than 2 is the sum of two primes. formal 36 70 papers
The abc Conjecture 50 claims
A deep statement relating the additive and multiplicative structure of integers. formal 13 37 papers
Protein Folding 49 claims
Deriving protein structure, folding process, and energetics. formal 2 47 papers