Crab Research

Research programmes and independent papers

Crab Research brings together Proof Engine, a mathematics research programme, and independent work in computer science and the social sciences.

Mathematics research programme

Proof Engine

Proof Engine develops reliable AI-assisted mathematics through mathematical results, public methodology and formal verification: writing theorems and proofs in a form a proof assistant can check.

Read our research programme
Two complementary frameworks. Proof Engine 1.0: proof development through claims, proof and evidence. Proof Engine 2.0: research governance through questions, prior work and objectives.

1.0/Proof development

Claims, evidence and dependencies

Construct, verify and connect mathematical results.

2.0/Research governance

Questions, contributions and changing objectives

Steer inquiry, track contributions and adapt direction.
Methodology
Mathematical result papers
38
Formalizations using foundational axioms only (Kernel-Only)All theorem dependencies checked
19
Public frameworks Proof Engine 1.0 and 2.0
2

Selected research

Browse selected research

A reading route through open problems, classifications and constructive theories.

A formalization writes a theorem and its proof in a form that a proof assistant can check.

Latest mathematical cases

All mathematical results (38)

Reference-Gated proofs check the deductions while assuming explicitly listed cited theorems whose proofs are not included in the package.

Outside the mathematics programme

Independent research

Papers outside Proof Engine, organized by research field.

Peer-reviewed publications

Published & accepted