Verify
Turn an informal claim into a proof obligation and separate exact proof from computation or conjecture.
Open ProofLab →Number theory · exact computation · trustworthy AI
Search equations.
Test claims.
Know what is proved.
Diophantix is an open research environment for polynomial Diophantine equations. Search for points, inspect arithmetic structure, and use ProofLab to verify whether an AI-generated argument is a theorem, a counterexample, a bounded computation, or still unknown.
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GPT-5.6 interprets. Exact mathematics decides.
ProofLab is a deterministic proof firewall for mathematical AI: it compiles informal claims into structured obligations, runs exact polynomial and modular verifiers, produces replayable certificates, and adversarially tries to break the argument.
Inspect the evidence ledger ↗Search
Find exact integer and rational points on polynomial Diophantine equations and elliptic-curve families.
Open solver →Investigate
Classify equations, inspect congruence obstructions, and explore arithmetic structure before brute force.
Open explorer →The evidence boundary
A language model never awards itself a proof.
GPT-5.6 extracts formulas, assumptions, variables, and the intended claim type.
Exact integer polynomial arithmetic and complete residue enumeration decide supported obligations.
Every proved or disproved result carries an integrity-checksummed certificate whose exact evidence can be replayed independently.