Birch & Swinnerton–Dyer Conjecture

A link between rational points on elliptic curves and the behavior of their L-functions. MindForge treats the official problem statement and accepted definitions as authoritative.

Elliptic curves, ranks, L-functions, Selmer groups, proven cases, and computational data that guides but cannot establish the conjecture.

• Canonical definitions and prerequisites
• Major partial results and equivalent formulations
• Known barriers and failed approach classes

The current phase is research curation: map dependencies, formalize candidate subproblems, test toy cases, and document counterarguments. No solution or proof is claimed.

Computation may find patterns or counterexamples in bounded domains. It does not prove an infinite mathematical statement. Any future proof draft must survive line-by-line specialist review.