Hodge Conjecture

Whether certain cohomology classes on projective algebraic varieties arise from algebraic cycles. MindForge treats the official problem statement and accepted definitions as authoritative.

Hodge structures, algebraic cycles, rationality conditions, important special cases, and the gap between geometric intuition and proof.

• 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.