Agenda Structural Challenge Canonical mathematics structural-challenge, mathematics Hodge classes on a projective complex manifold are rational linear combinations of cohomology classes of algebraic cycles.
Mathematics Structural Challenge Ledger

Hodge Conjecture

CB-HODGE canonical benchmark canonical benchmarks External: externally open τ response: structurally constrained

Hodge classes on a projective complex manifold are rational linear combinations of cohomology classes of algebraic cycles.

See the paired Hodge Conjecture — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.

Current status: structurally constrained.

Challenge statement

Hodge classes on a projective complex manifold are rational linear combinations of cohomology classes of algebraic cycles.

Why this challenge is in the ledger

Algebraic-geometric structural test connecting topology, complex analysis, and algebraic cycles.

τ-facing burden

Show whether τ’s categorical / structural-position machinery applies to Hodge classes and algebraic cycles.

Bibliography clusters whose prior art bears on this page. Each cluster links to its representative references and to the broader Deep Comparison briefing.

Source: prior-art cluster index · canonical data lives in corpus/data/bibliography/prior-art-clusters.yml

First reviewer questions

  1. Does τ have a notion of algebraic cycle?
  2. Can τ distinguish topologically meaningful classes from algebraic ones?
  3. Does τ produce constraints visible to standard motivic theory?

Source anchors

Source anchors are background references, not endorsements of Panta Rhei claims.

Save or share this page for inspection

Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.

Email to expert