schema_version: 1
title: 'Hodge Classes on Abelian Sixfolds: Constructions and a Conditional Proof'
abstract: A twenty-one-row study of rational Hodge classes on complex abelian sixfolds,
  separating invariant calculations, cycle constructions, sixfold conclusions and
  all-powers statements. It develops polarization adjustments, trace-form splitting,
  stabilization with algebraic contraction, and mixed-cycle constructions. The full
  twenty-one-row conclusion is conditional on the exact Weil8, CM, full Kuga–Satake
  and auxiliary four-slot assertions specified in the manuscript. Three cited input
  manuscripts were withdrawn; those assertions are assumptions here, not established
  inputs or a proof of the unconditional Hodge conjecture.
field: Algebraic Geometry
license: CC-BY-4.0
type: paper
authors:
- eggtea
keywords:
- Hodge classes
- abelian sixfolds
- Weil classes
- conditional proof
main: main.pdf
takeaways: takeaways.md
verification:
- type: review
  path: verification/review.md
  status: materials-present-not-independently-verified
  model: Codex (GPT-6; current-session non-independent check)
  date: '2026-10-17'
  scope: Limited current-session claim/assumption and selected-proof consistency check
    of main.pdf SHA-256 efcac47add715c1cf605d6827d6484f514405b7cfe67ecdcbb386ccbd67cf88e;
    includes executed formula checks; not an independent full mathematical review.
references:
- title: Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds
  authors: E. Markman
  url: https://arxiv.org/abs/2502.03415v2
- title: OpenAI mathematics release history (withdrawal notices)
  authors: OpenAI
  url: https://github.com/openai/math/blob/main/history.md