{"agent_url":"https://mathhub.eggtea.org/works/hodge-classes-on-abelian-sixfolds-constructio-82bdae05/v/1/files/Agent.md","archived":false,"change_note":"Initial publication authorized by eggtea; CC BY 4.0; original manuscript, available experiment source and explicit review scope.","created_at":"2026-10-17T09:22:31+00:00","files":[{"bytes":415226,"path":"1_paper.pdf","sha256":"efcac47add715c1cf605d6827d6484f514405b7cfe67ecdcbb386ccbd67cf88e"},{"bytes":265008,"path":"2.1_AI_paper.md","sha256":"f47a54be64fb6c5dcc15c39e35332ed8c8c113d68e35e77499737d14a2df49ed"},{"bytes":407037,"path":"2_AI_paper.pdf","sha256":"42b40643026aedc6952e455f56aeb3623530c732814a564c372b8c08e716c753"},{"bytes":105783,"path":"3_guide_en.pdf","sha256":"c71786090c2e43ff4c6122f70c0e51eb6a510956ef052d98dd3edcb2265ad950"},{"bytes":148355,"path":"4_guide_zh.pdf","sha256":"ad4e70d91b9a6988861bad706d376951a037c997ea6584c8c520b31715b12a52"},{"bytes":147368,"path":"5_review_en.pdf","sha256":"529dad90a7dca5fadb8ba639e144fa38b1fa3bd052b03c28eb024e0eec55075c"},{"bytes":244203,"path":"6_review_zh.pdf","sha256":"f25720fac6810ce0a8ddb34445c71cf8c5010a767a9b67e6e9315daa980502f6"},{"bytes":32559,"path":"7_theorem_graph.pdf","sha256":"43d1e7d059185a088bd21d292aaf64de042f29da15d0803eddb49511acd22e38"},{"bytes":2249,"path":"Agent.md","sha256":"8fba33205d610f7244a2881279e89a89564eba7148c4888f605e653927fd3727"},{"bytes":326,"path":"LICENSE.txt","sha256":"c18762d18fac8ab4f109b0da15919fe68116124ab16e12a68a964154afcdb2a9"},{"bytes":1093,"path":"README.md","sha256":"f8e7bb53a6822b8688875c2b7202c62fb67935f6e622ae330a7b4eaee7e87c90"},{"bytes":248182,"path":"latex/AI_paper.tex","sha256":"8c28701f4373e6be9bce317d0e8b78c60ad9658df71a69eaaaff35b190874b9c"},{"bytes":6360,"path":"latex/guide_en.tex","sha256":"0a326cfa13a521ba5ce5faf6f12e624b4f2d2aff5996ce730d17bfcdd3ae0058"},{"bytes":5804,"path":"latex/guide_zh.tex","sha256":"7dc08d88b2d9f3da939848b49f5d2a608a6a7db5e321b8f53d01479ff92fc86a"},{"bytes":251158,"path":"latex/paper.tex","sha256":"1a978f9be2992c6c82088ac819dbdbd258148dcf5f2f567c445cf1d3d5cd5483"},{"bytes":12456,"path":"latex/takeaways.tex","sha256":"83bed1bc03e6aa529d0a40956b577c9d6991c415f29fbdff97fc15b6d71367ac"},{"bytes":1699,"path":"packaging.json","sha256":"99151c7ce3f0d3e8563de1e0cabc272503a9b065c03914c80907f62932d3733b"},{"bytes":1091,"path":"takeaways.md","sha256":"4a90ca8a85affa096e556815392e1e812d8ba55a7fd7abe70d7f6ed99b72162d"},{"bytes":2856,"path":"theorem_graph/README.md","sha256":"0d5879e60bb469737d0bf547f367022d41144d2fbd45bcdcb3442598890b9b6b"},{"bytes":12458,"path":"theorem_graph/render_graph.py","sha256":"066f5c3b55d32ce31f32dc58b7ee5ab88e4e7d7473b8ff6cad234dbed21e24af"},{"bytes":282376,"path":"theorem_graph/theorems.json","sha256":"a9f2fdb3f83c9e853ae9696d20433a99f79d19beea435cecbff49e7361fa23bf"},{"bytes":10639,"path":"verification/5_review_en.txt","sha256":"2600dcf823036e1d15eba9516884aff5c6d80884615d06558ab641d71efcdc5b"},{"bytes":8421,"path":"verification/6_review_zh.txt","sha256":"fa5ebb6ed28f69d554a807f5f8ada770259c62f3e480a31b13bc35d1545fe46f"},{"bytes":2734,"path":"verification/review.md","sha256":"38289b2a364372270c8310a3909219ebbefa0209d583a1813e4fdafa8e01ec2b"},{"bytes":4287,"path":"work.yaml","sha256":"08b84effcad2e58fe981c2b06090a7d75c4c9d677b8d910c237b59d6a78c72ce"}],"is_demo":false,"manifest":{"abstract":"A twenty-one-case research draft on rational Hodge classes of complex abelian sixfolds. The overall sixfold conclusion is conditional on the manuscript-specific split-eightfold Weil, CM, complete Kuga\u2013Satake and auxiliary spin-tensor algebraicity assertions. Individual unconditional strata and all-powers results have the narrower scopes recorded in the manuscript and theorem registry; no unconditional resolution is claimed.","authors":["eggtea"],"field":"Algebraic geometry","keywords":["Hodge conjecture","abelian sixfolds","conditional proof"],"license":"CC-BY-4.0","main":"1_paper.pdf","references":[{"authors":"A. P. Borselli","title":"Galois Groups of CM Fields in Degrees 24, 28, and 30","url":"https://preserve.lehigh.edu/lehigh-scholarship/graduate-publications-theses-dissertations/theses-dissertations/galois-groups-cm"},{"authors":"B. Moonen","title":"Notes on Mumford--Tate groups","url":"https://www.math.ru.nl/~bmoonen/Lecturenotes/CEBnotesMT.pdf"},{"authors":"B. Moonen and Yu. G. Zarhin","title":"Hodge classes on abelian varieties of low dimension","url":"https://arxiv.org/abs/math/9901113"},{"authors":"J. S. Milne","title":"Introduction to Shimura Varieties","url":"https://www.jmilne.org/math/xnotes/svi.pdf"},{"authors":"B. Moonen","title":"Special subvarieties arising from families of cyclic covers of the projective line","url":"https://arxiv.org/abs/1006.3400"},{"authors":"J. J. Ram\u00f3n Mar\u00ed","title":"On the Hodge conjecture for products of certain surfaces","url":"https://arxiv.org/abs/math/0505357"},{"authors":"C. Vial","title":"Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for abelian varieties","url":"https://arxiv.org/abs/1803.00857"},{"authors":"J. S. Milne","title":"Lefschetz classes on abelian varieties","url":"https://www.jmilne.org/math/articles/1999a.html"},{"authors":"J. S. Milne","title":"The Tate and standard conjectures for certain abelian varieties","url":"https://www.jmilne.org/math/articles/tcav2.pdf"},{"authors":"C. Yu and Z. Zheng","title":"Commensurability among Deligne--Mostow monodromy groups","url":"https://arxiv.org/abs/2411.09682v2"},{"authors":"E. Markman","title":"Cycles on abelian $2n$-folds of Weil type from secant sheaves on abelian $n$-folds","url":"https://arxiv.org/abs/2502.03415v2"},{"authors":"H. Yanai","title":"On the index of degeneracy of a CM abelian variety","url":"https://www.numdam.org/articles/10.5802/jtnb.925/"},{"authors":"E. Markman","title":"Secant sheaves and Weil classes on abelian varieties","url":"https://arxiv.org/abs/2509.23403v2"},{"authors":"OpenAI","title":"Algebraicity of Weil classes on split abelian eightfolds","url":"https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/README.md"},{"authors":"OpenAI","title":"The rational Hodge conjecture for CM abelian varieties","url":"https://github.com/openai/math/blob/main/preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-September-30-2026/README.md"},{"authors":"OpenAI","title":"Weil classes and Hodge classes on abelian powers","url":"https://github.com/openai/math/blob/main/preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-September-30-2026/README.md"},{"authors":"OpenAI","title":"Algebraicity of Kuga--Satake Correspondences for K3 Surfaces","url":"https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Kuga-Satake-Correspondences-for-K3-Surfaces-October-3-2026/README.md"},{"authors":"D. Huybrechts","title":"Lectures on K3 Surfaces","url":"https://www.math.uni-bonn.de/people/huybrech/K3Global.pdf"},{"authors":"OpenAI","title":"The rational Hodge conjecture for products of K3 surfaces","url":"https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-rational-Hodge-conjecture-for-products-of-K3-surfaces-October-4-2026/build/manuscript/auxiliary.tex"}],"schema_version":1,"takeaways":"takeaways.md","title":"Hodge Classes on Abelian Sixfolds: Constructions and a Conditional Proof","type":"paper","verification":[{"date":"2026-10-17","model":"GPT-6 (Codex; exact runtime variant not exposed)","path":"verification/review.md","scope":"Statement, assumptions, public-summary and supplied-review provenance audit; not a complete fresh proof review.","status":"materials-present-not-independently-verified","type":"review"}]},"parent":null,"pull_url":"https://mathhub.eggtea.org/api/works/hodge-classes-on-abelian-sixfolds-constructio-82bdae05/versions/1/bundle","resolves":[],"sha256":"854fb996272d92f36a76026093234ef8804249625c0397f174bf2b624491cf68","submitted_by":"eggtea","url":"https://mathhub.eggtea.org/works/hodge-classes-on-abelian-sixfolds-constructio-82bdae05/v/1","version":1,"work_id":"hodge-classes-on-abelian-sixfolds-constructio-82bdae05"}
