{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SWWYYB4YW7RWGKVLIKEXKAXOMR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bad7dd1fa57fabfe1e71c51d5c55ca7b427b68ebbd8c8a3734921720a3e38080","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-03T08:53:56Z","title_canon_sha256":"a50aeb6b6e9886773cb55da231402d7e0cb9b9a95331f5631b3823606b6cfb1b"},"schema_version":"1.0","source":{"id":"2506.02638","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02638","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02638v1","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02638","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"SWWYYB4YW7RW","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_16","alias_value":"SWWYYB4YW7RWGKVL","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_8","alias_value":"SWWYYB4Y","created_at":"2026-07-05T11:15:05Z"}],"graph_snapshots":[{"event_id":"sha256:55ff7205f0e2076aeadb594768e2939806bbce1098e758095255a5efda5380cd","target":"graph","created_at":"2026-07-05T11:15:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.02638/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal'' toroidal embeddings for a Chevalley group scheme over $\\mathbb{Z}$ which specialize to classical toroidal embeddings via base change. In this paper, we establish the existence of ``universal'' equivariant toroidal embeddings for split reductive group schemes over $\\mathbb{Z}$. We also discuss several geometric properties of these embeddings.","authors_text":"Shang Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-03T08:53:56Z","title":"Toroidal embedding of Chevalley groups over $\\mathbb{Z}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02638","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b4f8cf8d8033428220cdfd5d142d2d4858a614f487843a4a13f1f17f00a5c668","target":"record","created_at":"2026-07-05T11:15:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bad7dd1fa57fabfe1e71c51d5c55ca7b427b68ebbd8c8a3734921720a3e38080","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-03T08:53:56Z","title_canon_sha256":"a50aeb6b6e9886773cb55da231402d7e0cb9b9a95331f5631b3823606b6cfb1b"},"schema_version":"1.0","source":{"id":"2506.02638","kind":"arxiv","version":1}},"canonical_sha256":"95ad8c0798b7e3632aab42897502ee645bc116e735ec67d0e00792856d610f64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95ad8c0798b7e3632aab42897502ee645bc116e735ec67d0e00792856d610f64","first_computed_at":"2026-07-05T11:15:05.779813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:05.779813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zuiCWPZHuxMm1mNuE2ucia5e7JteeV6gIfg5CeBKl89sVJqTfBaz0pDhtf1ncpzFB28xRDL5RbP42mP/Zsh+Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:05.780231Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02638","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4f8cf8d8033428220cdfd5d142d2d4858a614f487843a4a13f1f17f00a5c668","sha256:55ff7205f0e2076aeadb594768e2939806bbce1098e758095255a5efda5380cd"],"state_sha256":"e1383077145e25a5b0d6287531ff1917f15bf7f5b9413d1af2337338a223cd8d"}