{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ROSBLXUQFLJTQHVFMKCKSCJ5BJ","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":"2ba7ad193d209ce14dd8bc5eb9f2182998efefa27c7fde95fd23bdcabe97bfdf","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2007-03-28T11:31:57Z","title_canon_sha256":"5c3413eb07d6725c3a4ea37ae58f1cfd02fa4f894bf16cae37123900bf9ef597"},"schema_version":"1.0","source":{"id":"math/0703840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703840","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703840v1","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703840","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"ROSBLXUQFLJT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ROSBLXUQFLJTQHVF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ROSBLXUQ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:40cc41d1d56c18eeab58dd3874a62fe86b85eeb6c52039ed360ddf11dbdeda46","target":"graph","created_at":"2026-05-18T02:57:24Z","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"},"paper":{"abstract_excerpt":"We study group gradings on the Albert algebra and on the simple exceptional Lie algebra $\\frak{f}_4$ over algebraically closed fields of characteristic zero. There are eight nontoral nonequivalent gradings on the Albert algebra (three of them being fine) and nine on $\\frak{f}_4$ (also three of them fine).","authors_text":"C\\'andido Mart\\'in, Cristina Draper","cross_cats":[],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2007-03-28T11:31:57Z","title":"Gradings on the Albert Algebra and on $f_4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703840","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":"sha256:3785ea0e1cf9d3d932ed7214471aa6589e7cc0e3a8e8cf330083ba2995e616e3","target":"record","created_at":"2026-05-18T02:57:24Z","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":"2ba7ad193d209ce14dd8bc5eb9f2182998efefa27c7fde95fd23bdcabe97bfdf","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2007-03-28T11:31:57Z","title_canon_sha256":"5c3413eb07d6725c3a4ea37ae58f1cfd02fa4f894bf16cae37123900bf9ef597"},"schema_version":"1.0","source":{"id":"math/0703840","kind":"arxiv","version":1}},"canonical_sha256":"8ba415de902ad3381ea56284a9093d0a7c1da8b4884346f3f718f23609756ab8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ba415de902ad3381ea56284a9093d0a7c1da8b4884346f3f718f23609756ab8","first_computed_at":"2026-05-18T02:57:24.518616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:24.518616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XqqPTopC3vy/gsVAqzpKxWEXotHKuTemwvYFBo2ACimGdIzRbEtSPpGL1DQJfwjbtkXmnHIFXU0JtLBkDNMoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:24.519301Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3785ea0e1cf9d3d932ed7214471aa6589e7cc0e3a8e8cf330083ba2995e616e3","sha256:40cc41d1d56c18eeab58dd3874a62fe86b85eeb6c52039ed360ddf11dbdeda46"],"state_sha256":"28bf9786d277ebb43747276110037c02e9dc0c72d6d1406e0f11c2def716cdc4"}