{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:53CY5JZVMAEWICACO5XLADUW3Z","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":"9ef69b00a5035ccdcf071d012d94d727694ef90d128c574f6c9035cfd36e1a5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T17:55:43Z","title_canon_sha256":"bf4eb96b8a94a14da73dd58e15de01ce5884c9800e4d638be805b7a797b978da"},"schema_version":"1.0","source":{"id":"1211.1327","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1327","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1327v2","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1327","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"53CY5JZVMAEW","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"53CY5JZVMAEWICAC","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"53CY5JZV","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:a9df9078e95fefd9172f6f05fa26d181adeeee189f2efa30fa470974b428840a","target":"graph","created_at":"2026-05-18T02:29:39Z","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":"In this short note, we give an algorithm to get an explicit expression of the Luroth invariant in terms of the Dixmier-Ohno invariants. We also get the explicit factorized expression on the locus of Ciani quartics in terms of the coefficients. Finally, we answer two open questions on sub-loci of singular Luroth quartics.","authors_text":"Christophe Ritzenthaler, Jeroen Sijsling, Reynald Lercier, Romain Basson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T17:55:43Z","title":"An explicit expression of the Luroth invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1327","kind":"arxiv","version":2},"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":"sha256:65b786bf403b5229b6a561cfc2c42715713c76036ce176d2eb7d5bbb4b921581","target":"record","created_at":"2026-05-18T02:29:39Z","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":"9ef69b00a5035ccdcf071d012d94d727694ef90d128c574f6c9035cfd36e1a5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T17:55:43Z","title_canon_sha256":"bf4eb96b8a94a14da73dd58e15de01ce5884c9800e4d638be805b7a797b978da"},"schema_version":"1.0","source":{"id":"1211.1327","kind":"arxiv","version":2}},"canonical_sha256":"eec58ea7356009640802776eb00e96de468eaf6082f3f08e55edeff7d220489b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eec58ea7356009640802776eb00e96de468eaf6082f3f08e55edeff7d220489b","first_computed_at":"2026-05-18T02:29:39.361957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:39.361957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YiiloPiEktSl+ErPKF8WWvclRj0f47eAxsakFVKwByoePzQ1hS4wUlUc+XdAEiQ0OKFF1q6c3QlFsM7yzAQxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:39.362372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1327","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65b786bf403b5229b6a561cfc2c42715713c76036ce176d2eb7d5bbb4b921581","sha256:a9df9078e95fefd9172f6f05fa26d181adeeee189f2efa30fa470974b428840a"],"state_sha256":"77a4e9054ae72be41b8a92711daef387b3e1cf89fbc9e26aa0868cf04d23c999"}