{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YAUVBOPNUDQSZDEATG7T3ULEBX","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":"b6bc3102a03b3e672df1206a667a347fdde26bc1181763c5775a1b23e816e457","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T07:42:27Z","title_canon_sha256":"89787e70566e344d527f86a1dbfb031c881506ba7addeeb8fbb0214d6b3b0133"},"schema_version":"1.0","source":{"id":"1211.2526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2526","created_at":"2026-05-18T03:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2526v1","created_at":"2026-05-18T03:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2526","created_at":"2026-05-18T03:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"YAUVBOPNUDQS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YAUVBOPNUDQSZDEA","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YAUVBOPN","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:e24dfd0d84d7143f7e582ede87acbd354ae17f130c3a2a8f6310b2d0e682dceb","target":"graph","created_at":"2026-05-18T03:41:03Z","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":"Let $S$ and $T$ be reduced divisors on $\\mathbb{P}^2$ which have no common components, and $\\Delta=S+2\\,T.$ We assume $\\deg\\Delta=6.$ Let $\\pi:X\\to\\mathbb{P}^2$ be a normal triple cover with branch divisor $\\Delta,$ i.e. $\\pi$ is ramified along $S$ (resp. $T$) with the index 2 (resp. 3). In this note, we show that $X$ is either a $\\mathbb{P}^1$-bundle over an elliptic curve or a normal cubic surface in $\\mathbb{P}^3.$ Consequently, we give a necessary and sufficient condition for $\\Delta$ to be the branch divisor of a normal triple cover over $\\mathbb{P}^2.$","authors_text":"Taketo Shirane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T07:42:27Z","title":"A note on normal triple covers over $\\mathbb{P}^2$ with branch divisors of degree 6"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2526","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":"sha256:754cd8ede0f37d95f37b7b273f590e00bd365241b47b70f11b0734f4fb3a69a4","target":"record","created_at":"2026-05-18T03:41:03Z","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":"b6bc3102a03b3e672df1206a667a347fdde26bc1181763c5775a1b23e816e457","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T07:42:27Z","title_canon_sha256":"89787e70566e344d527f86a1dbfb031c881506ba7addeeb8fbb0214d6b3b0133"},"schema_version":"1.0","source":{"id":"1211.2526","kind":"arxiv","version":1}},"canonical_sha256":"c02950b9eda0e12c8c8099bf3dd1640de7fa3d6949f0defee33d1c1f7e937d97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c02950b9eda0e12c8c8099bf3dd1640de7fa3d6949f0defee33d1c1f7e937d97","first_computed_at":"2026-05-18T03:41:03.061281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:03.061281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sDthlwypVvsmnNEQxePnyTDYheW7UZicqX+B7wc9UIWwbb+aSfh3tsFQLHvbdDtZV9toVOSMirmvu3ovJRt/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:03.061773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:754cd8ede0f37d95f37b7b273f590e00bd365241b47b70f11b0734f4fb3a69a4","sha256:e24dfd0d84d7143f7e582ede87acbd354ae17f130c3a2a8f6310b2d0e682dceb"],"state_sha256":"316f038020d08888c4ea6d610b3d4a399c9ad56dfaa6fad3356f59e3e6212ba9"}