{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GEVIFLB3NGNLCSCVPVKLIGCZ3E","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":"aaf95373f67955712f77df1b185edec66dc134c46a2e6c3173936f5fec3d96fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-14T21:20:22Z","title_canon_sha256":"7fae0ae9bfc22610ebe658980e793e572fa8186b45a7dd5f8deeba3ea6547728"},"schema_version":"1.0","source":{"id":"1603.04480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04480","created_at":"2026-05-18T01:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04480v1","created_at":"2026-05-18T01:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04480","created_at":"2026-05-18T01:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"GEVIFLB3NGNL","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GEVIFLB3NGNLCSCV","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GEVIFLB3","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:6fc3d2a1a11c1942f3fb49dd8585006a7729fb7d827cb090aac9636f4f5c63fb","target":"graph","created_at":"2026-05-18T01:19:04Z","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":"For each $m\\ge 1$, Roulleau and Urz\\'ua give an implicit construction of a configuration of $4(3m^2-1)$ complex plane cubic curves. This construction was crucial for their work on surfaces of general type. We make this construction explicit by proving that the Roulleau-Urz\\'ua configuration consists precisely of the Halphen cubics of order $m$, and we determine specific equations of the cubics for $m=1$ (which were known) and for $m=2$ (which are new).","authors_text":"Brian Harbourne, Joaquim Ro\\'e, Thomas Bauer, Tomasz Szemberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-14T21:20:22Z","title":"The Halphen cubics of order two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04480","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:b7e096d61f64036448d97f965a73cc83c48a6cbf5f3a94fbb2416561c80c55b9","target":"record","created_at":"2026-05-18T01:19:04Z","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":"aaf95373f67955712f77df1b185edec66dc134c46a2e6c3173936f5fec3d96fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-14T21:20:22Z","title_canon_sha256":"7fae0ae9bfc22610ebe658980e793e572fa8186b45a7dd5f8deeba3ea6547728"},"schema_version":"1.0","source":{"id":"1603.04480","kind":"arxiv","version":1}},"canonical_sha256":"312a82ac3b699ab148557d54b41859d9199ab7876fa722fba40ad34496f12f99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"312a82ac3b699ab148557d54b41859d9199ab7876fa722fba40ad34496f12f99","first_computed_at":"2026-05-18T01:19:04.850753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:04.850753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XuC1Wk2pz+Y9CqB4H0pENP5TKNKFjuFxs9UWOKGh8VYSmjpYA3mw5QymbHaf/VK2TE3+PPCHjX1qKX49aSx8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:04.851288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7e096d61f64036448d97f965a73cc83c48a6cbf5f3a94fbb2416561c80c55b9","sha256:6fc3d2a1a11c1942f3fb49dd8585006a7729fb7d827cb090aac9636f4f5c63fb"],"state_sha256":"2aab397cdbfe11b3a50e220ceb03f03961dd8c3b19f5aa81e2d01c0ac81ee4bb"}