{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RR26BHOCT2HUZYP4Y3IRGLRWWG","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":"82db6155813b1b1981d3b88b3769d826da1f72a7267522fbd7978a109ebac80d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-10T15:01:08Z","title_canon_sha256":"a1bbad401834cbbf1959c9af06470e05c653f52bc049a6f1a67092224e7d0feb"},"schema_version":"1.0","source":{"id":"1312.2824","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2824","created_at":"2026-05-18T01:49:56Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2824v3","created_at":"2026-05-18T01:49:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2824","created_at":"2026-05-18T01:49:56Z"},{"alias_kind":"pith_short_12","alias_value":"RR26BHOCT2HU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RR26BHOCT2HUZYP4","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RR26BHOC","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:d79f445f77f93452fb36176a7921070ffc8e3c312092ea963411a057741655a9","target":"graph","created_at":"2026-05-18T01:49:56Z","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 the behavior of the bilinkage process in codimension $3$. In particular, we construct a smooth canonically embedded and linearly normal surface of general type of degree $18$ in $\\mathbb{P}^5$, this is probably the highest degree such surface may have. Next, we apply our construction to find a geometric description of Tonoli Calabi--Yau threefolds in $\\mathbb{P}^6$.","authors_text":"Grzegorz Kapustka, Michal Kapustka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-10T15:01:08Z","title":"Bilinkage in codimension $3$ and canonical surfaces of degree $18$ in $\\mathbb{P}^5$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2824","kind":"arxiv","version":3},"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":"sha256:9e07c02c757e60a45177699ba2789ed5093601e04a2d9384a6487e7d0810168f","target":"record","created_at":"2026-05-18T01:49:56Z","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":"82db6155813b1b1981d3b88b3769d826da1f72a7267522fbd7978a109ebac80d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-10T15:01:08Z","title_canon_sha256":"a1bbad401834cbbf1959c9af06470e05c653f52bc049a6f1a67092224e7d0feb"},"schema_version":"1.0","source":{"id":"1312.2824","kind":"arxiv","version":3}},"canonical_sha256":"8c75e09dc29e8f4ce1fcc6d1132e36b19e8105a3b5a059c6dfcaba09f5a6b5da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c75e09dc29e8f4ce1fcc6d1132e36b19e8105a3b5a059c6dfcaba09f5a6b5da","first_computed_at":"2026-05-18T01:49:56.147151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:56.147151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ko9k2vG7XwxezfcI3iNJqOIcw6nG/NrcCxVgk1ehPDk0cd4+VquoKE4k1mewIw1oNWyu0hekwzF2VfH6hWssDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:56.147668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2824","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e07c02c757e60a45177699ba2789ed5093601e04a2d9384a6487e7d0810168f","sha256:d79f445f77f93452fb36176a7921070ffc8e3c312092ea963411a057741655a9"],"state_sha256":"2e0592d4fff3ebe6b5e03bf2e26ac4ef4fb914f617134ef5d9644db277756e6b"}