{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QN662AR2ZW552T6T4TZRRNIQJL","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":"49706f9118594a9de73ea5531ad17011d666198d21d251e75f9d8cc6630d2778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-04-29T03:24:28Z","title_canon_sha256":"63530a493eb0234a361b97fdadbcffa7f94d4ed19a4ce4be30593ddf4366fed6"},"schema_version":"1.0","source":{"id":"2204.13860","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.13860","created_at":"2026-07-05T05:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"2204.13860v3","created_at":"2026-07-05T05:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.13860","created_at":"2026-07-05T05:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"QN662AR2ZW55","created_at":"2026-07-05T05:26:40Z"},{"alias_kind":"pith_short_16","alias_value":"QN662AR2ZW552T6T","created_at":"2026-07-05T05:26:40Z"},{"alias_kind":"pith_short_8","alias_value":"QN662AR2","created_at":"2026-07-05T05:26:40Z"}],"graph_snapshots":[{"event_id":"sha256:87b6b200da369b872ed82b3c05c2617b1c30cd993449d6e1f45fd920447178e3","target":"graph","created_at":"2026-07-05T05:26:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2204.13860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Analogous to a classical knot diagram, a surface-link can be generically projected to 3-space and given crossing information to create a broken sheet diagram. The triple point number of a surface-link is the minimal number of triple points among all broken sheet diagrams that lift to that surface-link. This paper generalizes a family of Oshiro to show that there are non-split surface-links of arbitrarily many trivial components whose triple point number can be made arbitrarily large.","authors_text":"Nicholas Cazet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-04-29T03:24:28Z","title":"Surface-link families with arbitrarily large triple point number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.13860","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":"sha256:4af6de0c42b19d2c62e40c3807b9726b01581bf3367b5a5f30d90ae72b0cf856","target":"record","created_at":"2026-07-05T05:26:40Z","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":"49706f9118594a9de73ea5531ad17011d666198d21d251e75f9d8cc6630d2778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-04-29T03:24:28Z","title_canon_sha256":"63530a493eb0234a361b97fdadbcffa7f94d4ed19a4ce4be30593ddf4366fed6"},"schema_version":"1.0","source":{"id":"2204.13860","kind":"arxiv","version":3}},"canonical_sha256":"837ded023acdbbdd4fd3e4f318b5104afd0e35020339ef6bc6faf2b802f2a8cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"837ded023acdbbdd4fd3e4f318b5104afd0e35020339ef6bc6faf2b802f2a8cc","first_computed_at":"2026-07-05T05:26:40.840548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:26:40.840548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yjeidI7GcRwg1zV72c0i+Saz+vpstDS4YVKmx0Tb2BDwLgFzNWR4/3YG4K2dLTTUPoMfrfBsfpi5MgTWSQ++Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:26:40.840975Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.13860","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4af6de0c42b19d2c62e40c3807b9726b01581bf3367b5a5f30d90ae72b0cf856","sha256:87b6b200da369b872ed82b3c05c2617b1c30cd993449d6e1f45fd920447178e3"],"state_sha256":"d7d614fd6e69bf235332521e61e1d1776dda569c49aa63e4f877be551109e864"}