{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TSE6BTRVUNUKZYC3ZBAOBFTMF5","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":"c7e84c0f904e758495991c1f54f9f3317fa9a8b6538615992c95fdb589f6be26","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-06-03T13:52:45Z","title_canon_sha256":"edf1172d1589378c718bbfb211ccbe2cb45418208d0d253d8867ed90eeeb1ab2"},"schema_version":"1.0","source":{"id":"2006.02276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.02276","created_at":"2026-07-05T04:53:38Z"},{"alias_kind":"arxiv_version","alias_value":"2006.02276v2","created_at":"2026-07-05T04:53:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.02276","created_at":"2026-07-05T04:53:38Z"},{"alias_kind":"pith_short_12","alias_value":"TSE6BTRVUNUK","created_at":"2026-07-05T04:53:38Z"},{"alias_kind":"pith_short_16","alias_value":"TSE6BTRVUNUKZYC3","created_at":"2026-07-05T04:53:38Z"},{"alias_kind":"pith_short_8","alias_value":"TSE6BTRV","created_at":"2026-07-05T04:53:38Z"}],"graph_snapshots":[{"event_id":"sha256:5aadcc33f7bc812b1926b5d3e1b0e85b829b5ea1b2e7b189263bfd5c245f50c5","target":"graph","created_at":"2026-07-05T04:53:38Z","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/2006.02276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce algebraic structures known as psybrackets and use them to define invariants of pseudoknots and singular knots and links. Psybrackets are Niebrzydowski tribrackets with additional structure inspired by the Reidemeister moves for pseudoknots and singular knots. Examples and computations are provided.","authors_text":"Jieon Kim, Sam Nelson, Suhyeon Jeong","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-06-03T13:52:45Z","title":"Psybrackets, Pseudoknots and Singular Knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02276","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:d8f40f9fb9aa55cadc1604214a1c7c9d64f928343ce074ac826548c5439f9f6c","target":"record","created_at":"2026-07-05T04:53:38Z","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":"c7e84c0f904e758495991c1f54f9f3317fa9a8b6538615992c95fdb589f6be26","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-06-03T13:52:45Z","title_canon_sha256":"edf1172d1589378c718bbfb211ccbe2cb45418208d0d253d8867ed90eeeb1ab2"},"schema_version":"1.0","source":{"id":"2006.02276","kind":"arxiv","version":2}},"canonical_sha256":"9c89e0ce35a368ace05bc840e0966c2f7c0c8bf818ab16ebb80836c4d92174f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c89e0ce35a368ace05bc840e0966c2f7c0c8bf818ab16ebb80836c4d92174f3","first_computed_at":"2026-07-05T04:53:38.455831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:53:38.455831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tQqz1k1T9j/ktfVO4P7DH/suEFuOvqeII+aggKvhYPDf7foC6+G7Cf20M/wS371dpQt7Ib6TIO57phRcsIdAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:53:38.456221Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.02276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8f40f9fb9aa55cadc1604214a1c7c9d64f928343ce074ac826548c5439f9f6c","sha256:5aadcc33f7bc812b1926b5d3e1b0e85b829b5ea1b2e7b189263bfd5c245f50c5"],"state_sha256":"856a8fd1a043e39c17c8d539c0cae27577f501898f7d3dbce8dff2d6f9ddb99d"}