{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:INWGOQZAZ4TZCZAFYRF3QJCM3O","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":"eb8242279f802f6dfd50956bfa703113fd60986148a534adc75b739b538dc9e7","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-10T20:16:02Z","title_canon_sha256":"0e03d66ac6ac0fe2bf3aa3d529895d918135e259711c6ca38f0757310c16951e"},"schema_version":"1.0","source":{"id":"1411.2569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2569","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2569v1","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2569","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"INWGOQZAZ4TZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"INWGOQZAZ4TZCZAF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"INWGOQZA","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:8994cad264dd56e5ce61d062178ac92145346d6ab4f1cf53e9ff8d2950d6dc8f","target":"graph","created_at":"2026-05-18T02:16:39Z","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":"Following the suggestion of arXiv:1407.6319 to lift the knot polynomials for virtual knots and links from Jones to HOMFLY, we apply the evolution method to calculate them for an infinite series of twist-like virtual knots and antiparallel 2-strand links. Within this family one can check topological invariance and understand how differential hierarchy is modified in virtual case. This opens a way towards a definition of colored (not only cabled) knot polynomials, though problems still persist beyond the first symmetric representation.","authors_text":"Alexei Morozov, Andrey Morozov, Anton Morozov, Ludmila Bishler","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-10T20:16:02Z","title":"Evolution method and HOMFLY polynomials for virtual knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2569","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:bacc9993884c95dbeb5ccb5f8aa23ffb6b0b78c21a12eefb01b79c5774884205","target":"record","created_at":"2026-05-18T02:16:39Z","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":"eb8242279f802f6dfd50956bfa703113fd60986148a534adc75b739b538dc9e7","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-10T20:16:02Z","title_canon_sha256":"0e03d66ac6ac0fe2bf3aa3d529895d918135e259711c6ca38f0757310c16951e"},"schema_version":"1.0","source":{"id":"1411.2569","kind":"arxiv","version":1}},"canonical_sha256":"436c674320cf27916405c44bb8244cdb928a49f61bef77472c8d8436720c8025","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"436c674320cf27916405c44bb8244cdb928a49f61bef77472c8d8436720c8025","first_computed_at":"2026-05-18T02:16:39.170120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:39.170120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7fzzOLpARqW/mzN7g0rZ1oLD+IfW0rGHQo3ijmBUHTeJk+k5Zacvbbfx3rpt7Lop7i//5AfO4zifm5IqGiFGBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:39.170518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bacc9993884c95dbeb5ccb5f8aa23ffb6b0b78c21a12eefb01b79c5774884205","sha256:8994cad264dd56e5ce61d062178ac92145346d6ab4f1cf53e9ff8d2950d6dc8f"],"state_sha256":"d12291ea62de28ab2cd9d8d7be25b653aab9ce701414fe1904586c6a836feeb0"}