{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:GIMLD3PH5CM3SG4LRKNJW65GFJ","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":"b3d844660d2c5a087db6c753e874842fb6239fc0146fe4ceafdaf2ff5cab28d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-05-24T16:33:41Z","title_canon_sha256":"1407079d581f114a396d2896cfd80cf118a7c7506e44cda20f8ff1894b39554c"},"schema_version":"1.0","source":{"id":"2005.11793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.11793","created_at":"2026-07-05T01:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"2005.11793v1","created_at":"2026-07-05T01:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.11793","created_at":"2026-07-05T01:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"GIMLD3PH5CM3","created_at":"2026-07-05T01:05:17Z"},{"alias_kind":"pith_short_16","alias_value":"GIMLD3PH5CM3SG4L","created_at":"2026-07-05T01:05:17Z"},{"alias_kind":"pith_short_8","alias_value":"GIMLD3PH","created_at":"2026-07-05T01:05:17Z"}],"graph_snapshots":[{"event_id":"sha256:09c9c9543282b4b9b9086b2de962a9e8541f084f254861ef1da371112ec1232e","target":"graph","created_at":"2026-07-05T01:05:17Z","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/2005.11793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dabkowski and Sahi defined an invariant of a link in the $3$-sphere, which is preserved under $4$-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to $4$-moves.","authors_text":"Akira Yasuhara, Haruko A. Miyazawa, Kodai Wada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-05-24T16:33:41Z","title":"The Dabkowski-Sahi invariant and $4$-moves for links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.11793","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":"sha256:53b259deacc4c31fd05f2a00f8d2d92acb9c9bca69ff5eac4272d3218cdcbb27","target":"record","created_at":"2026-07-05T01:05:17Z","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":"b3d844660d2c5a087db6c753e874842fb6239fc0146fe4ceafdaf2ff5cab28d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-05-24T16:33:41Z","title_canon_sha256":"1407079d581f114a396d2896cfd80cf118a7c7506e44cda20f8ff1894b39554c"},"schema_version":"1.0","source":{"id":"2005.11793","kind":"arxiv","version":1}},"canonical_sha256":"3218b1ede7e899b91b8b8a9a9b7ba62a6c9097eba810de198c744efd6deae15d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3218b1ede7e899b91b8b8a9a9b7ba62a6c9097eba810de198c744efd6deae15d","first_computed_at":"2026-07-05T01:05:17.514145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:05:17.514145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3T1VEopFvwSzkTw7hPKPHh7wbdcJ0Gx1wmBoM0t/W304hlb+4DQHYouWHKhGk45GL3mdpBCv0Yno2pM6TbZCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:05:17.514533Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.11793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53b259deacc4c31fd05f2a00f8d2d92acb9c9bca69ff5eac4272d3218cdcbb27","sha256:09c9c9543282b4b9b9086b2de962a9e8541f084f254861ef1da371112ec1232e"],"state_sha256":"9de14ec77bceb974b71fa85aaf25f270790a97e3bed6a273904f9bdc82ec6b68"}