{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:PMIGRF4DRQQMHIBGJSCS7Z6KVC","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":"473c0ee013172197de06c9d3531f9bc1df38ef701e293c7f0e11c4ad079ab63a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-11-11T13:22:36Z","title_canon_sha256":"61feb7f7c7d64613005214187d389e37b9844f50d59f838fcd042dc1f12acb17"},"schema_version":"1.0","source":{"id":"2011.05766","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.05766","created_at":"2026-07-05T04:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"2011.05766v4","created_at":"2026-07-05T04:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.05766","created_at":"2026-07-05T04:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"PMIGRF4DRQQM","created_at":"2026-07-05T04:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"PMIGRF4DRQQMHIBG","created_at":"2026-07-05T04:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"PMIGRF4D","created_at":"2026-07-05T04:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:baeeb3bff80709a766def4dd46091f460626eba8697e7c6f80192dfcc15dd901","target":"graph","created_at":"2026-07-05T04:28:25Z","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/2011.05766/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behavior of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting.","authors_text":"Makoto Sakuma, Yuya Koda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-11-11T13:22:36Z","title":"Homotopy motions of surfaces in $3$-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.05766","kind":"arxiv","version":4},"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":"sha256:8dcfc21456bfa8a454ef4029ccc05c36c410e74441dbd323b013fc0f9896ecf8","target":"record","created_at":"2026-07-05T04:28:25Z","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":"473c0ee013172197de06c9d3531f9bc1df38ef701e293c7f0e11c4ad079ab63a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-11-11T13:22:36Z","title_canon_sha256":"61feb7f7c7d64613005214187d389e37b9844f50d59f838fcd042dc1f12acb17"},"schema_version":"1.0","source":{"id":"2011.05766","kind":"arxiv","version":4}},"canonical_sha256":"7b106897838c20c3a0264c852fe7caa884d88033635976495559492e164de26e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b106897838c20c3a0264c852fe7caa884d88033635976495559492e164de26e","first_computed_at":"2026-07-05T04:28:25.827138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:28:25.827138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SBEyuZHAbUKwrZkMHoSC39XfKWxqHri+hR2uGHv1q+YfqZdlSoh0fNM+dIKsJ+T8j8Xq4NC843TA9RDKgE19CA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:28:25.827652Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.05766","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dcfc21456bfa8a454ef4029ccc05c36c410e74441dbd323b013fc0f9896ecf8","sha256:baeeb3bff80709a766def4dd46091f460626eba8697e7c6f80192dfcc15dd901"],"state_sha256":"a4e79f4f73ce5a3d51df1426c3c0d28e004de2de9e870d4e5357a607844973f5"}