{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LO26FP4IAPZYS4PG67AJ7LRTTZ","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":"5b0b2f2289bd2f97be4f92eea70b15f423e49c6e4a82a13368b2f9b999c520ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-08-26T13:24:18Z","title_canon_sha256":"5d41021ee912869b9b4a847d6fafff371a0fb02ac4f813bca0353fee7b64a75b"},"schema_version":"1.0","source":{"id":"2008.11548","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.11548","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"2008.11548v5","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.11548","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"LO26FP4IAPZY","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_16","alias_value":"LO26FP4IAPZYS4PG","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_8","alias_value":"LO26FP4I","created_at":"2026-06-02T01:03:27Z"}],"graph_snapshots":[{"event_id":"sha256:cb870e2b357eb64d89ec9aaee494b1131ed77f4585cac57293bb28dfb4092877","target":"graph","created_at":"2026-06-02T01:03:27Z","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/2008.11548/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a necessary and sufficient condition for the fundamental group of the space of Heegaard splittings of an irreducible $3$-manifold to be finitely generated. The condition is exactly the conclusion of the thick isotopy lemma proved by Colding, Gabai and Ketover, which says that any isotopy of a Heegaard surface is achieved by a $1$-parameter family of surfaces with area bounded above by a universal constant and with some ``thickness property''. We also prove that a Heegaard splitting of a hyperbolic or spherical $3$-manifold satisfies the condition if it is topologically minimal (in the ","authors_text":"Daiki Iguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-08-26T13:24:18Z","title":"Thick isotopy property and the mapping class groups of Heegaard splittings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.11548","kind":"arxiv","version":5},"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":"sha256:350afea813cf41ac9e3859b61c5dc313f885b87508a3e77d17474f6560f6b4a3","target":"record","created_at":"2026-06-02T01:03:27Z","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":"5b0b2f2289bd2f97be4f92eea70b15f423e49c6e4a82a13368b2f9b999c520ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-08-26T13:24:18Z","title_canon_sha256":"5d41021ee912869b9b4a847d6fafff371a0fb02ac4f813bca0353fee7b64a75b"},"schema_version":"1.0","source":{"id":"2008.11548","kind":"arxiv","version":5}},"canonical_sha256":"5bb5e2bf8803f38971e6f7c09fae339e43659e9cdb7a850aa531e0a434d0acaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bb5e2bf8803f38971e6f7c09fae339e43659e9cdb7a850aa531e0a434d0acaf","first_computed_at":"2026-06-02T01:03:27.501124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:27.501124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f61lPe+gF16753zjBPPOQdVo/CeAuCmAcUCjAsioBsYdvrLBJvxW6kL1CWzqiFC0o2EdfhGZ6Za/KCG7CpTkDw==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:27.501464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.11548","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:350afea813cf41ac9e3859b61c5dc313f885b87508a3e77d17474f6560f6b4a3","sha256:cb870e2b357eb64d89ec9aaee494b1131ed77f4585cac57293bb28dfb4092877"],"state_sha256":"0c5ac598600d4b957d095445850ca72c8c8bbe7315cb11a9e94d2f866c97d190"}