{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3LJGQ2BDI7QAI5I43Y2P5LJVJR","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":"d92844742750b746ebda8ab3cfcc19d4344e993c0d4ed9635fcebd1cca800bec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-06T03:37:01Z","title_canon_sha256":"48b4d36d0325eddc52073652537a896269bc732d2315d0e04366d2fce192c521"},"schema_version":"1.0","source":{"id":"1703.01718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01718","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01718v1","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01718","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"3LJGQ2BDI7QA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LJGQ2BDI7QAI5I4","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LJGQ2BD","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:51c1b454d6f3aeb51e42605ab140bfc3ffa5493f2899dfb4cf984c9b4895e3fd","target":"graph","created_at":"2026-05-18T00:49:29Z","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":"A Heegaard splitting which admits a unique pair of disjoint compression disks on distinct sides is said to be keen weakly reducible. This paper provides an construction of keen weakly reducible Heegaard splittings of arbitrary genus except 2. Furthermore, critical Heegaard splittings may yield if we change some conditions.","authors_text":"Qiang E","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-06T03:37:01Z","title":"On keen weakly reducbile Heegaard splittings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01718","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:a1064cea0c0652b4cb4a488642d590b1a631900f67608e099b4653d2742c5b67","target":"record","created_at":"2026-05-18T00:49:29Z","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":"d92844742750b746ebda8ab3cfcc19d4344e993c0d4ed9635fcebd1cca800bec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-06T03:37:01Z","title_canon_sha256":"48b4d36d0325eddc52073652537a896269bc732d2315d0e04366d2fce192c521"},"schema_version":"1.0","source":{"id":"1703.01718","kind":"arxiv","version":1}},"canonical_sha256":"dad268682347e004751cde34fead354c738a6902d72cbaebc102f0008fedfbbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dad268682347e004751cde34fead354c738a6902d72cbaebc102f0008fedfbbe","first_computed_at":"2026-05-18T00:49:29.872107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:29.872107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qj+Am3lkos1Is84F0RMWgXPvohuUPPMHisbQTMHS2t4RXDAVGo/C0i4eQ33n6OZY/eEi8k3uJJww3afAnZ2wBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:29.872690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1064cea0c0652b4cb4a488642d590b1a631900f67608e099b4653d2742c5b67","sha256:51c1b454d6f3aeb51e42605ab140bfc3ffa5493f2899dfb4cf984c9b4895e3fd"],"state_sha256":"f4788bd1c9f48f23f125ce693b5e130ee16630c40f2328038576887483a1a122"}