{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:A5RHH5SEXQZLWYEJAVB7ADJRAG","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":"407f7463e36a19a12e254df8c39c38ab85992ddd9aef1b8fa1f163bc2b4f48a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-01-27T10:15:43Z","title_canon_sha256":"4b4fa9cabca26224487164e38aa41880b7b4d2ad89e68f78e2c03cd927ede594"},"schema_version":"1.0","source":{"id":"2201.11420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.11420","created_at":"2026-07-05T06:55:20Z"},{"alias_kind":"arxiv_version","alias_value":"2201.11420v1","created_at":"2026-07-05T06:55:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.11420","created_at":"2026-07-05T06:55:20Z"},{"alias_kind":"pith_short_12","alias_value":"A5RHH5SEXQZL","created_at":"2026-07-05T06:55:20Z"},{"alias_kind":"pith_short_16","alias_value":"A5RHH5SEXQZLWYEJ","created_at":"2026-07-05T06:55:20Z"},{"alias_kind":"pith_short_8","alias_value":"A5RHH5SE","created_at":"2026-07-05T06:55:20Z"}],"graph_snapshots":[{"event_id":"sha256:5183d610433e498914e4c0e63fcbcd087ef04de27e78ee175dd4797675e6f44e","target":"graph","created_at":"2026-07-05T06:55:20Z","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/2201.11420/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the concept of a handlebody decomposition of a 3-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a closed orientable 3-manifold are stably equivalent. As an application to materials science, we consider a mathematical model of polycontinuous patterns and discuss a topological study of microphase separation of a block copolymer melt.","authors_text":"Kai Ishihara, Koya Shimokawa, Makoto Ozawa, Masaki Ogawa, Naoki Sakata, Ryosuke Mishina, Yuya Koda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-01-27T10:15:43Z","title":"Handlebody decompositions of 3-manifolds and polycontinuous patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.11420","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":"sha256:368e78d0459a28c5a0b8d33402580426743655676c0217ac21d928a26cfcda87","target":"record","created_at":"2026-07-05T06:55:20Z","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":"407f7463e36a19a12e254df8c39c38ab85992ddd9aef1b8fa1f163bc2b4f48a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-01-27T10:15:43Z","title_canon_sha256":"4b4fa9cabca26224487164e38aa41880b7b4d2ad89e68f78e2c03cd927ede594"},"schema_version":"1.0","source":{"id":"2201.11420","kind":"arxiv","version":1}},"canonical_sha256":"076273f644bc32bb60890543f00d3101a602d5b3322aa4dcffd985e399074259","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"076273f644bc32bb60890543f00d3101a602d5b3322aa4dcffd985e399074259","first_computed_at":"2026-07-05T06:55:20.490446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:55:20.490446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Pjo4L7Zl5QkEEzWBlpWczrs+xq/8xIeri/WZlmXjQ6k0dBeBeNYJfox1h9NcDW8/8V93DMaqWvjozuI9jGNBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:55:20.490913Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.11420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:368e78d0459a28c5a0b8d33402580426743655676c0217ac21d928a26cfcda87","sha256:5183d610433e498914e4c0e63fcbcd087ef04de27e78ee175dd4797675e6f44e"],"state_sha256":"fa700712e353b40bfdf1368e0d39d56d62b73c48529624d20159c880bf6344ba"}