{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:IY64XT27WSUCRXQOUOOXUHBMZX","short_pith_number":"pith:IY64XT27","schema_version":"1.0","canonical_sha256":"463dcbcf5fb4a828de0ea39d7a1c2ccdf9af84edfba3a9639e61336c92b9dc72","source":{"kind":"arxiv","id":"2306.12631","version":2},"attestation_state":"computed","paper":{"title":"Divides and hyperbolic volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ryoga Furutani, Yuya Koda","submitted_at":"2023-06-22T01:46:01Z","abstract_excerpt":"A divide is the image of a proper and generic immersion of a compact $1$-manifold into the $2$-disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere. In this paper, we reveal a hidden hyperbolic structure in the theory of links of divides. More precisely, we show that the complement of the link of a divide can be obtained by Dehn filling a hyperbolic $3$-manifold that admits a decomposition into several ideal regular tetrahedra, octahedra and cuboctahedra, where the number of each of those three polyhedra is determined by types of the double points of the divide."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2306.12631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-06-22T01:46:01Z","cross_cats_sorted":[],"title_canon_sha256":"8ae4ea68411cf490f1668c6008442cdd787c9f6a824037d64a9260fe13ef2fe6","abstract_canon_sha256":"5dd13918588758627f08c1e72cbe4b8a0ba71f19d9d66467402ae5900e0705f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:48:47.122358Z","signature_b64":"XhdqYxcGrww6iwGyt+yHAyWoR0+8iDnCx5l5Qc1LJHmwQQXC6c8lMqIeM1VViQdTxFFnEcSosS4ivBXQA7KBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"463dcbcf5fb4a828de0ea39d7a1c2ccdf9af84edfba3a9639e61336c92b9dc72","last_reissued_at":"2026-07-05T07:48:47.121842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:48:47.121842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Divides and hyperbolic volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ryoga Furutani, Yuya Koda","submitted_at":"2023-06-22T01:46:01Z","abstract_excerpt":"A divide is the image of a proper and generic immersion of a compact $1$-manifold into the $2$-disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere. In this paper, we reveal a hidden hyperbolic structure in the theory of links of divides. More precisely, we show that the complement of the link of a divide can be obtained by Dehn filling a hyperbolic $3$-manifold that admits a decomposition into several ideal regular tetrahedra, octahedra and cuboctahedra, where the number of each of those three polyhedra is determined by types of the double points of the divide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12631","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.12631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2306.12631","created_at":"2026-07-05T07:48:47.121911+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.12631v2","created_at":"2026-07-05T07:48:47.121911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.12631","created_at":"2026-07-05T07:48:47.121911+00:00"},{"alias_kind":"pith_short_12","alias_value":"IY64XT27WSUC","created_at":"2026-07-05T07:48:47.121911+00:00"},{"alias_kind":"pith_short_16","alias_value":"IY64XT27WSUCRXQO","created_at":"2026-07-05T07:48:47.121911+00:00"},{"alias_kind":"pith_short_8","alias_value":"IY64XT27","created_at":"2026-07-05T07:48:47.121911+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX","json":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX.json","graph_json":"https://pith.science/api/pith-number/IY64XT27WSUCRXQOUOOXUHBMZX/graph.json","events_json":"https://pith.science/api/pith-number/IY64XT27WSUCRXQOUOOXUHBMZX/events.json","paper":"https://pith.science/paper/IY64XT27"},"agent_actions":{"view_html":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX","download_json":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX.json","view_paper":"https://pith.science/paper/IY64XT27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.12631&json=true","fetch_graph":"https://pith.science/api/pith-number/IY64XT27WSUCRXQOUOOXUHBMZX/graph.json","fetch_events":"https://pith.science/api/pith-number/IY64XT27WSUCRXQOUOOXUHBMZX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX/action/storage_attestation","attest_author":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX/action/author_attestation","sign_citation":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX/action/citation_signature","submit_replication":"https://pith.science/pith/IY64XT27WSUCRXQOUOOXUHBMZX/action/replication_record"}},"created_at":"2026-07-05T07:48:47.121911+00:00","updated_at":"2026-07-05T07:48:47.121911+00:00"}