{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:BXUPFO757UZM4GXPTWFELVOBUC","short_pith_number":"pith:BXUPFO75","schema_version":"1.0","canonical_sha256":"0de8f2bbfdfd32ce1aef9d8a45d5c1a0a6d3f61b0a2ba94d5836d6400af0a425","source":{"kind":"arxiv","id":"2007.10053","version":3},"attestation_state":"computed","paper":{"title":"Counting essential surfaces in 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"J. Hyam Rubinstein, Nathan M. Dunfield, Stavros Garoufalidis","submitted_at":"2020-07-20T12:46:58Z","abstract_excerpt":"We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds. Our main result is that the count of (possibly disconnected) essential surfaces in terms of their Euler characteristic always has a short generating function and hence has quasi-polynomial behavior. This gives remarkably concise formulae for the number of such surfaces, as well as detailed asymptotics. We give algorithms that allow us to compute these generating functions and the underlying surfaces, and apply these "},"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":"2007.10053","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-07-20T12:46:58Z","cross_cats_sorted":[],"title_canon_sha256":"529cc40a57cf273a0cfcb3a8ffb65dd84f39af3c53ff6c1fddd0e4d99e9ce548","abstract_canon_sha256":"494daa3f97d3bae1049edc3729153b86eb0eb24ad86d4a268805a3ff123027d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:51:03.972369Z","signature_b64":"GLkdpaq1pI11FurA1+KfW4VrCEB3kj4XlDtJ7g4DaVmVO1702+DOk6q8wqoYR4ZpN7IwBYgaQUS5+llzKuy8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0de8f2bbfdfd32ce1aef9d8a45d5c1a0a6d3f61b0a2ba94d5836d6400af0a425","last_reissued_at":"2026-07-05T03:51:03.971979Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:51:03.971979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting essential surfaces in 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"J. Hyam Rubinstein, Nathan M. Dunfield, Stavros Garoufalidis","submitted_at":"2020-07-20T12:46:58Z","abstract_excerpt":"We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds. Our main result is that the count of (possibly disconnected) essential surfaces in terms of their Euler characteristic always has a short generating function and hence has quasi-polynomial behavior. This gives remarkably concise formulae for the number of such surfaces, as well as detailed asymptotics. We give algorithms that allow us to compute these generating functions and the underlying surfaces, and apply these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.10053","kind":"arxiv","version":3},"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/2007.10053/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":"2007.10053","created_at":"2026-07-05T03:51:03.972034+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.10053v3","created_at":"2026-07-05T03:51:03.972034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.10053","created_at":"2026-07-05T03:51:03.972034+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXUPFO757UZM","created_at":"2026-07-05T03:51:03.972034+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXUPFO757UZM4GXP","created_at":"2026-07-05T03:51:03.972034+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXUPFO75","created_at":"2026-07-05T03:51:03.972034+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/BXUPFO757UZM4GXPTWFELVOBUC","json":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC.json","graph_json":"https://pith.science/api/pith-number/BXUPFO757UZM4GXPTWFELVOBUC/graph.json","events_json":"https://pith.science/api/pith-number/BXUPFO757UZM4GXPTWFELVOBUC/events.json","paper":"https://pith.science/paper/BXUPFO75"},"agent_actions":{"view_html":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC","download_json":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC.json","view_paper":"https://pith.science/paper/BXUPFO75","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.10053&json=true","fetch_graph":"https://pith.science/api/pith-number/BXUPFO757UZM4GXPTWFELVOBUC/graph.json","fetch_events":"https://pith.science/api/pith-number/BXUPFO757UZM4GXPTWFELVOBUC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC/action/storage_attestation","attest_author":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC/action/author_attestation","sign_citation":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC/action/citation_signature","submit_replication":"https://pith.science/pith/BXUPFO757UZM4GXPTWFELVOBUC/action/replication_record"}},"created_at":"2026-07-05T03:51:03.972034+00:00","updated_at":"2026-07-05T03:51:03.972034+00:00"}