{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:6C5V4K5FY5REAY2T6VRNHEJSY2","short_pith_number":"pith:6C5V4K5F","schema_version":"1.0","canonical_sha256":"f0bb5e2ba5c762406353f562d39132c69e51d427d95af6438ec3b012d51c9746","source":{"kind":"arxiv","id":"1004.0872","version":2},"attestation_state":"computed","paper":{"title":"Normal surfaces as combinatorial slicings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Jonathan Spreer","submitted_at":"2010-04-06T15:26:37Z","abstract_excerpt":"We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. A focus is given to dimension 3 where slicings are normal surfaces. In the case of 2-neighborly 3-manifolds and quadrangulated slicings, a lower bound on the number of quadrilaterals of normal surfaces depending on the genus g is presented. It is shown to be sharp for infinitely many values of g. Furthermore we classify slicings of combinatorial 3-manifolds with a maximum number of edges in the slicing."},"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":"1004.0872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-06T15:26:37Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"b6b1594ea65e3990236aea0210f884730505f427d46969ce0a967d3444aab306","abstract_canon_sha256":"e0c352dff6e890020edc6f7d5b8227f1d683175559f8e5c602d2d08d311f7679"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:02.896521Z","signature_b64":"SbrAdhS9n1h+E+4uXcgZ2II3atv/V6kocxB52xHzd+xuGaAezBQbaFLyysHZIKxZGryh6Iqs8aoeHPvZRjrMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0bb5e2ba5c762406353f562d39132c69e51d427d95af6438ec3b012d51c9746","last_reissued_at":"2026-05-18T04:00:02.895826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:02.895826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal surfaces as combinatorial slicings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Jonathan Spreer","submitted_at":"2010-04-06T15:26:37Z","abstract_excerpt":"We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. A focus is given to dimension 3 where slicings are normal surfaces. In the case of 2-neighborly 3-manifolds and quadrangulated slicings, a lower bound on the number of quadrilaterals of normal surfaces depending on the genus g is presented. It is shown to be sharp for infinitely many values of g. Furthermore we classify slicings of combinatorial 3-manifolds with a maximum number of edges in the slicing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0872","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":""},"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":"1004.0872","created_at":"2026-05-18T04:00:02.895936+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.0872v2","created_at":"2026-05-18T04:00:02.895936+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0872","created_at":"2026-05-18T04:00:02.895936+00:00"},{"alias_kind":"pith_short_12","alias_value":"6C5V4K5FY5RE","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"6C5V4K5FY5REAY2T","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"6C5V4K5F","created_at":"2026-05-18T12:26:04.259169+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/6C5V4K5FY5REAY2T6VRNHEJSY2","json":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2.json","graph_json":"https://pith.science/api/pith-number/6C5V4K5FY5REAY2T6VRNHEJSY2/graph.json","events_json":"https://pith.science/api/pith-number/6C5V4K5FY5REAY2T6VRNHEJSY2/events.json","paper":"https://pith.science/paper/6C5V4K5F"},"agent_actions":{"view_html":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2","download_json":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2.json","view_paper":"https://pith.science/paper/6C5V4K5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.0872&json=true","fetch_graph":"https://pith.science/api/pith-number/6C5V4K5FY5REAY2T6VRNHEJSY2/graph.json","fetch_events":"https://pith.science/api/pith-number/6C5V4K5FY5REAY2T6VRNHEJSY2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2/action/storage_attestation","attest_author":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2/action/author_attestation","sign_citation":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2/action/citation_signature","submit_replication":"https://pith.science/pith/6C5V4K5FY5REAY2T6VRNHEJSY2/action/replication_record"}},"created_at":"2026-05-18T04:00:02.895936+00:00","updated_at":"2026-05-18T04:00:02.895936+00:00"}