{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JTUNHTJ6EJQPPAPEGLTOVPXLXG","short_pith_number":"pith:JTUNHTJ6","schema_version":"1.0","canonical_sha256":"4ce8d3cd3e2260f781e432e6eabeebb9a40420e71e33a99f99604e37f3a319cb","source":{"kind":"arxiv","id":"1409.1314","version":3},"attestation_state":"computed","paper":{"title":"Asymptotic enumeration of sparse uniform linear hypergraphs with given degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Greenhill, Vladimir Blinovsky","submitted_at":"2014-09-04T03:42:48Z","abstract_excerpt":"A hypergraph is simple if it has no loops and no repeated edges, and a hypergraph is linear if it is simple and each pair of edges intersects in at most one vertex. For $n\\geq 3$, let $r= r(n)\\geq 3$ be an integer and let $\\boldsymbol{k} = (k_1,\\ldots, k_n)$ be a vector of nonnegative integers, where each $k_j = k_j(n)$ may depend on $n$. Let $M = M(n) = \\sum_{j=1}^n k_j$ for all $n\\geq 3$, and define the set $\\mathcal{I} = \\{ n\\geq 3 \\mid r(n) \\text{ divides } M(n)\\}$. We assume that $\\mathcal{I}$ is infinite, and perform asymptotics as $n$ tends to infinity along $\\mathcal{I}$. Our main resu"},"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":"1409.1314","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-04T03:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"b0dc0d5bb7f7c37d03b5d8dde6e3923bda56a93f137eeeac0a1fa572493bfd2f","abstract_canon_sha256":"c1976d99b12cb2da3ed2b5947d147a0f1ccabc9c552fc8cd9ccb56d78776b8eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:54.639508Z","signature_b64":"dcxzXIxF2OPlKPdqahoGtcOWe8Ah7yZIHVAngygBKZcxk9GuZ4iTBqiew5h8hyjglMtvjOsMAAesPZy3lTR3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ce8d3cd3e2260f781e432e6eabeebb9a40420e71e33a99f99604e37f3a319cb","last_reissued_at":"2026-05-18T01:10:54.638939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:54.638939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic enumeration of sparse uniform linear hypergraphs with given degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Greenhill, Vladimir Blinovsky","submitted_at":"2014-09-04T03:42:48Z","abstract_excerpt":"A hypergraph is simple if it has no loops and no repeated edges, and a hypergraph is linear if it is simple and each pair of edges intersects in at most one vertex. For $n\\geq 3$, let $r= r(n)\\geq 3$ be an integer and let $\\boldsymbol{k} = (k_1,\\ldots, k_n)$ be a vector of nonnegative integers, where each $k_j = k_j(n)$ may depend on $n$. Let $M = M(n) = \\sum_{j=1}^n k_j$ for all $n\\geq 3$, and define the set $\\mathcal{I} = \\{ n\\geq 3 \\mid r(n) \\text{ divides } M(n)\\}$. We assume that $\\mathcal{I}$ is infinite, and perform asymptotics as $n$ tends to infinity along $\\mathcal{I}$. Our main resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1314","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":""},"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":"1409.1314","created_at":"2026-05-18T01:10:54.639032+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1314v3","created_at":"2026-05-18T01:10:54.639032+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1314","created_at":"2026-05-18T01:10:54.639032+00:00"},{"alias_kind":"pith_short_12","alias_value":"JTUNHTJ6EJQP","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JTUNHTJ6EJQPPAPE","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JTUNHTJ6","created_at":"2026-05-18T12:28:35.611951+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/JTUNHTJ6EJQPPAPEGLTOVPXLXG","json":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG.json","graph_json":"https://pith.science/api/pith-number/JTUNHTJ6EJQPPAPEGLTOVPXLXG/graph.json","events_json":"https://pith.science/api/pith-number/JTUNHTJ6EJQPPAPEGLTOVPXLXG/events.json","paper":"https://pith.science/paper/JTUNHTJ6"},"agent_actions":{"view_html":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG","download_json":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG.json","view_paper":"https://pith.science/paper/JTUNHTJ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1314&json=true","fetch_graph":"https://pith.science/api/pith-number/JTUNHTJ6EJQPPAPEGLTOVPXLXG/graph.json","fetch_events":"https://pith.science/api/pith-number/JTUNHTJ6EJQPPAPEGLTOVPXLXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG/action/storage_attestation","attest_author":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG/action/author_attestation","sign_citation":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG/action/citation_signature","submit_replication":"https://pith.science/pith/JTUNHTJ6EJQPPAPEGLTOVPXLXG/action/replication_record"}},"created_at":"2026-05-18T01:10:54.639032+00:00","updated_at":"2026-05-18T01:10:54.639032+00:00"}