{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UGZCFBEC5YNLYSTQXA6AYT4OY7","short_pith_number":"pith:UGZCFBEC","schema_version":"1.0","canonical_sha256":"a1b2228482ee1abc4a70b83c0c4f8ec7daf20ad81b05eb5c722bb6a76b7f9915","source":{"kind":"arxiv","id":"1806.05084","version":1},"attestation_state":"computed","paper":{"title":"Tilings, packings and expected Betti numbers in simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Jean-Yves Welschinger (ICJ), Nermin Salepci (ICJ)","submitted_at":"2018-06-13T14:24:56Z","abstract_excerpt":"Let $K$ be a finite simplicial complex. We prove that the normalized expected Betti numbers of a random subcomplex in its $d$-th barycentric subdivision $\\text{Sd}^d (K)$ converge to universal limits as $d$ grows to $+ \\infty$. In codimension one, we use canonical filtrations of $\\text{Sd}^d (K)$ to upper estimate these limits and get a monotony theorem which makes it possible to improve these estimates given any packing of disjoint simplices in $\\text{Sd}^d (K)$. We then introduce a notion of tiling of simplicial complexes having the property that skeletons and barycentric subdivisions of til"},"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":"1806.05084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-13T14:24:56Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1c2b913a1551219ad330795be3f0cf4bbf590065bad3f1d754a1cb3f36d44be2","abstract_canon_sha256":"eacbd809f9e1749e748769010e4adda2d4ac6fc62fa1ca17c74ee755c2be0162"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:20.162761Z","signature_b64":"F8Er18eSnCB3lsU18QJHI09BIpVjWmtpKUAArwfm0vxdGKAKU6yFE4El+OK/t3n2oXP2oP2FUmvs4UZvXhJmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1b2228482ee1abc4a70b83c0c4f8ec7daf20ad81b05eb5c722bb6a76b7f9915","last_reissued_at":"2026-05-18T00:13:20.162109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:20.162109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tilings, packings and expected Betti numbers in simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Jean-Yves Welschinger (ICJ), Nermin Salepci (ICJ)","submitted_at":"2018-06-13T14:24:56Z","abstract_excerpt":"Let $K$ be a finite simplicial complex. We prove that the normalized expected Betti numbers of a random subcomplex in its $d$-th barycentric subdivision $\\text{Sd}^d (K)$ converge to universal limits as $d$ grows to $+ \\infty$. In codimension one, we use canonical filtrations of $\\text{Sd}^d (K)$ to upper estimate these limits and get a monotony theorem which makes it possible to improve these estimates given any packing of disjoint simplices in $\\text{Sd}^d (K)$. We then introduce a notion of tiling of simplicial complexes having the property that skeletons and barycentric subdivisions of til"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05084","kind":"arxiv","version":1},"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":"1806.05084","created_at":"2026-05-18T00:13:20.162198+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.05084v1","created_at":"2026-05-18T00:13:20.162198+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05084","created_at":"2026-05-18T00:13:20.162198+00:00"},{"alias_kind":"pith_short_12","alias_value":"UGZCFBEC5YNL","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UGZCFBEC5YNLYSTQ","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UGZCFBEC","created_at":"2026-05-18T12:32:56.356000+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/UGZCFBEC5YNLYSTQXA6AYT4OY7","json":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7.json","graph_json":"https://pith.science/api/pith-number/UGZCFBEC5YNLYSTQXA6AYT4OY7/graph.json","events_json":"https://pith.science/api/pith-number/UGZCFBEC5YNLYSTQXA6AYT4OY7/events.json","paper":"https://pith.science/paper/UGZCFBEC"},"agent_actions":{"view_html":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7","download_json":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7.json","view_paper":"https://pith.science/paper/UGZCFBEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.05084&json=true","fetch_graph":"https://pith.science/api/pith-number/UGZCFBEC5YNLYSTQXA6AYT4OY7/graph.json","fetch_events":"https://pith.science/api/pith-number/UGZCFBEC5YNLYSTQXA6AYT4OY7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7/action/storage_attestation","attest_author":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7/action/author_attestation","sign_citation":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7/action/citation_signature","submit_replication":"https://pith.science/pith/UGZCFBEC5YNLYSTQXA6AYT4OY7/action/replication_record"}},"created_at":"2026-05-18T00:13:20.162198+00:00","updated_at":"2026-05-18T00:13:20.162198+00:00"}