{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G342ITHTKGGSF73RNY2CYDMR52","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e6a45e6be7e8747e2d62c46080efe5359f5835debe2d2328fef8ab039cd53d24","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2015-03-21T10:47:34Z","title_canon_sha256":"33a67c095ab9ea026111a8446fb8a093c07f6e5451d766a93acde930523f7e7b"},"schema_version":"1.0","source":{"id":"1503.06285","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06285","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06285v1","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06285","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"G342ITHTKGGS","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G342ITHTKGGSF73R","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G342ITHT","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:6065f693c15d5835eeb5545ff817de89d213140525dbecdbf3376a81b2308a2a","target":"graph","created_at":"2026-05-18T02:20:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we develop further the multi-parameter model of random simplicial complexes. Firstly, we give an intrinsic characterisation of the multi-parameter probability measure. Secondly, we show that in multi-parameter random simplicial complexes the links of simplexes and their intersections are also multi-parameter random simplicial complexes. Thirdly, we find conditions under which a multi-parameter random simplicial complex is connected and simply connected.","authors_text":"A. Costa, M. Farber","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2015-03-21T10:47:34Z","title":"Large random simplicial complexes, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06285","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4e10fd346b9d0cdeb14183123312629adde1e71be2a5595c37385edf997f9784","target":"record","created_at":"2026-05-18T02:20:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e6a45e6be7e8747e2d62c46080efe5359f5835debe2d2328fef8ab039cd53d24","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2015-03-21T10:47:34Z","title_canon_sha256":"33a67c095ab9ea026111a8446fb8a093c07f6e5451d766a93acde930523f7e7b"},"schema_version":"1.0","source":{"id":"1503.06285","kind":"arxiv","version":1}},"canonical_sha256":"36f9a44cf3518d22ff716e342c0d91ee9d68aa9a8a488b21dbdde96dc885f06d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36f9a44cf3518d22ff716e342c0d91ee9d68aa9a8a488b21dbdde96dc885f06d","first_computed_at":"2026-05-18T02:20:38.812203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:38.812203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rU/JCpj6l4QAFrrsw1cf54XDSroRdlA8Aw+X7SiONqoY/CiEiTjk90+7isqcNWP9si8y4cf4ELzfS54NiRChDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:38.812924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06285","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e10fd346b9d0cdeb14183123312629adde1e71be2a5595c37385edf997f9784","sha256:6065f693c15d5835eeb5545ff817de89d213140525dbecdbf3376a81b2308a2a"],"state_sha256":"8f73a519a07a9f484adf88b4c3d73eb78793b8fe4505d23d45ed508264a587c5"}