{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NHPYXJP3UGOSRON7F42U5PDOFH","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":"773b5720576a1cbf146a20d8c6615c8392e9a74dc743fa45e95c66493adac7af","cross_cats_sorted":["math.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T20:52:13Z","title_canon_sha256":"8dc172f9ee55f3ce57aac991f9345c5d2b31e7ebf65f0e4ecb3b89ae09dbeb17"},"schema_version":"1.0","source":{"id":"1806.03351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03351","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03351v1","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03351","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"NHPYXJP3UGOS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NHPYXJP3UGOSRON7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NHPYXJP3","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:8adc036d6d3d3e6c258a37d05ca5a39e483d4cb9410b353729f60144ec67a9e8","target":"graph","created_at":"2026-05-18T00:13:43Z","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":"The fundamental group of the $2$-dimensional Linial-Meshulam random simplicial complex $Y_2(n,p)$ was first studied by Babson, Hoffman and Kahle. They proved that the threshold probability for simple connectivity of $Y_2(n,p)$ is about $p\\approx n^{-1/2}$. In this paper, we show that this threshold probability is at most $p\\le (\\gamma n)^{-1/2}$, where $\\gamma = 4^4/3^3$, and conjecture that this threshold is sharp.\n  In fact, we show that $p=(\\gamma n)^{-1/2}$ is a sharp threshold probability for the stronger property that every cycle of length $3$ is the boundary of a subcomplex of $Y_2(n,p)","authors_text":"Yuval Peled, Zur Luria","cross_cats":["math.GT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T20:52:13Z","title":"On simple connectivity of random 2-complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03351","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:c461935e0d02bd477c9bacac4d69e74903492640717700274810eb301cc4f509","target":"record","created_at":"2026-05-18T00:13:43Z","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":"773b5720576a1cbf146a20d8c6615c8392e9a74dc743fa45e95c66493adac7af","cross_cats_sorted":["math.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T20:52:13Z","title_canon_sha256":"8dc172f9ee55f3ce57aac991f9345c5d2b31e7ebf65f0e4ecb3b89ae09dbeb17"},"schema_version":"1.0","source":{"id":"1806.03351","kind":"arxiv","version":1}},"canonical_sha256":"69df8ba5fba19d28b9bf2f354ebc6e29fc096925642453e3352845f77e92c28a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69df8ba5fba19d28b9bf2f354ebc6e29fc096925642453e3352845f77e92c28a","first_computed_at":"2026-05-18T00:13:43.678628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:43.678628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nCg4yCsSxGU0kp4Hhe9Xs9VujI/U70sg8X03K6oZa/XWu8io4YOaHkug/5z3ckX7ELjEKc6y24ofDJRB/yagAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:43.679341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c461935e0d02bd477c9bacac4d69e74903492640717700274810eb301cc4f509","sha256:8adc036d6d3d3e6c258a37d05ca5a39e483d4cb9410b353729f60144ec67a9e8"],"state_sha256":"44a32dd6ceceb76c5e1790d7d1cfc2cbd05a42ecee3709dee35d4a89686d8773"}