{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HACBHJSFS5IDO2PA2L5U3RFQLB","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":"3aae60c88ba4bf1de24bf5584412f7d86379c013f61c19f64e4630bf9701e5ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-13T20:12:18Z","title_canon_sha256":"354e974c2173955c6ec7a0645f3776510645f2ff8bc5ea120a41688459d1cc25"},"schema_version":"1.0","source":{"id":"1112.3013","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3013","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3013v2","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3013","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"HACBHJSFS5ID","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HACBHJSFS5IDO2PA","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HACBHJSF","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:83064d1ad530b2b308c341c57cdbf836bfa928527ed70d6ccf046024259719dd","target":"graph","created_at":"2026-05-18T03:04:50Z","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":"We study the typical behavior of the least common multiple of the elements of a random subset $A\\subset \\{1,\\dots, n\\}$. For example we prove that $\\text{lcm}\\{a:\\ a\\in A\\}=2^{n(1+o(1))}$ for almost all subsets $A\\subset\\{1,\\dots,n\\}$.","authors_text":"Ana Zumalac\\'arregui, Javier Cilleruelo, Juanjo Ru\\'e, Paulius \\v{S}arka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-13T20:12:18Z","title":"The least common multiple of random sets of positive integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3013","kind":"arxiv","version":2},"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":"sha256:0b83eaa6e5e5f5e5fefee53140af266c72194d05d8eb55d1e708a839fba3fef6","target":"record","created_at":"2026-05-18T03:04:50Z","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":"3aae60c88ba4bf1de24bf5584412f7d86379c013f61c19f64e4630bf9701e5ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-13T20:12:18Z","title_canon_sha256":"354e974c2173955c6ec7a0645f3776510645f2ff8bc5ea120a41688459d1cc25"},"schema_version":"1.0","source":{"id":"1112.3013","kind":"arxiv","version":2}},"canonical_sha256":"380413a64597503769e0d2fb4dc4b0586ae7b8260332139d24cc4fef85b5cd35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"380413a64597503769e0d2fb4dc4b0586ae7b8260332139d24cc4fef85b5cd35","first_computed_at":"2026-05-18T03:04:50.157696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:50.157696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"St7aOUmXfdgSF/tK9CR+Ov/sTrFqWnh1jD4/+b79K8jv3uNWu8IfdpFOryS5RTwofM0jzkbNX86AcLBMiT7iCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:50.158409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3013","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b83eaa6e5e5f5e5fefee53140af266c72194d05d8eb55d1e708a839fba3fef6","sha256:83064d1ad530b2b308c341c57cdbf836bfa928527ed70d6ccf046024259719dd"],"state_sha256":"0f28615e9f3927bbca98377355101eda5b2cde79ef775f180422434fe7d67f01"}