{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DUKCPWE6HR5OGX43ZIKQILTZCB","short_pith_number":"pith:DUKCPWE6","canonical_record":{"source":{"id":"1801.08934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-26T18:56:13Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8295dc487102855aff50400bea9a2228f418510b877f23e9b096fdd18e678d3c","abstract_canon_sha256":"113f4d05bf4e0323e493b884cc5584dbb73e6399f976b1dc28e14d39dbfe1da8"},"schema_version":"1.0"},"canonical_sha256":"1d1427d89e3c7ae35f9bca15042e791051349a675cd25f97e01b8ba8564ef394","source":{"kind":"arxiv","id":"1801.08934","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08934","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08934v1","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08934","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"DUKCPWE6HR5O","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DUKCPWE6HR5OGX43","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DUKCPWE6","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DUKCPWE6HR5OGX43ZIKQILTZCB","target":"record","payload":{"canonical_record":{"source":{"id":"1801.08934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-26T18:56:13Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8295dc487102855aff50400bea9a2228f418510b877f23e9b096fdd18e678d3c","abstract_canon_sha256":"113f4d05bf4e0323e493b884cc5584dbb73e6399f976b1dc28e14d39dbfe1da8"},"schema_version":"1.0"},"canonical_sha256":"1d1427d89e3c7ae35f9bca15042e791051349a675cd25f97e01b8ba8564ef394","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:02.639095Z","signature_b64":"Cf+BhG6UouqN3sbmDcYHyceOMyKLHUcqq3XLIdopzbLR7rkZfFoDhmHtQB/ZQriw5bia52ENyyEiJ4qqCaQ9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d1427d89e3c7ae35f9bca15042e791051349a675cd25f97e01b8ba8564ef394","last_reissued_at":"2026-05-18T00:25:02.638685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:02.638685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.08934","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aozUG/2zpIiSae4g5F+4Czo4ky+GdqZuLiWKnTj69MBdfBTWSCq34HLf5OCTtpZqE91/Zx8ll1oz9onFBpHMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:14:49.499381Z"},"content_sha256":"e2ed2fb6ea9ca714036949985271f73861d187eac8e5e0506c37503d642ae30b","schema_version":"1.0","event_id":"sha256:e2ed2fb6ea9ca714036949985271f73861d187eac8e5e0506c37503d642ae30b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DUKCPWE6HR5OGX43ZIKQILTZCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit theorems for the least common multiple of a random set of integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Gerold Alsmeyer, Zakhar Kabluchko","submitted_at":"2018-01-26T18:56:13Z","abstract_excerpt":"Let $L_{n}$ be the least common multiple of a random set of integers obtained from $\\{1,\\ldots,n\\}$ by retaining each element with probability $\\theta\\in (0,1)$ independently of the others. We prove that the process $(\\log L_{\\lfloor nt\\rfloor})_{t\\in [0,1]}$, after centering and normalization, converges weakly to a certain Gaussian process that is not Brownian motion. Further results include a strong law of large numbers for $\\log L_{n}$ as well as Poisson limit theorems in regimes when $\\theta$ depends on $n$ in an appropriate way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08934","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVxxwDRXzFzeF9c58lGp3aN7kwCsnOfLmubN71JwUlyzjTRScM1A5LuB4EF7I4PawcEpZPfxkc2khueuKw3aDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:14:49.499881Z"},"content_sha256":"46ece112374ac8075261e056e98c86d2b0f68877477a911722c82533aa63de15","schema_version":"1.0","event_id":"sha256:46ece112374ac8075261e056e98c86d2b0f68877477a911722c82533aa63de15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DUKCPWE6HR5OGX43ZIKQILTZCB/bundle.json","state_url":"https://pith.science/pith/DUKCPWE6HR5OGX43ZIKQILTZCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DUKCPWE6HR5OGX43ZIKQILTZCB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T01:14:49Z","links":{"resolver":"https://pith.science/pith/DUKCPWE6HR5OGX43ZIKQILTZCB","bundle":"https://pith.science/pith/DUKCPWE6HR5OGX43ZIKQILTZCB/bundle.json","state":"https://pith.science/pith/DUKCPWE6HR5OGX43ZIKQILTZCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DUKCPWE6HR5OGX43ZIKQILTZCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DUKCPWE6HR5OGX43ZIKQILTZCB","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":"113f4d05bf4e0323e493b884cc5584dbb73e6399f976b1dc28e14d39dbfe1da8","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-26T18:56:13Z","title_canon_sha256":"8295dc487102855aff50400bea9a2228f418510b877f23e9b096fdd18e678d3c"},"schema_version":"1.0","source":{"id":"1801.08934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08934","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08934v1","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08934","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"DUKCPWE6HR5O","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DUKCPWE6HR5OGX43","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DUKCPWE6","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:46ece112374ac8075261e056e98c86d2b0f68877477a911722c82533aa63de15","target":"graph","created_at":"2026-05-18T00:25:02Z","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":"Let $L_{n}$ be the least common multiple of a random set of integers obtained from $\\{1,\\ldots,n\\}$ by retaining each element with probability $\\theta\\in (0,1)$ independently of the others. We prove that the process $(\\log L_{\\lfloor nt\\rfloor})_{t\\in [0,1]}$, after centering and normalization, converges weakly to a certain Gaussian process that is not Brownian motion. Further results include a strong law of large numbers for $\\log L_{n}$ as well as Poisson limit theorems in regimes when $\\theta$ depends on $n$ in an appropriate way.","authors_text":"Alexander Marynych, Gerold Alsmeyer, Zakhar Kabluchko","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-26T18:56:13Z","title":"Limit theorems for the least common multiple of a random set of integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08934","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:e2ed2fb6ea9ca714036949985271f73861d187eac8e5e0506c37503d642ae30b","target":"record","created_at":"2026-05-18T00:25:02Z","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":"113f4d05bf4e0323e493b884cc5584dbb73e6399f976b1dc28e14d39dbfe1da8","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-26T18:56:13Z","title_canon_sha256":"8295dc487102855aff50400bea9a2228f418510b877f23e9b096fdd18e678d3c"},"schema_version":"1.0","source":{"id":"1801.08934","kind":"arxiv","version":1}},"canonical_sha256":"1d1427d89e3c7ae35f9bca15042e791051349a675cd25f97e01b8ba8564ef394","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d1427d89e3c7ae35f9bca15042e791051349a675cd25f97e01b8ba8564ef394","first_computed_at":"2026-05-18T00:25:02.638685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:02.638685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cf+BhG6UouqN3sbmDcYHyceOMyKLHUcqq3XLIdopzbLR7rkZfFoDhmHtQB/ZQriw5bia52ENyyEiJ4qqCaQ9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:02.639095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2ed2fb6ea9ca714036949985271f73861d187eac8e5e0506c37503d642ae30b","sha256:46ece112374ac8075261e056e98c86d2b0f68877477a911722c82533aa63de15"],"state_sha256":"406515649b780627b7ef9042c2cac3f7168aeb7ceb8daa79b2856c9a8dca0fbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXHXyEuTC7OyJY0kRYZkGAHqWZH88Z+QztXC840uBK5nVPSI9PbkPnCpKN9BbXQw4LPbqChV5Pb50q3gvF+3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:14:49.502090Z","bundle_sha256":"64d96758070b1019609333e51268c2b227f71d0d57eae2175051d473a5b11600"}}