{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GDR5VXAN23HCL3RSBOBPYM7DTQ","short_pith_number":"pith:GDR5VXAN","schema_version":"1.0","canonical_sha256":"30e3dadc0dd6ce25ee320b82fc33e39c2b4cd502a5fdf1cff58f493c91b45e87","source":{"kind":"arxiv","id":"1902.01102","version":2},"attestation_state":"computed","paper":{"title":"On Cilleruelo's conjecture for the least common multiple of polynomial sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sa'ar Zehavi, Ze\\'ev Rudnick","submitted_at":"2019-02-04T09:47:40Z","abstract_excerpt":"A conjecture due to Cilleruelo states that for an irreducible polynomial $f$ with integer coefficients of degree $d\\geq 2$, the least common multiple $L_f(N)$ of the sequence $f(1), f(2), \\dots, f(N)$ has asymptotic growth $\\log L_f(N)\\sim (d-1)N\\log N$ as $N\\to \\infty$. We establish a version of this conjecture for almost all shifts of a fixed polynomial, the range of $N$ depending on the range of shifts."},"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":"1902.01102","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-04T09:47:40Z","cross_cats_sorted":[],"title_canon_sha256":"b73553d27f2705c4b1ba864778a585acc96cfaea6648c6fc553f0ba633a9691f","abstract_canon_sha256":"f3f289e2d45eb074a1ca1a7fe330764a6831f72fbda348956a1c37077f3f997f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:39.509879Z","signature_b64":"RTTRzjAV4RBwMm4L2EJO24IuCkrhrrAbpXa6lApKE0mLMuCPhLsy5pOZ1PjTPk2Syx3L8WEWUJMU2S2vY3JmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30e3dadc0dd6ce25ee320b82fc33e39c2b4cd502a5fdf1cff58f493c91b45e87","last_reissued_at":"2026-05-17T23:48:39.509354Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:39.509354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Cilleruelo's conjecture for the least common multiple of polynomial sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sa'ar Zehavi, Ze\\'ev Rudnick","submitted_at":"2019-02-04T09:47:40Z","abstract_excerpt":"A conjecture due to Cilleruelo states that for an irreducible polynomial $f$ with integer coefficients of degree $d\\geq 2$, the least common multiple $L_f(N)$ of the sequence $f(1), f(2), \\dots, f(N)$ has asymptotic growth $\\log L_f(N)\\sim (d-1)N\\log N$ as $N\\to \\infty$. We establish a version of this conjecture for almost all shifts of a fixed polynomial, the range of $N$ depending on the range of shifts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01102","kind":"arxiv","version":2},"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":"1902.01102","created_at":"2026-05-17T23:48:39.509446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.01102v2","created_at":"2026-05-17T23:48:39.509446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01102","created_at":"2026-05-17T23:48:39.509446+00:00"},{"alias_kind":"pith_short_12","alias_value":"GDR5VXAN23HC","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GDR5VXAN23HCL3RS","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GDR5VXAN","created_at":"2026-05-18T12:33:18.533446+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/GDR5VXAN23HCL3RSBOBPYM7DTQ","json":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ.json","graph_json":"https://pith.science/api/pith-number/GDR5VXAN23HCL3RSBOBPYM7DTQ/graph.json","events_json":"https://pith.science/api/pith-number/GDR5VXAN23HCL3RSBOBPYM7DTQ/events.json","paper":"https://pith.science/paper/GDR5VXAN"},"agent_actions":{"view_html":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ","download_json":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ.json","view_paper":"https://pith.science/paper/GDR5VXAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.01102&json=true","fetch_graph":"https://pith.science/api/pith-number/GDR5VXAN23HCL3RSBOBPYM7DTQ/graph.json","fetch_events":"https://pith.science/api/pith-number/GDR5VXAN23HCL3RSBOBPYM7DTQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ/action/storage_attestation","attest_author":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ/action/author_attestation","sign_citation":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ/action/citation_signature","submit_replication":"https://pith.science/pith/GDR5VXAN23HCL3RSBOBPYM7DTQ/action/replication_record"}},"created_at":"2026-05-17T23:48:39.509446+00:00","updated_at":"2026-05-17T23:48:39.509446+00:00"}