{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5ZUKA6JAG2DXA5KFN24JGPIFKB","short_pith_number":"pith:5ZUKA6JA","schema_version":"1.0","canonical_sha256":"ee68a0792036877075456eb8933d055059493f6f2d100ee983e9ce449f21383b","source":{"kind":"arxiv","id":"1208.3402","version":1},"attestation_state":"computed","paper":{"title":"Partial quotients and representation of rational numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean Bourgain","submitted_at":"2012-08-16T15:49:31Z","abstract_excerpt":"It is shown that there is an absolute constant $C$ such that any rational $\\frac bq\\in]0, 1[, (b, q)=1$, admits a representation as a finite sum $\\frac bq=\\sum_\\alpha\\frac {b_\\alpha}{q_\\alpha}$ where $\\sum_\\alpha\\sum_ia_i(\\frac {b_\\alpha}{q_\\alpha})<C\\log q$ and $\\{a_i(x)\\}$ denotes the sequence of partial quotients of $x$."},"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":"1208.3402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-16T15:49:31Z","cross_cats_sorted":[],"title_canon_sha256":"589e749384b6686a12df19fbce418e59793e16befbedf989fc338fdfbcb167cc","abstract_canon_sha256":"5a936a1d7faa16c21c7db0f9047abeaa91adacb88c88516ca1bb2f8382637307"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:35.987191Z","signature_b64":"Gxoeznfpp0zzV2omxaH2HpPgqHCg+rbvr5FDylGymUcGjfrM7wXuAaB4voy+W1yOHtWzItnfWXpIkGRojCuLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee68a0792036877075456eb8933d055059493f6f2d100ee983e9ce449f21383b","last_reissued_at":"2026-05-18T03:48:35.986658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:35.986658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial quotients and representation of rational numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean Bourgain","submitted_at":"2012-08-16T15:49:31Z","abstract_excerpt":"It is shown that there is an absolute constant $C$ such that any rational $\\frac bq\\in]0, 1[, (b, q)=1$, admits a representation as a finite sum $\\frac bq=\\sum_\\alpha\\frac {b_\\alpha}{q_\\alpha}$ where $\\sum_\\alpha\\sum_ia_i(\\frac {b_\\alpha}{q_\\alpha})<C\\log q$ and $\\{a_i(x)\\}$ denotes the sequence of partial quotients of $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3402","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.3402","created_at":"2026-05-18T03:48:35.986743+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3402v1","created_at":"2026-05-18T03:48:35.986743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3402","created_at":"2026-05-18T03:48:35.986743+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZUKA6JAG2DX","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZUKA6JAG2DXA5KF","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZUKA6JA","created_at":"2026-05-18T12:26:56.085431+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/5ZUKA6JAG2DXA5KFN24JGPIFKB","json":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB.json","graph_json":"https://pith.science/api/pith-number/5ZUKA6JAG2DXA5KFN24JGPIFKB/graph.json","events_json":"https://pith.science/api/pith-number/5ZUKA6JAG2DXA5KFN24JGPIFKB/events.json","paper":"https://pith.science/paper/5ZUKA6JA"},"agent_actions":{"view_html":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB","download_json":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB.json","view_paper":"https://pith.science/paper/5ZUKA6JA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3402&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZUKA6JAG2DXA5KFN24JGPIFKB/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZUKA6JAG2DXA5KFN24JGPIFKB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB/action/storage_attestation","attest_author":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB/action/author_attestation","sign_citation":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB/action/citation_signature","submit_replication":"https://pith.science/pith/5ZUKA6JAG2DXA5KFN24JGPIFKB/action/replication_record"}},"created_at":"2026-05-18T03:48:35.986743+00:00","updated_at":"2026-05-18T03:48:35.986743+00:00"}