{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3FN4SRARPD4WIAIAXALJ6CNKWQ","short_pith_number":"pith:3FN4SRAR","schema_version":"1.0","canonical_sha256":"d95bc9441178f9640100b8169f09aab407a660d7dec3aae21aa607eb5acf9b6b","source":{"kind":"arxiv","id":"1606.03378","version":1},"attestation_state":"computed","paper":{"title":"Sur la variation totale de la suite des parties fractionnaires des quotients d'un nombre r{\\'e}el positif par les nombres entiers naturels cons{\\'e}cutifs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michel Balazard (I2M)","submitted_at":"2016-06-09T07:10:30Z","abstract_excerpt":"We give an asymptotic formula for the total variation of the sequence of fractional parts of the quotients of a positive real number by the consecutive natural numbers."},"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":"1606.03378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-09T07:10:30Z","cross_cats_sorted":[],"title_canon_sha256":"ef1a3bc5efcf572a945e3344c16e8c322a0fcc10445b9ac74f9aa0fb087faa47","abstract_canon_sha256":"fd27364d6f1853e91bde94f0ae42b17a404307e064f217de8a828814093bcbae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:37.001923Z","signature_b64":"Xfh1gSrpomY7wP+s9O8i+VcNCMsnq2pHCJIGy9vYryj7XwE3444GaSPMIRHbuylfKj1dL1IPqatOyfEHN1TJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d95bc9441178f9640100b8169f09aab407a660d7dec3aae21aa607eb5acf9b6b","last_reissued_at":"2026-05-18T01:12:37.001577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:37.001577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sur la variation totale de la suite des parties fractionnaires des quotients d'un nombre r{\\'e}el positif par les nombres entiers naturels cons{\\'e}cutifs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michel Balazard (I2M)","submitted_at":"2016-06-09T07:10:30Z","abstract_excerpt":"We give an asymptotic formula for the total variation of the sequence of fractional parts of the quotients of a positive real number by the consecutive natural numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03378","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":"1606.03378","created_at":"2026-05-18T01:12:37.001630+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.03378v1","created_at":"2026-05-18T01:12:37.001630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03378","created_at":"2026-05-18T01:12:37.001630+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FN4SRARPD4W","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FN4SRARPD4WIAIA","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FN4SRAR","created_at":"2026-05-18T12:29:55.572404+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/3FN4SRARPD4WIAIAXALJ6CNKWQ","json":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ.json","graph_json":"https://pith.science/api/pith-number/3FN4SRARPD4WIAIAXALJ6CNKWQ/graph.json","events_json":"https://pith.science/api/pith-number/3FN4SRARPD4WIAIAXALJ6CNKWQ/events.json","paper":"https://pith.science/paper/3FN4SRAR"},"agent_actions":{"view_html":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ","download_json":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ.json","view_paper":"https://pith.science/paper/3FN4SRAR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.03378&json=true","fetch_graph":"https://pith.science/api/pith-number/3FN4SRARPD4WIAIAXALJ6CNKWQ/graph.json","fetch_events":"https://pith.science/api/pith-number/3FN4SRARPD4WIAIAXALJ6CNKWQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ/action/storage_attestation","attest_author":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ/action/author_attestation","sign_citation":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ/action/citation_signature","submit_replication":"https://pith.science/pith/3FN4SRARPD4WIAIAXALJ6CNKWQ/action/replication_record"}},"created_at":"2026-05-18T01:12:37.001630+00:00","updated_at":"2026-05-18T01:12:37.001630+00:00"}