{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NNNSFZIAQBHNWUCHBIHHFEBPIW","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":"e346140732fa0aadca03aa529657706f8a918b908442908f375cd870d9fc92bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-09T07:27:14Z","title_canon_sha256":"352881947d4fb97d94b0b854bcb9c65b589d41b8a16e1f0f335575a6f3e67d66"},"schema_version":"1.0","source":{"id":"1606.03377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03377","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03377v1","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03377","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"NNNSFZIAQBHN","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNNSFZIAQBHNWUCH","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNNSFZIA","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:4f1ec2c6c04d5ab0eb2c79322d5898b3f6e896201918fa8ece59c7b2c0738323","target":"graph","created_at":"2026-05-18T01:12:37Z","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 give an asymptotic formula for the quadratic total variation of the sequence of fractional parts of the quotients of a positive real number by the consecutive natural numbers.","authors_text":"Michel Balazard (I2M)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-09T07:27:14Z","title":"Sur la variation quadratique totale de la suite des parties fractionnaires des quotients d'un nombre r\\'eel positif par les nombres entiers naturels cons\\'ecutifs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03377","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":"sha256:494c3af84e3a0d7c188f767c7cd94f0efbf73b980a7f00693c2923aa4901b0f7","target":"record","created_at":"2026-05-18T01:12:37Z","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":"e346140732fa0aadca03aa529657706f8a918b908442908f375cd870d9fc92bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-09T07:27:14Z","title_canon_sha256":"352881947d4fb97d94b0b854bcb9c65b589d41b8a16e1f0f335575a6f3e67d66"},"schema_version":"1.0","source":{"id":"1606.03377","kind":"arxiv","version":1}},"canonical_sha256":"6b5b22e500804edb50470a0e72902f45b0f82fdc26ccc42a8fcdb3fcce5de28b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b5b22e500804edb50470a0e72902f45b0f82fdc26ccc42a8fcdb3fcce5de28b","first_computed_at":"2026-05-18T01:12:37.006661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:37.006661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aCVIzKZqJBH8SrR7XIMZRLmgnphq526hXYuyPp0MN62oFIYG4aWvZa0s9L28SwwiW86thNGZ/l32abzrodIGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:37.007156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:494c3af84e3a0d7c188f767c7cd94f0efbf73b980a7f00693c2923aa4901b0f7","sha256:4f1ec2c6c04d5ab0eb2c79322d5898b3f6e896201918fa8ece59c7b2c0738323"],"state_sha256":"9fad9765b37d31a836b2441836233ea9fd9a98de0bd4838aa0c93445acfc9212"}