{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6N2MIDU5EMWS3RF76BSEX222RO","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":"4191cf74560c6a58cf13b181c3b92e8162f69bb745b9c3aca7c384c2adecfce1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-01T06:42:52Z","title_canon_sha256":"eca19bba466552d177930a4d97a722ea45c405c8c9b0e70c01f88395bb19f234"},"schema_version":"1.0","source":{"id":"1808.00188","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00188","created_at":"2026-05-18T00:03:15Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00188v3","created_at":"2026-05-18T00:03:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00188","created_at":"2026-05-18T00:03:15Z"},{"alias_kind":"pith_short_12","alias_value":"6N2MIDU5EMWS","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6N2MIDU5EMWS3RF7","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6N2MIDU5","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:e998a1f7ab48b6a6e9d994565e580a1ab2b95e58aa3cc50b779b735f1f18141b","target":"graph","created_at":"2026-05-18T00:03:15Z","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 obtain reasonably tight upper and lower bounds on the sum $\\sum_{n \\leqslant x} \\varphi \\left( \\left\\lfloor{x/n}\\right\\rfloor\\right)$, involving the Euler functions $\\varphi$ and the integer parts $\\left\\lfloor{x/n}\\right\\rfloor$ of the reciprocals of integers.","authors_text":"Hao Pan, Igor E. Shparlinski, Lixia Dai, Olivier Bordell\\`es, Randell Heyman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-01T06:42:52Z","title":"On a sum involving the Euler function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00188","kind":"arxiv","version":3},"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":"sha256:1738d20e528eb9051160ee2e1c8ca8731b1e9a0af96e1a4b1142866dd0f91c88","target":"record","created_at":"2026-05-18T00:03:15Z","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":"4191cf74560c6a58cf13b181c3b92e8162f69bb745b9c3aca7c384c2adecfce1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-01T06:42:52Z","title_canon_sha256":"eca19bba466552d177930a4d97a722ea45c405c8c9b0e70c01f88395bb19f234"},"schema_version":"1.0","source":{"id":"1808.00188","kind":"arxiv","version":3}},"canonical_sha256":"f374c40e9d232d2dc4bff0644beb5a8baba3e5f6c85f548caac5cea0ebda9d9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f374c40e9d232d2dc4bff0644beb5a8baba3e5f6c85f548caac5cea0ebda9d9c","first_computed_at":"2026-05-18T00:03:15.568709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:15.568709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d+rOacTRAzFqLjm+68JPsAafDNdVt3VPlXZP442z66BHN+nYEw4rDCqcSZ/pu7u71q2dLKnLlTp2ePOvGVEUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:15.569150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00188","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1738d20e528eb9051160ee2e1c8ca8731b1e9a0af96e1a4b1142866dd0f91c88","sha256:e998a1f7ab48b6a6e9d994565e580a1ab2b95e58aa3cc50b779b735f1f18141b"],"state_sha256":"48498b4779517e38ee8b5dc07a3c949cba1b15d26ca0b69a853fb4060faab6c3"}