{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VC2IT5INYMWPXO4V7C2QXLJQSQ","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":"65c99a27460147deb20e9eb0c791cf27c096855495adc6caef2c5863355e378a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-20T17:41:11Z","title_canon_sha256":"b046dad36cda5e70eefbcce1fc8a892ea3e16ccad918accd34534e917b0e2517"},"schema_version":"1.0","source":{"id":"1703.06865","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06865","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06865v2","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06865","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"VC2IT5INYMWP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VC2IT5INYMWPXO4V","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VC2IT5IN","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:253824287b1af13ff414fa292a6cc31e5cf73b6827dc473e78ce7025ba105c52","target":"graph","created_at":"2026-05-17T23:48:12Z","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":"Part-and-parcel of the study of \"multiplicative number theory\" is the study of the distribution of multiplicative functions in arithmetic progressions. Although appropriate analogies to the Bombieri-Vingradov Theorem have been proved for particular examples of multiplicative functions, there has not previously been headway on a general theory; seemingly none of the different proofs of the Bombieri-Vingradov Theorem for primes adapt well to this situation. In this article we find out why such a result has been so elusive, and discover what can be proved along these lines and develop some limita","authors_text":"Andrew Granville, Xuancheng Shao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-20T17:41:11Z","title":"Bombieri-Vinogradov for multiplicative functions, and beyond the $x^{1/2}$-barrier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06865","kind":"arxiv","version":2},"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":"sha256:6bdc11f20bce5b734c9cfcca809dd496e356f2969b32f3c2631c4d881c025c0b","target":"record","created_at":"2026-05-17T23:48:12Z","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":"65c99a27460147deb20e9eb0c791cf27c096855495adc6caef2c5863355e378a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-20T17:41:11Z","title_canon_sha256":"b046dad36cda5e70eefbcce1fc8a892ea3e16ccad918accd34534e917b0e2517"},"schema_version":"1.0","source":{"id":"1703.06865","kind":"arxiv","version":2}},"canonical_sha256":"a8b489f50dc32cfbbb95f8b50bad3094096f7917da4e0efef492bbcd05b9d8b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b489f50dc32cfbbb95f8b50bad3094096f7917da4e0efef492bbcd05b9d8b1","first_computed_at":"2026-05-17T23:48:12.074384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:12.074384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WHPE9/uFysle9LZHR6JNMDY0HwcF9ZZFg8lrueP///xLlGu+PevX0iCB1SRVXCGtQmloTxTU50k0uYqVkvllBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:12.075015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06865","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bdc11f20bce5b734c9cfcca809dd496e356f2969b32f3c2631c4d881c025c0b","sha256:253824287b1af13ff414fa292a6cc31e5cf73b6827dc473e78ce7025ba105c52"],"state_sha256":"fb7e113d1ba9911c609c197f72a155c970c6bd314cbb9407616fb2aeb8ac6ee8"}