{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NEAB4I4TOC74SAW32H4PGX37DE","short_pith_number":"pith:NEAB4I4T","schema_version":"1.0","canonical_sha256":"69001e239370bfc902dbd1f8f35f7f191df65f8f9e14a610216c0c2b082aed68","source":{"kind":"arxiv","id":"1306.5322","version":4},"attestation_state":"computed","paper":{"title":"Explicit formulae for primes in arithmetic progressions, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tomohiro Yamada","submitted_at":"2013-06-22T13:27:17Z","abstract_excerpt":"We shall give an explicit formula for $\\psi(x, q, a)$ with an error term of the form $C/\\log^\\alpha x$ under the condition that $q<\\log^{\\alpha_1} x$ is nonexceptional, for various values of $\\alpha$ and $\\alpha_1$. We shall also give an explicit formula for $\\psi(x, q, a)$ with error terms $C/\\log^A x$ working whether $q$ is exceptional or nonexceptional, but under the condition that $\\frac{0.4923A}{\\pi}q^{1/2}\\log^2 q<\\log x/\\log\\log x$. Moreover, we shall give an explicit form of Bombieri-Vinogradov theorem over non-exceptional moduli."},"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":"1306.5322","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-22T13:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"7357e808fc397d337da750f3ca3c451c167f09b3877d30bd713fb8845a82a546","abstract_canon_sha256":"2d717fe35fdb3827099e69e9be065d8d9866dbcdae50479cc9d30af42665c8de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:29.012831Z","signature_b64":"mrgeXZZnKgoNeEe0P0jVHLwu4l8mX/vr6ZHLAl800rbQE1OB03ahZFeOk7ZSS1+PJcgFDUK68R0+9W/E015TBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69001e239370bfc902dbd1f8f35f7f191df65f8f9e14a610216c0c2b082aed68","last_reissued_at":"2026-05-18T01:27:29.012221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:29.012221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit formulae for primes in arithmetic progressions, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tomohiro Yamada","submitted_at":"2013-06-22T13:27:17Z","abstract_excerpt":"We shall give an explicit formula for $\\psi(x, q, a)$ with an error term of the form $C/\\log^\\alpha x$ under the condition that $q<\\log^{\\alpha_1} x$ is nonexceptional, for various values of $\\alpha$ and $\\alpha_1$. We shall also give an explicit formula for $\\psi(x, q, a)$ with error terms $C/\\log^A x$ working whether $q$ is exceptional or nonexceptional, but under the condition that $\\frac{0.4923A}{\\pi}q^{1/2}\\log^2 q<\\log x/\\log\\log x$. Moreover, we shall give an explicit form of Bombieri-Vinogradov theorem over non-exceptional moduli."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5322","kind":"arxiv","version":4},"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":"1306.5322","created_at":"2026-05-18T01:27:29.012308+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.5322v4","created_at":"2026-05-18T01:27:29.012308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5322","created_at":"2026-05-18T01:27:29.012308+00:00"},{"alias_kind":"pith_short_12","alias_value":"NEAB4I4TOC74","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NEAB4I4TOC74SAW3","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NEAB4I4T","created_at":"2026-05-18T12:27:52.871228+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/NEAB4I4TOC74SAW32H4PGX37DE","json":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE.json","graph_json":"https://pith.science/api/pith-number/NEAB4I4TOC74SAW32H4PGX37DE/graph.json","events_json":"https://pith.science/api/pith-number/NEAB4I4TOC74SAW32H4PGX37DE/events.json","paper":"https://pith.science/paper/NEAB4I4T"},"agent_actions":{"view_html":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE","download_json":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE.json","view_paper":"https://pith.science/paper/NEAB4I4T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.5322&json=true","fetch_graph":"https://pith.science/api/pith-number/NEAB4I4TOC74SAW32H4PGX37DE/graph.json","fetch_events":"https://pith.science/api/pith-number/NEAB4I4TOC74SAW32H4PGX37DE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE/action/storage_attestation","attest_author":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE/action/author_attestation","sign_citation":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE/action/citation_signature","submit_replication":"https://pith.science/pith/NEAB4I4TOC74SAW32H4PGX37DE/action/replication_record"}},"created_at":"2026-05-18T01:27:29.012308+00:00","updated_at":"2026-05-18T01:27:29.012308+00:00"}