{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OJH3VWLW22TKTP7G2C7NPI2IZI","short_pith_number":"pith:OJH3VWLW","schema_version":"1.0","canonical_sha256":"724fbad976d6a6a9bfe6d0bed7a348ca3d7a58c7fb86c661540de18d05b2a0b7","source":{"kind":"arxiv","id":"1401.2689","version":2},"attestation_state":"computed","paper":{"title":"Updating the error term in the prime number theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tim Trudgian","submitted_at":"2014-01-13T00:47:15Z","abstract_excerpt":"An improved estimate is given for $|\\theta(x) -x|$, where $\\theta(x) = \\sum_{p\\leq x} \\log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the third to a conjecture by C. Pomerance."},"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":"1401.2689","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-13T00:47:15Z","cross_cats_sorted":[],"title_canon_sha256":"9b755cada97fabe4b9c07a31e4d6ce45386d8406555a468abb46a62de4e5bf41","abstract_canon_sha256":"6b1a6c52f5fd5a9120116fee8304263e10c6a9fa3d6e3aca5439a9522db93ca7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:55.654119Z","signature_b64":"6pjCHKCq7LcHRGa7KpodbKhy9zC40Ztg3sxDimy0FP+M76sk6N10xxsJHxvPkhgP3o4yCUvN96iOHZKRBx9rDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"724fbad976d6a6a9bfe6d0bed7a348ca3d7a58c7fb86c661540de18d05b2a0b7","last_reissued_at":"2026-05-18T02:39:55.653708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:55.653708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Updating the error term in the prime number theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tim Trudgian","submitted_at":"2014-01-13T00:47:15Z","abstract_excerpt":"An improved estimate is given for $|\\theta(x) -x|$, where $\\theta(x) = \\sum_{p\\leq x} \\log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the third to a conjecture by C. Pomerance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2689","kind":"arxiv","version":2},"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":"1401.2689","created_at":"2026-05-18T02:39:55.653766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.2689v2","created_at":"2026-05-18T02:39:55.653766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2689","created_at":"2026-05-18T02:39:55.653766+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJH3VWLW22TK","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJH3VWLW22TKTP7G","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJH3VWLW","created_at":"2026-05-18T12:28:41.024544+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/OJH3VWLW22TKTP7G2C7NPI2IZI","json":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI.json","graph_json":"https://pith.science/api/pith-number/OJH3VWLW22TKTP7G2C7NPI2IZI/graph.json","events_json":"https://pith.science/api/pith-number/OJH3VWLW22TKTP7G2C7NPI2IZI/events.json","paper":"https://pith.science/paper/OJH3VWLW"},"agent_actions":{"view_html":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI","download_json":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI.json","view_paper":"https://pith.science/paper/OJH3VWLW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.2689&json=true","fetch_graph":"https://pith.science/api/pith-number/OJH3VWLW22TKTP7G2C7NPI2IZI/graph.json","fetch_events":"https://pith.science/api/pith-number/OJH3VWLW22TKTP7G2C7NPI2IZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI/action/storage_attestation","attest_author":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI/action/author_attestation","sign_citation":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI/action/citation_signature","submit_replication":"https://pith.science/pith/OJH3VWLW22TKTP7G2C7NPI2IZI/action/replication_record"}},"created_at":"2026-05-18T02:39:55.653766+00:00","updated_at":"2026-05-18T02:39:55.653766+00:00"}