{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:YTZWFZPYMDT2UYDAY5GVZRGJN4","short_pith_number":"pith:YTZWFZPY","schema_version":"1.0","canonical_sha256":"c4f362e5f860e7aa6060c74d5cc4c96f29d4f4a44b25963fc1c2685159679e1c","source":{"kind":"arxiv","id":"2505.11295","version":1},"attestation_state":"computed","paper":{"title":"Prime Number Error Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nathan Ng","submitted_at":"2025-05-16T14:26:19Z","abstract_excerpt":"In 1980 Montgomery made a conjecture about the true order of the error term in the prime number theorem. In 2012 the author made an analogous conjecture for the true order of the sum of the M\\\"{o}bius function, $M(x)$. This refined an earlier conjecture of Gonek from the 1990's. In this article we speculate on the true size of a large class of prime number error terms and present a general conjecture. This general conjecture includes both Montgomery's conjecture and the conjecture for $M(x)$ as special cases. Recently, Lamzouri (Springer volume: Essays in Analytic Number Theory, In Honor of He"},"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":"2505.11295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-16T14:26:19Z","cross_cats_sorted":[],"title_canon_sha256":"53831c89713bb3b5fa13b2c6e98aa0a2e94520804856f6269d734d64c877369f","abstract_canon_sha256":"d46b36d0104290962aeb70cd44a25865b410735420be4ff25ef132ed6154a604"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:13.986773Z","signature_b64":"OsK1f8Fu9BZx9mk/jSp6FX3Zkef/em6yImquqe8au9UaycuWHUlod6r43xvGgZ6OkkX0pH1Oz33CpQS3GgpHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4f362e5f860e7aa6060c74d5cc4c96f29d4f4a44b25963fc1c2685159679e1c","last_reissued_at":"2026-07-05T11:04:13.986237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:13.986237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prime Number Error Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nathan Ng","submitted_at":"2025-05-16T14:26:19Z","abstract_excerpt":"In 1980 Montgomery made a conjecture about the true order of the error term in the prime number theorem. In 2012 the author made an analogous conjecture for the true order of the sum of the M\\\"{o}bius function, $M(x)$. This refined an earlier conjecture of Gonek from the 1990's. In this article we speculate on the true size of a large class of prime number error terms and present a general conjecture. This general conjecture includes both Montgomery's conjecture and the conjecture for $M(x)$ as special cases. Recently, Lamzouri (Springer volume: Essays in Analytic Number Theory, In Honor of He"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11295","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.11295/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.11295","created_at":"2026-07-05T11:04:13.986296+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.11295v1","created_at":"2026-07-05T11:04:13.986296+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11295","created_at":"2026-07-05T11:04:13.986296+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTZWFZPYMDT2","created_at":"2026-07-05T11:04:13.986296+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTZWFZPYMDT2UYDA","created_at":"2026-07-05T11:04:13.986296+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTZWFZPY","created_at":"2026-07-05T11:04:13.986296+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.25094","citing_title":"Negative discrete second moments of Dirichlet $L$-functions","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2606.12376","citing_title":"A note on a conjecture of Ng","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2603.20093","citing_title":"A Wasserstein metric approach to generalized Skewes' numbers. I. Prime number races","ref_index":30,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4","json":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4.json","graph_json":"https://pith.science/api/pith-number/YTZWFZPYMDT2UYDAY5GVZRGJN4/graph.json","events_json":"https://pith.science/api/pith-number/YTZWFZPYMDT2UYDAY5GVZRGJN4/events.json","paper":"https://pith.science/paper/YTZWFZPY"},"agent_actions":{"view_html":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4","download_json":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4.json","view_paper":"https://pith.science/paper/YTZWFZPY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.11295&json=true","fetch_graph":"https://pith.science/api/pith-number/YTZWFZPYMDT2UYDAY5GVZRGJN4/graph.json","fetch_events":"https://pith.science/api/pith-number/YTZWFZPYMDT2UYDAY5GVZRGJN4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4/action/storage_attestation","attest_author":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4/action/author_attestation","sign_citation":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4/action/citation_signature","submit_replication":"https://pith.science/pith/YTZWFZPYMDT2UYDAY5GVZRGJN4/action/replication_record"}},"created_at":"2026-07-05T11:04:13.986296+00:00","updated_at":"2026-07-05T11:04:13.986296+00:00"}