{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3B3R5M23QY4322X7I4TBAMG5P7","short_pith_number":"pith:3B3R5M23","schema_version":"1.0","canonical_sha256":"d8771eb35b8639bd6aff47261030dd7ff893a67fcc03f6841a0b23af1bae5561","source":{"kind":"arxiv","id":"1011.1667","version":2},"attestation_state":"computed","paper":{"title":"On the asymptotic expansion of the sum of the first n primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nilotpal Kanti Sinha","submitted_at":"2010-11-07T18:16:43Z","abstract_excerpt":"An asymptotic formula for the sum of the first n primes is derived. This result improves the previous results of P. Dusart. Using this asymptotic expansion, we prove the conjectures of R. Mandl and G. Robin on the upper and the lower bound of the sum of the first n primes respectively."},"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":"1011.1667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-07T18:16:43Z","cross_cats_sorted":[],"title_canon_sha256":"ce58cc6dba2e267060a8c769827cc8a90941dc989c1acf96de0109e09dfd366a","abstract_canon_sha256":"e6d7f53890c9237b986ff00210961419d3280c1879752bbdba18a68bf1ffb1d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:00.394043Z","signature_b64":"2GPrn64P94dz1PK43udwCg0A6+d8Jq2FmWFxPLwg5Zc2MLUseO+oIR1x9RYsLTTB/x5CnntPxBXxzn1v5wavBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8771eb35b8639bd6aff47261030dd7ff893a67fcc03f6841a0b23af1bae5561","last_reissued_at":"2026-05-18T01:41:00.393605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:00.393605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the asymptotic expansion of the sum of the first n primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nilotpal Kanti Sinha","submitted_at":"2010-11-07T18:16:43Z","abstract_excerpt":"An asymptotic formula for the sum of the first n primes is derived. This result improves the previous results of P. Dusart. Using this asymptotic expansion, we prove the conjectures of R. Mandl and G. Robin on the upper and the lower bound of the sum of the first n primes respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1667","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":"1011.1667","created_at":"2026-05-18T01:41:00.393669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.1667v2","created_at":"2026-05-18T01:41:00.393669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1667","created_at":"2026-05-18T01:41:00.393669+00:00"},{"alias_kind":"pith_short_12","alias_value":"3B3R5M23QY43","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3B3R5M23QY4322X7","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3B3R5M23","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.04951","citing_title":"On the arithmetic average of the first $n$ primes","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7","json":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7.json","graph_json":"https://pith.science/api/pith-number/3B3R5M23QY4322X7I4TBAMG5P7/graph.json","events_json":"https://pith.science/api/pith-number/3B3R5M23QY4322X7I4TBAMG5P7/events.json","paper":"https://pith.science/paper/3B3R5M23"},"agent_actions":{"view_html":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7","download_json":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7.json","view_paper":"https://pith.science/paper/3B3R5M23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.1667&json=true","fetch_graph":"https://pith.science/api/pith-number/3B3R5M23QY4322X7I4TBAMG5P7/graph.json","fetch_events":"https://pith.science/api/pith-number/3B3R5M23QY4322X7I4TBAMG5P7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7/action/storage_attestation","attest_author":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7/action/author_attestation","sign_citation":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7/action/citation_signature","submit_replication":"https://pith.science/pith/3B3R5M23QY4322X7I4TBAMG5P7/action/replication_record"}},"created_at":"2026-05-18T01:41:00.393669+00:00","updated_at":"2026-05-18T01:41:00.393669+00:00"}