{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7BBESBNLNNVSYEXLXVW2LNX3P2","short_pith_number":"pith:7BBESBNL","schema_version":"1.0","canonical_sha256":"f8424905ab6b6b2c12ebbd6da5b6fb7e9e641d8866095803db167a330e075bc6","source":{"kind":"arxiv","id":"1103.1253","version":3},"attestation_state":"computed","paper":{"title":"On the Discrepancy of the Roots of $x^2+1$ and $x^2+2$ to Prime Moduli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Timothy Foo","submitted_at":"2011-03-07T11:34:08Z","abstract_excerpt":"In this paper, we make a conjecture (conjecture 1) related to the Bateman-Horn conjecture and proceed to study the roots of $x^2+1$ and $x^2+2$ to prime moduli, assuming the truth of the Bateman-Horn conjecture and conjecture 1 and using the Erd\\H{o}s-Turan-Koksma inequality."},"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":"1103.1253","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-07T11:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"cf2aa53f5d114b712f0f830e41da0d7a16fe01d30d1d4286e8f7434c4d00447d","abstract_canon_sha256":"8d5f050d2b6269503e22b27973c0e5c67f68e1f35c72692fd0d8fb2370ff7991"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:13.769841Z","signature_b64":"PL8EddT61BdbM++2TP/OGCxuGvapBaoYihAZX8pqTa5wapYD9pG4F0izAcGa7CtmFu06GQ10bZudR3tJe3bVDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8424905ab6b6b2c12ebbd6da5b6fb7e9e641d8866095803db167a330e075bc6","last_reissued_at":"2026-05-18T03:44:13.769323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:13.769323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Discrepancy of the Roots of $x^2+1$ and $x^2+2$ to Prime Moduli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Timothy Foo","submitted_at":"2011-03-07T11:34:08Z","abstract_excerpt":"In this paper, we make a conjecture (conjecture 1) related to the Bateman-Horn conjecture and proceed to study the roots of $x^2+1$ and $x^2+2$ to prime moduli, assuming the truth of the Bateman-Horn conjecture and conjecture 1 and using the Erd\\H{o}s-Turan-Koksma inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1253","kind":"arxiv","version":3},"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":"1103.1253","created_at":"2026-05-18T03:44:13.769403+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1253v3","created_at":"2026-05-18T03:44:13.769403+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1253","created_at":"2026-05-18T03:44:13.769403+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BBESBNLNNVS","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BBESBNLNNVSYEXL","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BBESBNL","created_at":"2026-05-18T12:26:22.705136+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/7BBESBNLNNVSYEXLXVW2LNX3P2","json":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2.json","graph_json":"https://pith.science/api/pith-number/7BBESBNLNNVSYEXLXVW2LNX3P2/graph.json","events_json":"https://pith.science/api/pith-number/7BBESBNLNNVSYEXLXVW2LNX3P2/events.json","paper":"https://pith.science/paper/7BBESBNL"},"agent_actions":{"view_html":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2","download_json":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2.json","view_paper":"https://pith.science/paper/7BBESBNL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1253&json=true","fetch_graph":"https://pith.science/api/pith-number/7BBESBNLNNVSYEXLXVW2LNX3P2/graph.json","fetch_events":"https://pith.science/api/pith-number/7BBESBNLNNVSYEXLXVW2LNX3P2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2/action/storage_attestation","attest_author":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2/action/author_attestation","sign_citation":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2/action/citation_signature","submit_replication":"https://pith.science/pith/7BBESBNLNNVSYEXLXVW2LNX3P2/action/replication_record"}},"created_at":"2026-05-18T03:44:13.769403+00:00","updated_at":"2026-05-18T03:44:13.769403+00:00"}