{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6M6OUG6Q2YYJUHLENI47STFFMD","short_pith_number":"pith:6M6OUG6Q","schema_version":"1.0","canonical_sha256":"f33cea1bd0d6309a1d646a39f94ca560edc3b2fc8bd07a4f21bb461e9004d279","source":{"kind":"arxiv","id":"1504.00533","version":2},"attestation_state":"computed","paper":{"title":"Almost prime triples and Chen's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D.R. Heath-Brown, Xiannan Li","submitted_at":"2015-04-02T13:03:07Z","abstract_excerpt":"We show that there are infinitely many primes $p$ such that not only does $p + 2$ have at most two prime factors, but $p + 6$ also has a bounded number of prime divisors. This refines the well known result of Chen."},"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":"1504.00533","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-02T13:03:07Z","cross_cats_sorted":[],"title_canon_sha256":"104e688a944c27e0fd7c22cf6c4d6c21fda2f11c1ef7220d8a5dbc454b78405b","abstract_canon_sha256":"39e8aadc23670b97b46ff62300bd02588f61da268be1344d1849209167dbdc0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:11.184675Z","signature_b64":"Ww4MOoA7CsHPMi1Nry8zbYighTRpczqMWszdzebL4sxY+2Pc3fLC1LqXZbf7IS1ARjulYoQlUlTu3SSqco+3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f33cea1bd0d6309a1d646a39f94ca560edc3b2fc8bd07a4f21bb461e9004d279","last_reissued_at":"2026-05-18T01:31:11.184165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:11.184165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost prime triples and Chen's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D.R. Heath-Brown, Xiannan Li","submitted_at":"2015-04-02T13:03:07Z","abstract_excerpt":"We show that there are infinitely many primes $p$ such that not only does $p + 2$ have at most two prime factors, but $p + 6$ also has a bounded number of prime divisors. This refines the well known result of Chen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00533","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":"1504.00533","created_at":"2026-05-18T01:31:11.184245+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00533v2","created_at":"2026-05-18T01:31:11.184245+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00533","created_at":"2026-05-18T01:31:11.184245+00:00"},{"alias_kind":"pith_short_12","alias_value":"6M6OUG6Q2YYJ","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6M6OUG6Q2YYJUHLE","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6M6OUG6Q","created_at":"2026-05-18T12:29:07.941421+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/6M6OUG6Q2YYJUHLENI47STFFMD","json":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD.json","graph_json":"https://pith.science/api/pith-number/6M6OUG6Q2YYJUHLENI47STFFMD/graph.json","events_json":"https://pith.science/api/pith-number/6M6OUG6Q2YYJUHLENI47STFFMD/events.json","paper":"https://pith.science/paper/6M6OUG6Q"},"agent_actions":{"view_html":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD","download_json":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD.json","view_paper":"https://pith.science/paper/6M6OUG6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00533&json=true","fetch_graph":"https://pith.science/api/pith-number/6M6OUG6Q2YYJUHLENI47STFFMD/graph.json","fetch_events":"https://pith.science/api/pith-number/6M6OUG6Q2YYJUHLENI47STFFMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD/action/storage_attestation","attest_author":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD/action/author_attestation","sign_citation":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD/action/citation_signature","submit_replication":"https://pith.science/pith/6M6OUG6Q2YYJUHLENI47STFFMD/action/replication_record"}},"created_at":"2026-05-18T01:31:11.184245+00:00","updated_at":"2026-05-18T01:31:11.184245+00:00"}