{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BJ6H32KMHS7F75LX45H3EIWFTU","short_pith_number":"pith:BJ6H32KM","schema_version":"1.0","canonical_sha256":"0a7c7de94c3cbe5ff577e74fb222c59d2bc814399ecd24ceeba3a1a274c97d04","source":{"kind":"arxiv","id":"1203.5240","version":7},"attestation_state":"computed","paper":{"title":"Twin Prime Sieve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"H. J. Weber","submitted_at":"2012-03-23T13:56:50Z","abstract_excerpt":"A sieve is constructed for ordinary twin primes of the form 6m+/-1 that are characterized by their twin rank m. It has no parity problem. Non-rank numbers are identified and counted using odd primes p>=5. Twin- and non-ranks make up the set of positive integers. Regularities of non-ranks allow gathering information on them to obtain a Legendre-type formula for the number of twin-ranks near primorial arguments."},"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":"1203.5240","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-23T13:56:50Z","cross_cats_sorted":[],"title_canon_sha256":"f709c02fb21b0ab0672f3ac9a0c0b9154d10df132d46b55763faf710a6cfe57b","abstract_canon_sha256":"54f05f7f0eeab6925606009254d5637a14579dc6448b6626e8b615e5a528ab6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:04.384062Z","signature_b64":"xXXkKfG5Ol/6wRVHe0rOXvMTAim0TVz/r2GTXzhc1BZTM++R0R0O2ypclbvibJqKjYp4YYrb9Q8l3rduozy/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a7c7de94c3cbe5ff577e74fb222c59d2bc814399ecd24ceeba3a1a274c97d04","last_reissued_at":"2026-05-18T02:52:04.383404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:04.383404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twin Prime Sieve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"H. J. Weber","submitted_at":"2012-03-23T13:56:50Z","abstract_excerpt":"A sieve is constructed for ordinary twin primes of the form 6m+/-1 that are characterized by their twin rank m. It has no parity problem. Non-rank numbers are identified and counted using odd primes p>=5. Twin- and non-ranks make up the set of positive integers. Regularities of non-ranks allow gathering information on them to obtain a Legendre-type formula for the number of twin-ranks near primorial arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5240","kind":"arxiv","version":7},"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":"1203.5240","created_at":"2026-05-18T02:52:04.383515+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.5240v7","created_at":"2026-05-18T02:52:04.383515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5240","created_at":"2026-05-18T02:52:04.383515+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJ6H32KMHS7F","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJ6H32KMHS7F75LX","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJ6H32KM","created_at":"2026-05-18T12:27:01.376967+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/BJ6H32KMHS7F75LX45H3EIWFTU","json":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU.json","graph_json":"https://pith.science/api/pith-number/BJ6H32KMHS7F75LX45H3EIWFTU/graph.json","events_json":"https://pith.science/api/pith-number/BJ6H32KMHS7F75LX45H3EIWFTU/events.json","paper":"https://pith.science/paper/BJ6H32KM"},"agent_actions":{"view_html":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU","download_json":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU.json","view_paper":"https://pith.science/paper/BJ6H32KM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.5240&json=true","fetch_graph":"https://pith.science/api/pith-number/BJ6H32KMHS7F75LX45H3EIWFTU/graph.json","fetch_events":"https://pith.science/api/pith-number/BJ6H32KMHS7F75LX45H3EIWFTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU/action/storage_attestation","attest_author":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU/action/author_attestation","sign_citation":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU/action/citation_signature","submit_replication":"https://pith.science/pith/BJ6H32KMHS7F75LX45H3EIWFTU/action/replication_record"}},"created_at":"2026-05-18T02:52:04.383515+00:00","updated_at":"2026-05-18T02:52:04.383515+00:00"}