{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FWWI4SC26FH32XY7R33AAXHS3M","short_pith_number":"pith:FWWI4SC2","schema_version":"1.0","canonical_sha256":"2dac8e485af14fbd5f1f8ef6005cf2db35eda7d1383551bdd1764127a3abc798","source":{"kind":"arxiv","id":"1306.0511","version":2},"attestation_state":"computed","paper":{"title":"Bounded prime gaps in short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Johan Andersson","submitted_at":"2013-06-03T17:26:57Z","abstract_excerpt":"We generalise Zhang's and Pintz recent results on bounded prime gaps to give a lower bound for the the number of prime pairs bounded by 6*10^7 in the short interval $[x,x+x (\\log x)^{-A}]$. Our result follows only by analysing Zhang's proof of Theorem 1, but we also explain how a sharper variant of Zhang's Theorem 2 would imply the same result for shorter intervals."},"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":"1306.0511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-03T17:26:57Z","cross_cats_sorted":[],"title_canon_sha256":"2366ec146f55e080e831a0ee55a759df2fe43279586d3faa64ee0940476a8d9e","abstract_canon_sha256":"17a2a461381cd78a9b2c0016977973aa5362f1db548f556dd11dbfb5df40107a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:42.939837Z","signature_b64":"6Y4AGgM9a5oBkZYTY6YOAhAVoDLhIcN1hwfKgh+HDOAoqsEUeQclXD1W385nNImcV56E0ovMCsO6j57wcyVUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dac8e485af14fbd5f1f8ef6005cf2db35eda7d1383551bdd1764127a3abc798","last_reissued_at":"2026-05-18T03:21:42.939122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:42.939122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded prime gaps in short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Johan Andersson","submitted_at":"2013-06-03T17:26:57Z","abstract_excerpt":"We generalise Zhang's and Pintz recent results on bounded prime gaps to give a lower bound for the the number of prime pairs bounded by 6*10^7 in the short interval $[x,x+x (\\log x)^{-A}]$. Our result follows only by analysing Zhang's proof of Theorem 1, but we also explain how a sharper variant of Zhang's Theorem 2 would imply the same result for shorter intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0511","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":"1306.0511","created_at":"2026-05-18T03:21:42.939244+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.0511v2","created_at":"2026-05-18T03:21:42.939244+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0511","created_at":"2026-05-18T03:21:42.939244+00:00"},{"alias_kind":"pith_short_12","alias_value":"FWWI4SC26FH3","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FWWI4SC26FH32XY7","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FWWI4SC2","created_at":"2026-05-18T12:27:45.050594+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/FWWI4SC26FH32XY7R33AAXHS3M","json":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M.json","graph_json":"https://pith.science/api/pith-number/FWWI4SC26FH32XY7R33AAXHS3M/graph.json","events_json":"https://pith.science/api/pith-number/FWWI4SC26FH32XY7R33AAXHS3M/events.json","paper":"https://pith.science/paper/FWWI4SC2"},"agent_actions":{"view_html":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M","download_json":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M.json","view_paper":"https://pith.science/paper/FWWI4SC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.0511&json=true","fetch_graph":"https://pith.science/api/pith-number/FWWI4SC26FH32XY7R33AAXHS3M/graph.json","fetch_events":"https://pith.science/api/pith-number/FWWI4SC26FH32XY7R33AAXHS3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M/action/storage_attestation","attest_author":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M/action/author_attestation","sign_citation":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M/action/citation_signature","submit_replication":"https://pith.science/pith/FWWI4SC26FH32XY7R33AAXHS3M/action/replication_record"}},"created_at":"2026-05-18T03:21:42.939244+00:00","updated_at":"2026-05-18T03:21:42.939244+00:00"}