{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DCUEIMTA4RHDMAJFIZ45K656VI","short_pith_number":"pith:DCUEIMTA","schema_version":"1.0","canonical_sha256":"18a8443260e44e3601254679d57bbeaa329307faaabfba886c1d3c068199a7b4","source":{"kind":"arxiv","id":"2506.12063","version":1},"attestation_state":"computed","paper":{"title":"On the Density of Prime Imbalances in the Unit Interval","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Paul Alexander Bilokon","submitted_at":"2025-06-01T08:37:10Z","abstract_excerpt":"We prove that the set of normalized differences between primes, defined as $S = \\{(p-q)/(p+q) : p > q \\text{ are primes}\\}$, is dense in the open unit interval $(0,1)$. Our proof provides an explicit construction algorithm with quantitative bounds, relying on elementary results from prime number theory including Bertrand's postulate and explicit bounds on prime gaps in long 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":"2506.12063","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2025-06-01T08:37:10Z","cross_cats_sorted":[],"title_canon_sha256":"dc0cd8a97c7d1b5fa060e50d363357f49be0e9f9d176b48f5f80c13a45d7def0","abstract_canon_sha256":"a2d720582a176bec2f76a06e4b1d1dfd4d355f984ad532db2d3c1e5855e0f7cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:16.501742Z","signature_b64":"J4jTuvVhft6E7cEpVFz364hY7b6xuF+kdJ7rou8mhLJy2Afi2u1b8ABnLunYj+M0MG/RjM8TQ6LRW7ZWVlLOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18a8443260e44e3601254679d57bbeaa329307faaabfba886c1d3c068199a7b4","last_reissued_at":"2026-07-05T11:21:16.501350Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:16.501350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Density of Prime Imbalances in the Unit Interval","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Paul Alexander Bilokon","submitted_at":"2025-06-01T08:37:10Z","abstract_excerpt":"We prove that the set of normalized differences between primes, defined as $S = \\{(p-q)/(p+q) : p > q \\text{ are primes}\\}$, is dense in the open unit interval $(0,1)$. Our proof provides an explicit construction algorithm with quantitative bounds, relying on elementary results from prime number theory including Bertrand's postulate and explicit bounds on prime gaps in long intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12063","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.12063/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.12063","created_at":"2026-07-05T11:21:16.501422+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.12063v1","created_at":"2026-07-05T11:21:16.501422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12063","created_at":"2026-07-05T11:21:16.501422+00:00"},{"alias_kind":"pith_short_12","alias_value":"DCUEIMTA4RHD","created_at":"2026-07-05T11:21:16.501422+00:00"},{"alias_kind":"pith_short_16","alias_value":"DCUEIMTA4RHDMAJF","created_at":"2026-07-05T11:21:16.501422+00:00"},{"alias_kind":"pith_short_8","alias_value":"DCUEIMTA","created_at":"2026-07-05T11:21:16.501422+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/DCUEIMTA4RHDMAJFIZ45K656VI","json":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI.json","graph_json":"https://pith.science/api/pith-number/DCUEIMTA4RHDMAJFIZ45K656VI/graph.json","events_json":"https://pith.science/api/pith-number/DCUEIMTA4RHDMAJFIZ45K656VI/events.json","paper":"https://pith.science/paper/DCUEIMTA"},"agent_actions":{"view_html":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI","download_json":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI.json","view_paper":"https://pith.science/paper/DCUEIMTA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.12063&json=true","fetch_graph":"https://pith.science/api/pith-number/DCUEIMTA4RHDMAJFIZ45K656VI/graph.json","fetch_events":"https://pith.science/api/pith-number/DCUEIMTA4RHDMAJFIZ45K656VI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI/action/storage_attestation","attest_author":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI/action/author_attestation","sign_citation":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI/action/citation_signature","submit_replication":"https://pith.science/pith/DCUEIMTA4RHDMAJFIZ45K656VI/action/replication_record"}},"created_at":"2026-07-05T11:21:16.501422+00:00","updated_at":"2026-07-05T11:21:16.501422+00:00"}