{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TAEJAVWFPXA56RG6FYSE2OLQEY","short_pith_number":"pith:TAEJAVWF","schema_version":"1.0","canonical_sha256":"98089056c57dc1df44de2e244d3970263f8e40bb1283e9273336c41ac448d7b9","source":{"kind":"arxiv","id":"1401.4233","version":1},"attestation_state":"computed","paper":{"title":"An Explicit Result for Primes Between Cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian Dudek","submitted_at":"2014-01-17T03:50:27Z","abstract_excerpt":"We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \\geq \\exp(\\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-function with explicit bounds on the error term. We use this along with other recent explicit estimates regarding the zeroes of the Riemann zeta-function to obtain the result. Furthermore, we show that there is a prime between any two consecutive $m$th powers for $m \\geq 4.971 \\times 10^9$."},"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":"1401.4233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-17T03:50:27Z","cross_cats_sorted":[],"title_canon_sha256":"be59215cf2fe11b2c7e3a1da981cf4cffca363eb984770ba618174474d6fe18d","abstract_canon_sha256":"0154e87135b7c14f8f1859c0fc4a97c084e3d2218d641392896a2f65fab44adb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:55.645826Z","signature_b64":"J8kyVgFStE4QkBEiFxyGd8HwWH/SqnboEig4mjnS2R/4P7ps5Nno6KrsHdFmrusA6mKZgQun+G9gAZFa79SRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98089056c57dc1df44de2e244d3970263f8e40bb1283e9273336c41ac448d7b9","last_reissued_at":"2026-05-18T03:01:55.645191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:55.645191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Explicit Result for Primes Between Cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian Dudek","submitted_at":"2014-01-17T03:50:27Z","abstract_excerpt":"We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \\geq \\exp(\\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-function with explicit bounds on the error term. We use this along with other recent explicit estimates regarding the zeroes of the Riemann zeta-function to obtain the result. Furthermore, we show that there is a prime between any two consecutive $m$th powers for $m \\geq 4.971 \\times 10^9$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4233","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":""},"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":"1401.4233","created_at":"2026-05-18T03:01:55.645276+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.4233v1","created_at":"2026-05-18T03:01:55.645276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4233","created_at":"2026-05-18T03:01:55.645276+00:00"},{"alias_kind":"pith_short_12","alias_value":"TAEJAVWFPXA5","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TAEJAVWFPXA56RG6","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TAEJAVWF","created_at":"2026-05-18T12:28:49.207871+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/TAEJAVWFPXA56RG6FYSE2OLQEY","json":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY.json","graph_json":"https://pith.science/api/pith-number/TAEJAVWFPXA56RG6FYSE2OLQEY/graph.json","events_json":"https://pith.science/api/pith-number/TAEJAVWFPXA56RG6FYSE2OLQEY/events.json","paper":"https://pith.science/paper/TAEJAVWF"},"agent_actions":{"view_html":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY","download_json":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY.json","view_paper":"https://pith.science/paper/TAEJAVWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.4233&json=true","fetch_graph":"https://pith.science/api/pith-number/TAEJAVWFPXA56RG6FYSE2OLQEY/graph.json","fetch_events":"https://pith.science/api/pith-number/TAEJAVWFPXA56RG6FYSE2OLQEY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY/action/storage_attestation","attest_author":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY/action/author_attestation","sign_citation":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY/action/citation_signature","submit_replication":"https://pith.science/pith/TAEJAVWFPXA56RG6FYSE2OLQEY/action/replication_record"}},"created_at":"2026-05-18T03:01:55.645276+00:00","updated_at":"2026-05-18T03:01:55.645276+00:00"}