{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OMULC344CXDNDM4HF3U5IVDFUG","short_pith_number":"pith:OMULC344","schema_version":"1.0","canonical_sha256":"7328b16f9c15c6d1b3872ee9d45465a1af0559c3c4bdcace851884de7cfc8d16","source":{"kind":"arxiv","id":"1412.0574","version":4},"attestation_state":"computed","paper":{"title":"Gaps of Smallest Possible Order between Primes in an Arithmetic Progression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liangyi Zhao, Roger C. Baker","submitted_at":"2014-12-01T18:29:52Z","abstract_excerpt":"Let $t \\in \\mathbb{N}$, $\\eta >0$. Suppose that $x$ is a sufficiently large real number and $q$ is a natural number with $q \\leq x^{5/12-\\eta}$, $q$ not a multiple of the conductor of the exceptional character $\\chi^*$ (if it exists). Suppose further that, \\[ \\max \\{p : p | q \\} < \\exp (\\frac{\\log x}{C \\log \\log x}) \\; \\; {and} \\; \\; \\prod_{p | q} p < x^{\\delta}, \\] where $C$ and $\\delta$ are suitable positive constants depending on $t$ and $\\eta$. Let $a \\in \\mathbb{Z}$, $(a,q)=1$ and \\[ \\mathcal{A} = \\{n \\in (x/2, x]: n \\equiv a \\pmod{q} \\} . \\] We prove that there are primes $p_1 < p_2 < .."},"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":"1412.0574","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-01T18:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"9f1e5110e88f28e20f82188ac279e5af394e848cca6eac91fe4a18aa7426be9a","abstract_canon_sha256":"2d973bf1646dff95585906860b1c1626f8924bba45087ce5b8f530b508221e28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:03.275579Z","signature_b64":"Z1/osSjEASj2b5VOHby6dPEvB70PNFQ18gRh1bOw0yNe77fWXXhTjxLUXKLkxL0+Fp2nYq6kgzxwJxZP2u+3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7328b16f9c15c6d1b3872ee9d45465a1af0559c3c4bdcace851884de7cfc8d16","last_reissued_at":"2026-05-18T01:22:03.275128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:03.275128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaps of Smallest Possible Order between Primes in an Arithmetic Progression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liangyi Zhao, Roger C. Baker","submitted_at":"2014-12-01T18:29:52Z","abstract_excerpt":"Let $t \\in \\mathbb{N}$, $\\eta >0$. Suppose that $x$ is a sufficiently large real number and $q$ is a natural number with $q \\leq x^{5/12-\\eta}$, $q$ not a multiple of the conductor of the exceptional character $\\chi^*$ (if it exists). Suppose further that, \\[ \\max \\{p : p | q \\} < \\exp (\\frac{\\log x}{C \\log \\log x}) \\; \\; {and} \\; \\; \\prod_{p | q} p < x^{\\delta}, \\] where $C$ and $\\delta$ are suitable positive constants depending on $t$ and $\\eta$. Let $a \\in \\mathbb{Z}$, $(a,q)=1$ and \\[ \\mathcal{A} = \\{n \\in (x/2, x]: n \\equiv a \\pmod{q} \\} . \\] We prove that there are primes $p_1 < p_2 < .."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0574","kind":"arxiv","version":4},"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":"1412.0574","created_at":"2026-05-18T01:22:03.275207+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0574v4","created_at":"2026-05-18T01:22:03.275207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0574","created_at":"2026-05-18T01:22:03.275207+00:00"},{"alias_kind":"pith_short_12","alias_value":"OMULC344CXDN","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OMULC344CXDNDM4H","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OMULC344","created_at":"2026-05-18T12:28:41.024544+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/OMULC344CXDNDM4HF3U5IVDFUG","json":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG.json","graph_json":"https://pith.science/api/pith-number/OMULC344CXDNDM4HF3U5IVDFUG/graph.json","events_json":"https://pith.science/api/pith-number/OMULC344CXDNDM4HF3U5IVDFUG/events.json","paper":"https://pith.science/paper/OMULC344"},"agent_actions":{"view_html":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG","download_json":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG.json","view_paper":"https://pith.science/paper/OMULC344","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0574&json=true","fetch_graph":"https://pith.science/api/pith-number/OMULC344CXDNDM4HF3U5IVDFUG/graph.json","fetch_events":"https://pith.science/api/pith-number/OMULC344CXDNDM4HF3U5IVDFUG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG/action/storage_attestation","attest_author":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG/action/author_attestation","sign_citation":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG/action/citation_signature","submit_replication":"https://pith.science/pith/OMULC344CXDNDM4HF3U5IVDFUG/action/replication_record"}},"created_at":"2026-05-18T01:22:03.275207+00:00","updated_at":"2026-05-18T01:22:03.275207+00:00"}