{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GVI4BRRJU6PPCGC3DT4YI7L6C6","short_pith_number":"pith:GVI4BRRJ","schema_version":"1.0","canonical_sha256":"3551c0c629a79ef1185b1cf9847d7e17997f1e45990003e903b050eda9f72ac1","source":{"kind":"arxiv","id":"2606.03781","version":1},"attestation_state":"computed","paper":{"title":"Pair correlation of $\\alpha n^{\\theta}$ for random $\\theta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrei Shubin","submitted_at":"2026-06-02T15:36:08Z","abstract_excerpt":"For fixed $\\alpha>0$, we show that the sequence $\\{\\alpha n^{\\theta}\\}$ has Poissonian pair correlation for Lebesgue-almost all $\\theta \\in (0,\\frac{3}{5})\\cup(3,\\infty)$. This improves a result of Technau and Yesha, who proved the same for almost all $\\theta>7$. The approach of Technau and Yesha was based on a repulsion principle, which roughly allows one to estimate the variance of the pair correlation function using the fourth derivative of the phase. In our approach, we split the $\\theta$-integration in the variance into many short intervals and show that most of the integrals can be estim"},"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":"2606.03781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-02T15:36:08Z","cross_cats_sorted":[],"title_canon_sha256":"5c6df680c4e0b7a32847658be598c9eaf71866decea6a4f6a52b96a5e854e4c9","abstract_canon_sha256":"7e095532193150a6e0b02dd64cbf3077ef6382dc71aef5893d787b3f12f00320"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:06:02.256675Z","signature_b64":"kvHhlioLTxxJ9mt6qJJRNlhfo4+UKKStblHKuWKXF1Ofi66/Hs3+Z5ibwMczHRdJtNmtp3ofQ3Pk9g2DI84MDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3551c0c629a79ef1185b1cf9847d7e17997f1e45990003e903b050eda9f72ac1","last_reissued_at":"2026-06-03T02:06:02.256147Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:06:02.256147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pair correlation of $\\alpha n^{\\theta}$ for random $\\theta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrei Shubin","submitted_at":"2026-06-02T15:36:08Z","abstract_excerpt":"For fixed $\\alpha>0$, we show that the sequence $\\{\\alpha n^{\\theta}\\}$ has Poissonian pair correlation for Lebesgue-almost all $\\theta \\in (0,\\frac{3}{5})\\cup(3,\\infty)$. This improves a result of Technau and Yesha, who proved the same for almost all $\\theta>7$. The approach of Technau and Yesha was based on a repulsion principle, which roughly allows one to estimate the variance of the pair correlation function using the fourth derivative of the phase. In our approach, we split the $\\theta$-integration in the variance into many short intervals and show that most of the integrals can be estim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03781","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/2606.03781/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":"2606.03781","created_at":"2026-06-03T02:06:02.256205+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.03781v1","created_at":"2026-06-03T02:06:02.256205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03781","created_at":"2026-06-03T02:06:02.256205+00:00"},{"alias_kind":"pith_short_12","alias_value":"GVI4BRRJU6PP","created_at":"2026-06-03T02:06:02.256205+00:00"},{"alias_kind":"pith_short_16","alias_value":"GVI4BRRJU6PPCGC3","created_at":"2026-06-03T02:06:02.256205+00:00"},{"alias_kind":"pith_short_8","alias_value":"GVI4BRRJ","created_at":"2026-06-03T02:06:02.256205+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/GVI4BRRJU6PPCGC3DT4YI7L6C6","json":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6.json","graph_json":"https://pith.science/api/pith-number/GVI4BRRJU6PPCGC3DT4YI7L6C6/graph.json","events_json":"https://pith.science/api/pith-number/GVI4BRRJU6PPCGC3DT4YI7L6C6/events.json","paper":"https://pith.science/paper/GVI4BRRJ"},"agent_actions":{"view_html":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6","download_json":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6.json","view_paper":"https://pith.science/paper/GVI4BRRJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.03781&json=true","fetch_graph":"https://pith.science/api/pith-number/GVI4BRRJU6PPCGC3DT4YI7L6C6/graph.json","fetch_events":"https://pith.science/api/pith-number/GVI4BRRJU6PPCGC3DT4YI7L6C6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6/action/storage_attestation","attest_author":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6/action/author_attestation","sign_citation":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6/action/citation_signature","submit_replication":"https://pith.science/pith/GVI4BRRJU6PPCGC3DT4YI7L6C6/action/replication_record"}},"created_at":"2026-06-03T02:06:02.256205+00:00","updated_at":"2026-06-03T02:06:02.256205+00:00"}