{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:UOST6FUYXQFBOKSIGLV372T63N","short_pith_number":"pith:UOST6FUY","schema_version":"1.0","canonical_sha256":"a3a53f1698bc0a172a4832ebbfea7edb5af6df25da1185676bc9e939536145dc","source":{"kind":"arxiv","id":"2112.11524","version":1},"attestation_state":"computed","paper":{"title":"Correlations of the Fractional Parts of $\\alpha n^\\theta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Lutsko, Niclas Technau","submitted_at":"2021-12-21T21:15:41Z","abstract_excerpt":"Let $m\\geq 3$, we prove that $(\\alpha n^\\theta \\mod 1)_{n>0}$ has Poissonian $m$-point correlation for all $\\alpha>0$, provided $\\theta<\\theta_m$, where $\\theta_m$ is an explicit bound which goes to $0$ as $m$ increases. This work builds on the method developed in Lutsko-Sourmelidis-Technau (2021), and introduces a new combinatorial argument for higher correlation levels, and new Fourier analytic techniques. A key point is to introduce an `extra' frequency variable to de-correlate the sequence variables and to eventually exploit a repulsion principle for oscillatory integrals. Presently, this "},"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":"2112.11524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-12-21T21:15:41Z","cross_cats_sorted":[],"title_canon_sha256":"ae98c61602544aa55e70729466987d6746f2c67bb2d0e54696fa0a7dc116574e","abstract_canon_sha256":"cf00525bd9e4d3a6bc52e43c3bde81f10fe351b67ddc0eded3913e846e973ede"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:43:07.867529Z","signature_b64":"segQ5UJe3Xjteme5DXGQEaZ6oHGl9kZnvXQcCTa8oCUgOq7RxHjaw0BvoPOv8WvtnPGS1DjywXRXgeMYOzDJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3a53f1698bc0a172a4832ebbfea7edb5af6df25da1185676bc9e939536145dc","last_reissued_at":"2026-07-05T03:43:07.867090Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:43:07.867090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlations of the Fractional Parts of $\\alpha n^\\theta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Lutsko, Niclas Technau","submitted_at":"2021-12-21T21:15:41Z","abstract_excerpt":"Let $m\\geq 3$, we prove that $(\\alpha n^\\theta \\mod 1)_{n>0}$ has Poissonian $m$-point correlation for all $\\alpha>0$, provided $\\theta<\\theta_m$, where $\\theta_m$ is an explicit bound which goes to $0$ as $m$ increases. This work builds on the method developed in Lutsko-Sourmelidis-Technau (2021), and introduces a new combinatorial argument for higher correlation levels, and new Fourier analytic techniques. A key point is to introduce an `extra' frequency variable to de-correlate the sequence variables and to eventually exploit a repulsion principle for oscillatory integrals. Presently, this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.11524","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/2112.11524/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":"2112.11524","created_at":"2026-07-05T03:43:07.867151+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.11524v1","created_at":"2026-07-05T03:43:07.867151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.11524","created_at":"2026-07-05T03:43:07.867151+00:00"},{"alias_kind":"pith_short_12","alias_value":"UOST6FUYXQFB","created_at":"2026-07-05T03:43:07.867151+00:00"},{"alias_kind":"pith_short_16","alias_value":"UOST6FUYXQFBOKSI","created_at":"2026-07-05T03:43:07.867151+00:00"},{"alias_kind":"pith_short_8","alias_value":"UOST6FUY","created_at":"2026-07-05T03:43:07.867151+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.01736","citing_title":"The bad and rough rotation is Poissonian","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N","json":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N.json","graph_json":"https://pith.science/api/pith-number/UOST6FUYXQFBOKSIGLV372T63N/graph.json","events_json":"https://pith.science/api/pith-number/UOST6FUYXQFBOKSIGLV372T63N/events.json","paper":"https://pith.science/paper/UOST6FUY"},"agent_actions":{"view_html":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N","download_json":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N.json","view_paper":"https://pith.science/paper/UOST6FUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.11524&json=true","fetch_graph":"https://pith.science/api/pith-number/UOST6FUYXQFBOKSIGLV372T63N/graph.json","fetch_events":"https://pith.science/api/pith-number/UOST6FUYXQFBOKSIGLV372T63N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N/action/storage_attestation","attest_author":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N/action/author_attestation","sign_citation":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N/action/citation_signature","submit_replication":"https://pith.science/pith/UOST6FUYXQFBOKSIGLV372T63N/action/replication_record"}},"created_at":"2026-07-05T03:43:07.867151+00:00","updated_at":"2026-07-05T03:43:07.867151+00:00"}