{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:R3MXZAM5AUWRHI4O2SBR5X623R","short_pith_number":"pith:R3MXZAM5","schema_version":"1.0","canonical_sha256":"8ed97c819d052d13a38ed4831edfdadc6438c9a3882ca17ed01151dc0f308118","source":{"kind":"arxiv","id":"2506.15274","version":1},"attestation_state":"computed","paper":{"title":"Metric Poissonian pair correlationa and additive energy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"E. Malavika, Tanmoy Bera","submitted_at":"2025-06-18T08:48:51Z","abstract_excerpt":"In this article we prove that if the additive energy of a strictly increasing sequence $(a_n)$ of natural numbers is less than $N^3/(\\log N)^C$ for some $C\\geq13.155$, then $(\\{a_n\\alpha\\})$ has Poissonian pair correlation for almost all $\\alpha\\in\\mathbb{R}.$ This provides a lower bound for the exponent $C$ in the additive energy bound established by Bloom and Walker[3]."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":true,"weak_author_claims":0,"strong_author_claims":1,"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":"2506.15274","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-18T08:48:51Z","cross_cats_sorted":[],"title_canon_sha256":"473846cfca1466ec43f31b04bae52f627108735be7036b0994cabcce0a25cd95","abstract_canon_sha256":"5d0a627c3563ba02ee0685f64a957943dffecfe9a93e707e9344385f8aeca7ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:23:40.580932Z","signature_b64":"m7pQNlT5lFayer85ZSKlqXowdpozN1AH0cqO29XUpXGv5xfQrdNeNVopUJq0kLJsu55SH7PMVzdL0ZxQlFeOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ed97c819d052d13a38ed4831edfdadc6438c9a3882ca17ed01151dc0f308118","last_reissued_at":"2026-07-05T11:23:40.580519Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:23:40.580519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metric Poissonian pair correlationa and additive energy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"E. Malavika, Tanmoy Bera","submitted_at":"2025-06-18T08:48:51Z","abstract_excerpt":"In this article we prove that if the additive energy of a strictly increasing sequence $(a_n)$ of natural numbers is less than $N^3/(\\log N)^C$ for some $C\\geq13.155$, then $(\\{a_n\\alpha\\})$ has Poissonian pair correlation for almost all $\\alpha\\in\\mathbb{R}.$ This provides a lower bound for the exponent $C$ in the additive energy bound established by Bloom and Walker[3]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.15274","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/2506.15274/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":"2506.15274","created_at":"2026-07-05T11:23:40.580578+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.15274v1","created_at":"2026-07-05T11:23:40.580578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.15274","created_at":"2026-07-05T11:23:40.580578+00:00"},{"alias_kind":"pith_short_12","alias_value":"R3MXZAM5AUWR","created_at":"2026-07-05T11:23:40.580578+00:00"},{"alias_kind":"pith_short_16","alias_value":"R3MXZAM5AUWRHI4O","created_at":"2026-07-05T11:23:40.580578+00:00"},{"alias_kind":"pith_short_8","alias_value":"R3MXZAM5","created_at":"2026-07-05T11:23:40.580578+00:00"}],"events":[],"event_summary":{},"paper_claims":[{"claim_id":"46fb2c60-747e-4880-a963-79abf02a741b","handle":null,"display_name":"Malavika E","verification":"orcid_verified","verification_note":"Auto-claimed from ORCID 0009-0009-5342-8821 at registration","role_label":null,"open_disputes":0}],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R","json":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R.json","graph_json":"https://pith.science/api/pith-number/R3MXZAM5AUWRHI4O2SBR5X623R/graph.json","events_json":"https://pith.science/api/pith-number/R3MXZAM5AUWRHI4O2SBR5X623R/events.json","paper":"https://pith.science/paper/R3MXZAM5"},"agent_actions":{"view_html":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R","download_json":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R.json","view_paper":"https://pith.science/paper/R3MXZAM5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.15274&json=true","fetch_graph":"https://pith.science/api/pith-number/R3MXZAM5AUWRHI4O2SBR5X623R/graph.json","fetch_events":"https://pith.science/api/pith-number/R3MXZAM5AUWRHI4O2SBR5X623R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R/action/storage_attestation","attest_author":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R/action/author_attestation","sign_citation":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R/action/citation_signature","submit_replication":"https://pith.science/pith/R3MXZAM5AUWRHI4O2SBR5X623R/action/replication_record"}},"created_at":"2026-07-05T11:23:40.580578+00:00","updated_at":"2026-07-05T11:23:40.580578+00:00"}