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As a combinatorial consequence, we obtain that the primes contain infinitely many pairs whose difference belongs to the Piatetski-Shapiro sequence $\\bigl\\{\\lfloor m^c \\rfloor \\colon m \\in \\mathbb{N} \\bigr\\}$ for any non-integer $c > 2$."},"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":"2411.17599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-26T17:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"492d423bf38737b577b9f5321f9f68e7bef75c85d59963d9963ddf95a8c42125","abstract_canon_sha256":"fb0a935a9953cb99f1c1a6c791362e239215c2b23c9f814a66a693e3c3f420b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:49.466120Z","signature_b64":"zfFfgi7MKiBARtguUtk49CKG6GjCiOw3CeLRCZ010LyR/zCM5U4J9FV5l6rpZGBMUtz0DKr3QGJtJowjc5xmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67f54ee5b569e98ce0a3ce9e659dd889b02129408905b5083aadfb2fc2812088","last_reissued_at":"2026-07-05T09:40:49.465658Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:49.465658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Popular differences in primes along fractional powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bora \\c{C}al{\\i}m, Deborah Wooton, Ioannis Iakovakis, Jack Moffatt, Sophie Long","submitted_at":"2024-11-26T17:06:47Z","abstract_excerpt":"We prove that $\\mathop{\\mathbb{E}}_{m \\leq M} \\mathop{\\mathbb{E}}_{n \\leq N} \\Lambda(n) \\Lambda\\bigl(n + \\lfloor m^c \\rfloor\\bigr) = 1 + \\rm{O}(\\log^{2 - Bc} N)$, where $c > 2$ is a non-integer, $B \\geq 3/c$, and $M$ is of order $N^{1/c} \\log^{-B} N$. As a combinatorial consequence, we obtain that the primes contain infinitely many pairs whose difference belongs to the Piatetski-Shapiro sequence $\\bigl\\{\\lfloor m^c \\rfloor \\colon m \\in \\mathbb{N} \\bigr\\}$ for any non-integer $c > 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17599","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/2411.17599/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":"2411.17599","created_at":"2026-07-05T09:40:49.465718+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.17599v1","created_at":"2026-07-05T09:40:49.465718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17599","created_at":"2026-07-05T09:40:49.465718+00:00"},{"alias_kind":"pith_short_12","alias_value":"M72U5ZNVNHUY","created_at":"2026-07-05T09:40:49.465718+00:00"},{"alias_kind":"pith_short_16","alias_value":"M72U5ZNVNHUYZYFD","created_at":"2026-07-05T09:40:49.465718+00:00"},{"alias_kind":"pith_short_8","alias_value":"M72U5ZNV","created_at":"2026-07-05T09:40:49.465718+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/M72U5ZNVNHUYZYFDZ2PGLHOYRG","json":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG.json","graph_json":"https://pith.science/api/pith-number/M72U5ZNVNHUYZYFDZ2PGLHOYRG/graph.json","events_json":"https://pith.science/api/pith-number/M72U5ZNVNHUYZYFDZ2PGLHOYRG/events.json","paper":"https://pith.science/paper/M72U5ZNV"},"agent_actions":{"view_html":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG","download_json":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG.json","view_paper":"https://pith.science/paper/M72U5ZNV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.17599&json=true","fetch_graph":"https://pith.science/api/pith-number/M72U5ZNVNHUYZYFDZ2PGLHOYRG/graph.json","fetch_events":"https://pith.science/api/pith-number/M72U5ZNVNHUYZYFDZ2PGLHOYRG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG/action/storage_attestation","attest_author":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG/action/author_attestation","sign_citation":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG/action/citation_signature","submit_replication":"https://pith.science/pith/M72U5ZNVNHUYZYFDZ2PGLHOYRG/action/replication_record"}},"created_at":"2026-07-05T09:40:49.465718+00:00","updated_at":"2026-07-05T09:40:49.465718+00:00"}