{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HBFMTWC5U4V3H7DKABXZ33LBAF","short_pith_number":"pith:HBFMTWC5","schema_version":"1.0","canonical_sha256":"384ac9d85da72bb3fc6a006f9ded61015931595f08e734aae8f54a3ec38f00b2","source":{"kind":"arxiv","id":"1610.07395","version":1},"attestation_state":"computed","paper":{"title":"Squares in Piatetski--Shapiro Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Kui Liu, Tianping Zhang","submitted_at":"2016-10-24T13:02:10Z","abstract_excerpt":"We study the distribution of squares in a Piatetski-Shapiro sequence $\\left(\\lfloor n^c\\rfloor\\right)_{n\\in\\mathbb N}$ with $c>1$ and $c\\not\\in\\mathbb N$. We also study more general equations $\\lfloor{n^c}\\rfloor = sm^2$, $n,m\\in \\mathbb N$, $1\\le n \\le N$ for an integer $s$ and obtain several bounds on the number of solutions for a fixed $s$ and on average over $s$ in an interval. These results are based on various techniques chosen depending on the range of the parameters."},"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":"1610.07395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-24T13:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"5d98d2ffa52551b1db62996e785a801a0b161be29134f6c3f4665c1c6ac4c037","abstract_canon_sha256":"ea4e3fdbf43b0e2cb561d2921362f7fd60d6f809bbbcc3460e22a2ff69604ff3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:30.196660Z","signature_b64":"DAkbk/qvs3OcjJRZRaFuYLzarBeU1N2Qv90CuhUCdeHIF5YnmP+7PJJYsuU1rz66s7yEUxxdG+CA1A8mkr4HDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"384ac9d85da72bb3fc6a006f9ded61015931595f08e734aae8f54a3ec38f00b2","last_reissued_at":"2026-05-18T01:01:30.196234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:30.196234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Squares in Piatetski--Shapiro Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Kui Liu, Tianping Zhang","submitted_at":"2016-10-24T13:02:10Z","abstract_excerpt":"We study the distribution of squares in a Piatetski-Shapiro sequence $\\left(\\lfloor n^c\\rfloor\\right)_{n\\in\\mathbb N}$ with $c>1$ and $c\\not\\in\\mathbb N$. We also study more general equations $\\lfloor{n^c}\\rfloor = sm^2$, $n,m\\in \\mathbb N$, $1\\le n \\le N$ for an integer $s$ and obtain several bounds on the number of solutions for a fixed $s$ and on average over $s$ in an interval. These results are based on various techniques chosen depending on the range of the parameters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07395","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":""},"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":"1610.07395","created_at":"2026-05-18T01:01:30.196292+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07395v1","created_at":"2026-05-18T01:01:30.196292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07395","created_at":"2026-05-18T01:01:30.196292+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBFMTWC5U4V3","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBFMTWC5U4V3H7DK","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBFMTWC5","created_at":"2026-05-18T12:30:19.053100+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/HBFMTWC5U4V3H7DKABXZ33LBAF","json":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF.json","graph_json":"https://pith.science/api/pith-number/HBFMTWC5U4V3H7DKABXZ33LBAF/graph.json","events_json":"https://pith.science/api/pith-number/HBFMTWC5U4V3H7DKABXZ33LBAF/events.json","paper":"https://pith.science/paper/HBFMTWC5"},"agent_actions":{"view_html":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF","download_json":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF.json","view_paper":"https://pith.science/paper/HBFMTWC5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07395&json=true","fetch_graph":"https://pith.science/api/pith-number/HBFMTWC5U4V3H7DKABXZ33LBAF/graph.json","fetch_events":"https://pith.science/api/pith-number/HBFMTWC5U4V3H7DKABXZ33LBAF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF/action/storage_attestation","attest_author":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF/action/author_attestation","sign_citation":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF/action/citation_signature","submit_replication":"https://pith.science/pith/HBFMTWC5U4V3H7DKABXZ33LBAF/action/replication_record"}},"created_at":"2026-05-18T01:01:30.196292+00:00","updated_at":"2026-05-18T01:01:30.196292+00:00"}