{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:W7LJYHYWSQLV5AOECDQ5ARC6OE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a7c448b94b9b6c989c0097de784a1236debb67887b9cdcc1af383bcdac90179e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-30T17:23:02Z","title_canon_sha256":"0f259228f12a960946c23d4fa69e80d69f69382aa1f5167e4314043d7235a507"},"schema_version":"1.0","source":{"id":"2306.17813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.17813","created_at":"2026-07-05T12:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"2306.17813v2","created_at":"2026-07-05T12:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.17813","created_at":"2026-07-05T12:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"W7LJYHYWSQLV","created_at":"2026-07-05T12:07:52Z"},{"alias_kind":"pith_short_16","alias_value":"W7LJYHYWSQLV5AOE","created_at":"2026-07-05T12:07:52Z"},{"alias_kind":"pith_short_8","alias_value":"W7LJYHYW","created_at":"2026-07-05T12:07:52Z"}],"graph_snapshots":[{"event_id":"sha256:c1d0afd6b8496240262aac93be09e4752f9d163fd73d5acbf0e47005463d75db","target":"graph","created_at":"2026-07-05T12:07:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.17813/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A sequence of integers of the form $\\lfloor n^{\\alpha}\\rfloor$ $(n=1,2,\\ldots)$ for some fixed non-integral $\\alpha>1$ is called a Piatetski-Shapiro sequence, where $\\lfloor x\\rfloor$ denotes the integer part of $x$. Let $\\mathrm{PS}(\\alpha)$ denote the set of all those terms. In this article, we show that $x+y=z$ has only finitely many solutions $(x,y,z)\\in \\mathrm{PS}(\\alpha)^3$ for almost every $\\alpha>3$. Furthermore, we show that $\\mathrm{PS}(\\alpha)$ has only finitely many arithmetic progressions of length $3$ for almost every $\\alpha>10$. In addition, we estimate upper bounds for the Ha","authors_text":"Kota Saito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-30T17:23:02Z","title":"Finiteness of solutions to linear Diophantine equations on Piatetski-Shapiro sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.17813","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3f82ca14f02a09e4665c3c37b32db574be3fa52298758cd56dc01d11ebca15f4","target":"record","created_at":"2026-07-05T12:07:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a7c448b94b9b6c989c0097de784a1236debb67887b9cdcc1af383bcdac90179e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-30T17:23:02Z","title_canon_sha256":"0f259228f12a960946c23d4fa69e80d69f69382aa1f5167e4314043d7235a507"},"schema_version":"1.0","source":{"id":"2306.17813","kind":"arxiv","version":2}},"canonical_sha256":"b7d69c1f1694175e81c410e1d0445e71231e01c56048cf539b0c119178a48e2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7d69c1f1694175e81c410e1d0445e71231e01c56048cf539b0c119178a48e2f","first_computed_at":"2026-07-05T12:07:52.318543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:52.318543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09GqrhLwK2bik+Bw/U5kX5tHoKs8d6nobA60OUDboEOsN61omgysjMbLUuAKelCyWLkFs3PM7vi0NH0tfclDDw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:52.319151Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.17813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f82ca14f02a09e4665c3c37b32db574be3fa52298758cd56dc01d11ebca15f4","sha256:c1d0afd6b8496240262aac93be09e4752f9d163fd73d5acbf0e47005463d75db"],"state_sha256":"715db92a4c68fddeb81ca5640d9ca161bdbdaf487cb64b3de0705dfdbe4d25ad"}