{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IAC74QP7IKJ27AYH7FDV5OJBHT","short_pith_number":"pith:IAC74QP7","schema_version":"1.0","canonical_sha256":"4005fe41ff4293af8307f9475eb9213cc9373a00cda5f5092e1f443742116a55","source":{"kind":"arxiv","id":"1011.2251","version":1},"attestation_state":"computed","paper":{"title":"A characterization of B\\\"uchi's integer sequences of length 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pablo Sa\\'ez, Xavier Vidaux","submitted_at":"2010-11-10T01:34:52Z","abstract_excerpt":"We give a new characterization of generalized B\\\"uchi sequences (sequences whose sequence of squares has constant second difference $(a)$, for some fixed integer $a$) of length 3 over the integers and a strategy for attacking B\\\"uchi's n Squares Problem. Known characterizations of integer B\\\"uchi sequences of length 3 are actually characterizations over the rationals, plus some divisibility criterions that keep integer sequences."},"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":"1011.2251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-10T01:34:52Z","cross_cats_sorted":[],"title_canon_sha256":"29bda8e013b7ebf0314b234c01ec93384062536dc34f76739d9e9808c667bdf2","abstract_canon_sha256":"5f368168a8e9010aec90ef8bfcf626b3b85c431f6061c362c5380de66e29dd4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:30.748071Z","signature_b64":"a21m3o4x6KUH2+tM3gTm7ttQZnuHa3QE/FKAAzCXF2WvRRYgR1YcQlqMzqYNoPJyilQ7m8JPAcJvcr+aXL2eCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4005fe41ff4293af8307f9475eb9213cc9373a00cda5f5092e1f443742116a55","last_reissued_at":"2026-05-18T04:36:30.747426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:30.747426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of B\\\"uchi's integer sequences of length 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pablo Sa\\'ez, Xavier Vidaux","submitted_at":"2010-11-10T01:34:52Z","abstract_excerpt":"We give a new characterization of generalized B\\\"uchi sequences (sequences whose sequence of squares has constant second difference $(a)$, for some fixed integer $a$) of length 3 over the integers and a strategy for attacking B\\\"uchi's n Squares Problem. Known characterizations of integer B\\\"uchi sequences of length 3 are actually characterizations over the rationals, plus some divisibility criterions that keep integer sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2251","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":"1011.2251","created_at":"2026-05-18T04:36:30.747535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.2251v1","created_at":"2026-05-18T04:36:30.747535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2251","created_at":"2026-05-18T04:36:30.747535+00:00"},{"alias_kind":"pith_short_12","alias_value":"IAC74QP7IKJ2","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IAC74QP7IKJ27AYH","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IAC74QP7","created_at":"2026-05-18T12:26:09.077623+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/IAC74QP7IKJ27AYH7FDV5OJBHT","json":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT.json","graph_json":"https://pith.science/api/pith-number/IAC74QP7IKJ27AYH7FDV5OJBHT/graph.json","events_json":"https://pith.science/api/pith-number/IAC74QP7IKJ27AYH7FDV5OJBHT/events.json","paper":"https://pith.science/paper/IAC74QP7"},"agent_actions":{"view_html":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT","download_json":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT.json","view_paper":"https://pith.science/paper/IAC74QP7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.2251&json=true","fetch_graph":"https://pith.science/api/pith-number/IAC74QP7IKJ27AYH7FDV5OJBHT/graph.json","fetch_events":"https://pith.science/api/pith-number/IAC74QP7IKJ27AYH7FDV5OJBHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT/action/storage_attestation","attest_author":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT/action/author_attestation","sign_citation":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT/action/citation_signature","submit_replication":"https://pith.science/pith/IAC74QP7IKJ27AYH7FDV5OJBHT/action/replication_record"}},"created_at":"2026-05-18T04:36:30.747535+00:00","updated_at":"2026-05-18T04:36:30.747535+00:00"}