{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AFYMCLHZH7E5EVTCCUBKIKBXHG","short_pith_number":"pith:AFYMCLHZ","schema_version":"1.0","canonical_sha256":"0170c12cf93fc9d256621502a42837399b411ce79cd2c4ad57bd53e9aa0aaccb","source":{"kind":"arxiv","id":"1503.03325","version":2},"attestation_state":"computed","paper":{"title":"A bound for Dickson's lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Helmut Schwichtenberg, Josef Berger","submitted_at":"2015-03-11T13:34:10Z","abstract_excerpt":"We consider a special case of Dickson's lemma: for any two functions $f,g$ on the natural numbers there are two numbers $i<j$ such that both $f$ and $g$ weakly increase on them, i.e., $f_i\\le f_j$ and $g_i \\le g_j$. By a combinatorial argument (due to the first author) a simple bound for such $i,j$ is constructed. The combinatorics is based on the finite pigeon hole principle and results in a descent lemma. From the descent lemma one can prove Dickson's lemma, then guess what the bound might be, and verify it by an appropriate proof. We also extract (via realizability) a bound from (a formaliz"},"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":"1503.03325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-11T13:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"d655e2f7e13ed4e66e3ef6a67bd86bb1d680fc5899c09caa1cb15afb721ea812","abstract_canon_sha256":"7d78ff7e10988205036199ce116c2e6c19390f3af6218e38bed4cd292c70c1d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:23.935849Z","signature_b64":"5luybs2uK0c86mphaxLgiE36GKC5j2fcRc38Y9Nqt5MBReQJuGl0R06L02EpkZs8TCYK5LoNkxcMrTvcXtEPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0170c12cf93fc9d256621502a42837399b411ce79cd2c4ad57bd53e9aa0aaccb","last_reissued_at":"2026-05-17T23:51:23.935300Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:23.935300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A bound for Dickson's lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Helmut Schwichtenberg, Josef Berger","submitted_at":"2015-03-11T13:34:10Z","abstract_excerpt":"We consider a special case of Dickson's lemma: for any two functions $f,g$ on the natural numbers there are two numbers $i<j$ such that both $f$ and $g$ weakly increase on them, i.e., $f_i\\le f_j$ and $g_i \\le g_j$. By a combinatorial argument (due to the first author) a simple bound for such $i,j$ is constructed. The combinatorics is based on the finite pigeon hole principle and results in a descent lemma. From the descent lemma one can prove Dickson's lemma, then guess what the bound might be, and verify it by an appropriate proof. We also extract (via realizability) a bound from (a formaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03325","kind":"arxiv","version":2},"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":"1503.03325","created_at":"2026-05-17T23:51:23.935394+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03325v2","created_at":"2026-05-17T23:51:23.935394+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03325","created_at":"2026-05-17T23:51:23.935394+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFYMCLHZH7E5","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFYMCLHZH7E5EVTC","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFYMCLHZ","created_at":"2026-05-18T12:29:10.953037+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/AFYMCLHZH7E5EVTCCUBKIKBXHG","json":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG.json","graph_json":"https://pith.science/api/pith-number/AFYMCLHZH7E5EVTCCUBKIKBXHG/graph.json","events_json":"https://pith.science/api/pith-number/AFYMCLHZH7E5EVTCCUBKIKBXHG/events.json","paper":"https://pith.science/paper/AFYMCLHZ"},"agent_actions":{"view_html":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG","download_json":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG.json","view_paper":"https://pith.science/paper/AFYMCLHZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03325&json=true","fetch_graph":"https://pith.science/api/pith-number/AFYMCLHZH7E5EVTCCUBKIKBXHG/graph.json","fetch_events":"https://pith.science/api/pith-number/AFYMCLHZH7E5EVTCCUBKIKBXHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG/action/storage_attestation","attest_author":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG/action/author_attestation","sign_citation":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG/action/citation_signature","submit_replication":"https://pith.science/pith/AFYMCLHZH7E5EVTCCUBKIKBXHG/action/replication_record"}},"created_at":"2026-05-17T23:51:23.935394+00:00","updated_at":"2026-05-17T23:51:23.935394+00:00"}