{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AFYMCLHZH7E5EVTCCUBKIKBXHG","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":"7d78ff7e10988205036199ce116c2e6c19390f3af6218e38bed4cd292c70c1d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-11T13:34:10Z","title_canon_sha256":"d655e2f7e13ed4e66e3ef6a67bd86bb1d680fc5899c09caa1cb15afb721ea812"},"schema_version":"1.0","source":{"id":"1503.03325","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03325","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03325v2","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03325","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"AFYMCLHZH7E5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AFYMCLHZH7E5EVTC","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AFYMCLHZ","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:b31c00e8dd2bf861af057aa525c66133f7ec45624cb84b972365b05942f8741b","target":"graph","created_at":"2026-05-17T23:51:23Z","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"},"paper":{"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","authors_text":"Helmut Schwichtenberg, Josef Berger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-11T13:34:10Z","title":"A bound for Dickson's lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03325","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:bbb0eec5ce365424f85eb597b7a01df251ad9bbcda184c75e86f912a04cf9410","target":"record","created_at":"2026-05-17T23:51:23Z","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":"7d78ff7e10988205036199ce116c2e6c19390f3af6218e38bed4cd292c70c1d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-11T13:34:10Z","title_canon_sha256":"d655e2f7e13ed4e66e3ef6a67bd86bb1d680fc5899c09caa1cb15afb721ea812"},"schema_version":"1.0","source":{"id":"1503.03325","kind":"arxiv","version":2}},"canonical_sha256":"0170c12cf93fc9d256621502a42837399b411ce79cd2c4ad57bd53e9aa0aaccb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0170c12cf93fc9d256621502a42837399b411ce79cd2c4ad57bd53e9aa0aaccb","first_computed_at":"2026-05-17T23:51:23.935300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:23.935300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5luybs2uK0c86mphaxLgiE36GKC5j2fcRc38Y9Nqt5MBReQJuGl0R06L02EpkZs8TCYK5LoNkxcMrTvcXtEPDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:23.935849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03325","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbb0eec5ce365424f85eb597b7a01df251ad9bbcda184c75e86f912a04cf9410","sha256:b31c00e8dd2bf861af057aa525c66133f7ec45624cb84b972365b05942f8741b"],"state_sha256":"3950037849df01c2c99b0632960c9c9e4dd1c86fc1e7da2a127851bb85d4b883"}