{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EXPI33NSMEGB4DT5R4KCDY3JKQ","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":"85b4f15ad6c201d6fa76387652987ea38866505785188c4bcfad575605735246","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-10-09T16:17:23Z","title_canon_sha256":"3f3b910d2d0305aa59cf9770e1ae1060a18599a06dcf1c012cf825a46701d955"},"schema_version":"1.0","source":{"id":"1410.2520","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2520","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2520v4","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2520","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"EXPI33NSMEGB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EXPI33NSMEGB4DT5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EXPI33NS","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:f4903bcb46baa3a82079d895f67dd23e3da5ec0a81f87bd8c8300e55a28d20ac","target":"graph","created_at":"2026-05-18T01:11:08Z","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":"Given a cardinal $\\kappa$ and a sequence $\\left(\\alpha_i\\right)_{i\\in\\kappa}$ of ordinals, we determine the least ordinal $\\beta$ (when one exists) such that the topological partition relation \\[\\beta\\rightarrow\\left(top\\,\\alpha_i\\right)^1_{i\\in\\kappa}\\] holds, including an independence result for one class of cases. Here the prefix \"$top$\" means that the homogeneous set must have the correct topology rather than the correct order type. The answer is linked to the non-topological pigeonhole principle of Milner and Rado.","authors_text":"Jacob Hilton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-10-09T16:17:23Z","title":"The topological pigeonhole principle for ordinals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2520","kind":"arxiv","version":4},"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":"sha256:9b1bd8119c33a5426b868ae198d7759b9da285095eac76ade68fd2c7e5ebebc8","target":"record","created_at":"2026-05-18T01:11:08Z","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":"85b4f15ad6c201d6fa76387652987ea38866505785188c4bcfad575605735246","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-10-09T16:17:23Z","title_canon_sha256":"3f3b910d2d0305aa59cf9770e1ae1060a18599a06dcf1c012cf825a46701d955"},"schema_version":"1.0","source":{"id":"1410.2520","kind":"arxiv","version":4}},"canonical_sha256":"25de8dedb2610c1e0e7d8f1421e36954128817f79735361f8d9d467f293de1a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25de8dedb2610c1e0e7d8f1421e36954128817f79735361f8d9d467f293de1a3","first_computed_at":"2026-05-18T01:11:08.699197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:08.699197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1MUxSZYHq1HkdqoovlZdXK4XXtys4jgSK3ScsHTWv1rb1Bcei5lJkFDUVMGbNHkToVkQqSqzD4ma8qQC8EI3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:08.699692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2520","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b1bd8119c33a5426b868ae198d7759b9da285095eac76ade68fd2c7e5ebebc8","sha256:f4903bcb46baa3a82079d895f67dd23e3da5ec0a81f87bd8c8300e55a28d20ac"],"state_sha256":"67e48b0c095a1a3af3191d4811bfa771881fdb4ed94152fcf7c68ff858308c42"}