{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:46MHGSZXNWZFM6IK636NLDDYV5","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":"a02362c1356940dcf3b3d1c040b5638cd065324b45a9207968aff9ea205040e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T15:43:17Z","title_canon_sha256":"9ead1424b6a196ae7df4406ae62162bca9cf18816a1276e29efc56c1b3359efe"},"schema_version":"1.0","source":{"id":"1303.2926","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2926","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2926v3","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2926","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"46MHGSZXNWZF","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"46MHGSZXNWZFM6IK","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"46MHGSZX","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:ac5f978a4cb4052da14b533327b570005fd5c15b449acda3dc7c516443cd43e9","target":"graph","created_at":"2026-05-18T02:56:58Z","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":"In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and cardinality of the collection of the initial intervals. The first theorem states that a partial order has no infinite antichains if and only if its initial intervals are finite unions of ideals. The second one asserts that a countable partial order is scattered and does not contain infinite antichains if and only if it has countably many initial intervals. We show that the left to right directions of these theorems are equivalent to ACA_0 and ATR_0, respectivel","authors_text":"Alberto Marcone, Emanuele Frittaion","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T15:43:17Z","title":"Reverse Mathematics and initial intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2926","kind":"arxiv","version":3},"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:bcadbf146c8716ec720ef586489b0d8b6a6537597e6858e6df5d4c1894af07ff","target":"record","created_at":"2026-05-18T02:56:58Z","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":"a02362c1356940dcf3b3d1c040b5638cd065324b45a9207968aff9ea205040e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T15:43:17Z","title_canon_sha256":"9ead1424b6a196ae7df4406ae62162bca9cf18816a1276e29efc56c1b3359efe"},"schema_version":"1.0","source":{"id":"1303.2926","kind":"arxiv","version":3}},"canonical_sha256":"e798734b376db256790af6fcd58c78af7b2884db72afa22b17ae836a1550c9bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e798734b376db256790af6fcd58c78af7b2884db72afa22b17ae836a1550c9bc","first_computed_at":"2026-05-18T02:56:58.496641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:58.496641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tRrXouU8t5lOWcYs0ESdPmRXzzPvB8eQTlNDOHVNZnJHqXwWdJ7eAs+3zCciPiBbS+FpxzeuwFXnee986BdFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:58.497065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2926","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcadbf146c8716ec720ef586489b0d8b6a6537597e6858e6df5d4c1894af07ff","sha256:ac5f978a4cb4052da14b533327b570005fd5c15b449acda3dc7c516443cd43e9"],"state_sha256":"6f474c04c570d1e1e87cd8d9f06994b8bca3adfe6f381f3caca89135ad9a8d08"}