{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ORQJ2T3XU32MBZYXC2AK3ONLW6","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":"32b79f01a14911496a44285fe0dcab5201a06551b13aadacb6e43383472d8052","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-01-20T13:51:25Z","title_canon_sha256":"6d96fb91adcfc0d478af9daadbc13a16cbcc1bd571e201193de2402eed7020b3"},"schema_version":"1.0","source":{"id":"1701.05791","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05791","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05791v3","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05791","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"ORQJ2T3XU32M","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"ORQJ2T3XU32MBZYX","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"ORQJ2T3X","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:bd082e92cda4348a2afcccd8ade39cccce247619100745e48e19c791d2a17e59","target":"graph","created_at":"2026-05-18T00:15:30Z","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 1956, 48 years after Hausdorff provided a comprehensive account on ordered sets and defined the notion of a scattered order, Erd\\H{o}s and Rado founded the partition calculus in a seminal paper. The present paper gives an account of investigations into generalisations of scattered linear orders and their partition relations for both singletons and pairs. It provides analogues of the Milner-Rado paradox for these orders instead of ordinals. For infinite, regular $\\kappa$, we investigate the extent to which the classes of $\\kappa$-scattered, weakly $\\kappa$-scattered, and $\\kappa$-saturated l","authors_text":"Chris Lambie-Hanson, Thilo Weinert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-01-20T13:51:25Z","title":"Partitioning subsets of generalised scattered orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05791","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:c20a60a932259b2ca36f392f811cb472d8fff46eef807a765ad82e2819e32514","target":"record","created_at":"2026-05-18T00:15:30Z","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":"32b79f01a14911496a44285fe0dcab5201a06551b13aadacb6e43383472d8052","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-01-20T13:51:25Z","title_canon_sha256":"6d96fb91adcfc0d478af9daadbc13a16cbcc1bd571e201193de2402eed7020b3"},"schema_version":"1.0","source":{"id":"1701.05791","kind":"arxiv","version":3}},"canonical_sha256":"74609d4f77a6f4c0e7171680adb9abb79e3f0a463062f792c91eceaf77683c17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74609d4f77a6f4c0e7171680adb9abb79e3f0a463062f792c91eceaf77683c17","first_computed_at":"2026-05-18T00:15:30.906811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:30.906811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kJJLA2vLbJbUB1AYOlt34zx3r55Rgv10QBx+sgo2zICPqabYtDYGcOwilBvHPd+p+tjw2YkUH1lR80vKmRbSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:30.907366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05791","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c20a60a932259b2ca36f392f811cb472d8fff46eef807a765ad82e2819e32514","sha256:bd082e92cda4348a2afcccd8ade39cccce247619100745e48e19c791d2a17e59"],"state_sha256":"8937c2469b44b2852eecf3e3f580ddb9abdac5b4c73f75e4ab427a3c3a8068b5"}