{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HNKZZFGS6UIDZ4NVNHOWACZVVV","short_pith_number":"pith:HNKZZFGS","canonical_record":{"source":{"id":"1303.2828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T10:31:54Z","cross_cats_sorted":[],"title_canon_sha256":"6888163817db91f008ce5e8b72f1a1609e0dec3b7270c151a616440210993f7c","abstract_canon_sha256":"4fccd38bfe83251de1caa60158d5b3b1b44d587ddbf322d87138bcf89d9854ee"},"schema_version":"1.0"},"canonical_sha256":"3b559c94d2f5103cf1b569dd600b35ad7eaa47688e25b92b47f313f654e17ae1","source":{"kind":"arxiv","id":"1303.2828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2828","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2828v1","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2828","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"HNKZZFGS6UID","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HNKZZFGS6UIDZ4NV","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HNKZZFGS","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HNKZZFGS6UIDZ4NVNHOWACZVVV","target":"record","payload":{"canonical_record":{"source":{"id":"1303.2828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T10:31:54Z","cross_cats_sorted":[],"title_canon_sha256":"6888163817db91f008ce5e8b72f1a1609e0dec3b7270c151a616440210993f7c","abstract_canon_sha256":"4fccd38bfe83251de1caa60158d5b3b1b44d587ddbf322d87138bcf89d9854ee"},"schema_version":"1.0"},"canonical_sha256":"3b559c94d2f5103cf1b569dd600b35ad7eaa47688e25b92b47f313f654e17ae1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:32.115999Z","signature_b64":"V+gD6kbMj3GiDWo3iutsO3erG6Ajr60/xcd4z/EJfq6P4Ctc3BKVt7TMTn6vYS055AN4q3Ut3M9qMgbTvEblBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b559c94d2f5103cf1b569dd600b35ad7eaa47688e25b92b47f313f654e17ae1","last_reissued_at":"2026-05-18T00:34:32.115529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:32.115529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.2828","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7dxWvFoSslM23ORo/b4hW0lXwFq8OKjVHA4kOZIQ5LePsq37Z6SOKM5Xb3O50AXli4eGxpQq3ZOE98d7zTWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:45:13.787864Z"},"content_sha256":"632f6935bdce746ccca1d586dc3f51711b6dd54ec8e4e5e3323ac476fa9519f1","schema_version":"1.0","event_id":"sha256:632f6935bdce746ccca1d586dc3f51711b6dd54ec8e4e5e3323ac476fa9519f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HNKZZFGS6UIDZ4NVNHOWACZVVV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Borisa Kuzeljevic, Milos S. Kurilic","submitted_at":"2013-03-12T10:31:54Z","abstract_excerpt":"We investigate the poset (P(X),\\subset), where P(X) is the set of isomorphic suborders of a countable ultrahomogeneous partial order X. For X different from (resp. equal to) a countable antichain the order types of maximal chains in (P(X)\\cup \\{\\emptyset \\},\\subset) are characterized as the order types of compact (resp. compact and nowhere dense) sets of reals having the minimum non-isolated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2828","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HxZiatPtKz573ORZ1tS7NOuNzXbNB/dlkpwS0d5gA1cTmNQQzxXkpdGYaA9nbxnX+pd7wBAt1Oe5hGlLy9NECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:45:13.788214Z"},"content_sha256":"182cd91a949eccb12016cb941377e1d53bfc1415ef224fed35afc7e1c3096c66","schema_version":"1.0","event_id":"sha256:182cd91a949eccb12016cb941377e1d53bfc1415ef224fed35afc7e1c3096c66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNKZZFGS6UIDZ4NVNHOWACZVVV/bundle.json","state_url":"https://pith.science/pith/HNKZZFGS6UIDZ4NVNHOWACZVVV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNKZZFGS6UIDZ4NVNHOWACZVVV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T21:45:13Z","links":{"resolver":"https://pith.science/pith/HNKZZFGS6UIDZ4NVNHOWACZVVV","bundle":"https://pith.science/pith/HNKZZFGS6UIDZ4NVNHOWACZVVV/bundle.json","state":"https://pith.science/pith/HNKZZFGS6UIDZ4NVNHOWACZVVV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNKZZFGS6UIDZ4NVNHOWACZVVV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HNKZZFGS6UIDZ4NVNHOWACZVVV","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":"4fccd38bfe83251de1caa60158d5b3b1b44d587ddbf322d87138bcf89d9854ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T10:31:54Z","title_canon_sha256":"6888163817db91f008ce5e8b72f1a1609e0dec3b7270c151a616440210993f7c"},"schema_version":"1.0","source":{"id":"1303.2828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2828","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2828v1","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2828","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"HNKZZFGS6UID","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HNKZZFGS6UIDZ4NV","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HNKZZFGS","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:182cd91a949eccb12016cb941377e1d53bfc1415ef224fed35afc7e1c3096c66","target":"graph","created_at":"2026-05-18T00:34:32Z","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 investigate the poset (P(X),\\subset), where P(X) is the set of isomorphic suborders of a countable ultrahomogeneous partial order X. For X different from (resp. equal to) a countable antichain the order types of maximal chains in (P(X)\\cup \\{\\emptyset \\},\\subset) are characterized as the order types of compact (resp. compact and nowhere dense) sets of reals having the minimum non-isolated.","authors_text":"Borisa Kuzeljevic, Milos S. Kurilic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T10:31:54Z","title":"Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2828","kind":"arxiv","version":1},"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":"sha256:632f6935bdce746ccca1d586dc3f51711b6dd54ec8e4e5e3323ac476fa9519f1","target":"record","created_at":"2026-05-18T00:34:32Z","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":"4fccd38bfe83251de1caa60158d5b3b1b44d587ddbf322d87138bcf89d9854ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-12T10:31:54Z","title_canon_sha256":"6888163817db91f008ce5e8b72f1a1609e0dec3b7270c151a616440210993f7c"},"schema_version":"1.0","source":{"id":"1303.2828","kind":"arxiv","version":1}},"canonical_sha256":"3b559c94d2f5103cf1b569dd600b35ad7eaa47688e25b92b47f313f654e17ae1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b559c94d2f5103cf1b569dd600b35ad7eaa47688e25b92b47f313f654e17ae1","first_computed_at":"2026-05-18T00:34:32.115529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:32.115529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V+gD6kbMj3GiDWo3iutsO3erG6Ajr60/xcd4z/EJfq6P4Ctc3BKVt7TMTn6vYS055AN4q3Ut3M9qMgbTvEblBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:32.115999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:632f6935bdce746ccca1d586dc3f51711b6dd54ec8e4e5e3323ac476fa9519f1","sha256:182cd91a949eccb12016cb941377e1d53bfc1415ef224fed35afc7e1c3096c66"],"state_sha256":"14958ac1d10739f03a2e67dd9921a32a4437c7a2592f6c190f5b6808ef874160"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vz0CNPNsNuiGP09FJQzgVvyT+CNuVF0mi3gAl9zov5nvCHA61vmXog8Y2S4Evdgjt1JhIHwslIKeqqRJ23TPDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:45:13.790502Z","bundle_sha256":"b82a0d1fcff4362136ad5222acb5739984ba830e5acfb1ec92434926c497e677"}}