{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SDZKGXMN664PR2WLE5L7IHR66H","short_pith_number":"pith:SDZKGXMN","canonical_record":{"source":{"id":"1904.00656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-01T09:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"82a0b78a48bed2a3784745f8e065c685b9bfc715218df5ca6105563127c7e073","abstract_canon_sha256":"18a5df26ec54482b06bd9fd1736a818e336bf746d5d18526180eab7951918d8d"},"schema_version":"1.0"},"canonical_sha256":"90f2a35d8df7b8f8eacb2757f41e3ef1f2b321bf8b201c8af2a0866d6251289d","source":{"kind":"arxiv","id":"1904.00656","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00656","created_at":"2026-05-17T23:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00656v1","created_at":"2026-05-17T23:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00656","created_at":"2026-05-17T23:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"SDZKGXMN664P","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SDZKGXMN664PR2WL","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SDZKGXMN","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SDZKGXMN664PR2WLE5L7IHR66H","target":"record","payload":{"canonical_record":{"source":{"id":"1904.00656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-01T09:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"82a0b78a48bed2a3784745f8e065c685b9bfc715218df5ca6105563127c7e073","abstract_canon_sha256":"18a5df26ec54482b06bd9fd1736a818e336bf746d5d18526180eab7951918d8d"},"schema_version":"1.0"},"canonical_sha256":"90f2a35d8df7b8f8eacb2757f41e3ef1f2b321bf8b201c8af2a0866d6251289d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:47.770115Z","signature_b64":"XKWM9rA+hsKn7VXcNSiKAwm7Eu4QAGnUlqSTDY6G4a5Fbjc9aqWEjTtvLN4nvfNoVRzy0dciKo9SqG6bLdcFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90f2a35d8df7b8f8eacb2757f41e3ef1f2b321bf8b201c8af2a0866d6251289d","last_reissued_at":"2026-05-17T23:49:47.769229Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:47.769229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.00656","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":"2026-05-17T23:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"daV877zRAeKH3Jioqu8HygdRU6/0ouXm4o8kmOldzosHb/kW7l//7cKvyPZdc9QHJWPIL0N+MluqPToRQ2l6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:08:16.313131Z"},"content_sha256":"4a67efffc86f6cfa9ff36c33d0799d6e1c92fbc86742373566e90bf0215b81d1","schema_version":"1.0","event_id":"sha256:4a67efffc86f6cfa9ff36c33d0799d6e1c92fbc86742373566e90bf0215b81d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SDZKGXMN664PR2WLE5L7IHR66H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Antichains of Copies of Ultrahomogeneous Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bori\\v{s}a Kuzeljevi\\'c, Milo\\v{s} S. Kurili\\'c","submitted_at":"2019-04-01T09:33:29Z","abstract_excerpt":"We investigate possible cardinalities of maximal antichains in the poset of copies $\\langle \\mathbb P(\\mathbb X),\\subset \\rangle$ of a countable ultrahomogeneous relational structure $\\mathbb X$. It turns out that if the age of $\\mathbb X$ has the strong amalgamation property, then, defining a copy of $\\mathbb X$ to be large iff it has infinite intersection with each orbit of $\\mathbb X$, the structure $\\mathbb X$ can be partitioned into countably many large copies, there are almost disjoint families of large copies of size continuum and, hence, there are (maximal) antichains of size continuum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00656","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":"2026-05-17T23:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N8ZvyGqGeYXBkUj6/mwSYEg5HsXt7ClGO3Dkt3fT7xXwvpNpFyoUYjrPJtj0TejlsJwDIe3PaRRq1CWdptxnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:08:16.313491Z"},"content_sha256":"9d5bc4002ceb8d953f4afe70add27bb2dd9357f4fd2ac942a2ce13fe31fb59fc","schema_version":"1.0","event_id":"sha256:9d5bc4002ceb8d953f4afe70add27bb2dd9357f4fd2ac942a2ce13fe31fb59fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SDZKGXMN664PR2WLE5L7IHR66H/bundle.json","state_url":"https://pith.science/pith/SDZKGXMN664PR2WLE5L7IHR66H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SDZKGXMN664PR2WLE5L7IHR66H/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":"2026-06-21T22:08:16Z","links":{"resolver":"https://pith.science/pith/SDZKGXMN664PR2WLE5L7IHR66H","bundle":"https://pith.science/pith/SDZKGXMN664PR2WLE5L7IHR66H/bundle.json","state":"https://pith.science/pith/SDZKGXMN664PR2WLE5L7IHR66H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SDZKGXMN664PR2WLE5L7IHR66H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SDZKGXMN664PR2WLE5L7IHR66H","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":"18a5df26ec54482b06bd9fd1736a818e336bf746d5d18526180eab7951918d8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-01T09:33:29Z","title_canon_sha256":"82a0b78a48bed2a3784745f8e065c685b9bfc715218df5ca6105563127c7e073"},"schema_version":"1.0","source":{"id":"1904.00656","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00656","created_at":"2026-05-17T23:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00656v1","created_at":"2026-05-17T23:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00656","created_at":"2026-05-17T23:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"SDZKGXMN664P","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SDZKGXMN664PR2WL","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SDZKGXMN","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:9d5bc4002ceb8d953f4afe70add27bb2dd9357f4fd2ac942a2ce13fe31fb59fc","target":"graph","created_at":"2026-05-17T23:49:47Z","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 possible cardinalities of maximal antichains in the poset of copies $\\langle \\mathbb P(\\mathbb X),\\subset \\rangle$ of a countable ultrahomogeneous relational structure $\\mathbb X$. It turns out that if the age of $\\mathbb X$ has the strong amalgamation property, then, defining a copy of $\\mathbb X$ to be large iff it has infinite intersection with each orbit of $\\mathbb X$, the structure $\\mathbb X$ can be partitioned into countably many large copies, there are almost disjoint families of large copies of size continuum and, hence, there are (maximal) antichains of size continuum","authors_text":"Bori\\v{s}a Kuzeljevi\\'c, Milo\\v{s} S. Kurili\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-01T09:33:29Z","title":"Antichains of Copies of Ultrahomogeneous Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00656","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":"sha256:4a67efffc86f6cfa9ff36c33d0799d6e1c92fbc86742373566e90bf0215b81d1","target":"record","created_at":"2026-05-17T23:49:47Z","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":"18a5df26ec54482b06bd9fd1736a818e336bf746d5d18526180eab7951918d8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-01T09:33:29Z","title_canon_sha256":"82a0b78a48bed2a3784745f8e065c685b9bfc715218df5ca6105563127c7e073"},"schema_version":"1.0","source":{"id":"1904.00656","kind":"arxiv","version":1}},"canonical_sha256":"90f2a35d8df7b8f8eacb2757f41e3ef1f2b321bf8b201c8af2a0866d6251289d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f2a35d8df7b8f8eacb2757f41e3ef1f2b321bf8b201c8af2a0866d6251289d","first_computed_at":"2026-05-17T23:49:47.769229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:47.769229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XKWM9rA+hsKn7VXcNSiKAwm7Eu4QAGnUlqSTDY6G4a5Fbjc9aqWEjTtvLN4nvfNoVRzy0dciKo9SqG6bLdcFBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:47.770115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00656","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a67efffc86f6cfa9ff36c33d0799d6e1c92fbc86742373566e90bf0215b81d1","sha256:9d5bc4002ceb8d953f4afe70add27bb2dd9357f4fd2ac942a2ce13fe31fb59fc"],"state_sha256":"78781d45f5acf752c689e115ee1be31f20ed4f96825c0c0869ab88171ade17e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnJSLElU6N1U4ZYjktcQ+izeXdFZqhQZ7G25AWmnuvIqWrh064kHi7IDiQozYMuDULU7PtqDvyZiTxY9kdyHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:08:16.315372Z","bundle_sha256":"879f418805ec6dc5e137473e021e2e63cb039173e7d1dcb0b0f8547e932a8a23"}}