{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PMANBULPBHSAWCV2SJIB3CTYSH","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":"1af1db43ad05ad9248564e9d5c8c63a334bca19954d82f7079179bbc689335f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-11T14:25:29Z","title_canon_sha256":"e0c79a1fe0b84ef9743ba76494c6a57ddf7253737ea030ef3d2f06ebd4b7b72c"},"schema_version":"1.0","source":{"id":"1204.2460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2460","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2460v1","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2460","created_at":"2026-05-18T03:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"PMANBULPBHSA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PMANBULPBHSAWCV2","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PMANBULP","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:dc8cbd3723ab860b46e83315c41887e3b849c306d4da81665c49acb11145cfc7","target":"graph","created_at":"2026-05-18T03:58:05Z","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 consider a set $\\mbK = \\bigcup_{n \\in \\mbbN}\\mbK_n$ of {\\em finite} structures such that all members of $\\mbK_n$ have the same universe, the cardinality of which approaches $\\infty$ as $n\\to\\infty$. Each structure in $\\mbK$ may have a nontrivial underlying pregeometry and on each $\\mbK_n$ we consider a probability measure, either the uniform measure, or what we call the {\\em dimension conditional measure}. The main questions are: What conditions imply that for every extension axiom $\\varphi$, compatible with the defining properties of $\\mbK$, the probability that $\\varphi$ is true in a memb","authors_text":"Vera Koponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-11T14:25:29Z","title":"Asymptotic probabilities of extension properties and random $l$-colourable structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2460","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":"sha256:17563b27583ee48f18d53f0b3d8c3f4d9902f7909fb4301683e254239c590284","target":"record","created_at":"2026-05-18T03:58:05Z","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":"1af1db43ad05ad9248564e9d5c8c63a334bca19954d82f7079179bbc689335f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-11T14:25:29Z","title_canon_sha256":"e0c79a1fe0b84ef9743ba76494c6a57ddf7253737ea030ef3d2f06ebd4b7b72c"},"schema_version":"1.0","source":{"id":"1204.2460","kind":"arxiv","version":1}},"canonical_sha256":"7b00d0d16f09e40b0aba92501d8a7891c877babb2a2d631a15ea07cb75394e19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b00d0d16f09e40b0aba92501d8a7891c877babb2a2d631a15ea07cb75394e19","first_computed_at":"2026-05-18T03:58:05.290184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:05.290184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DkzOfLFLcWcXyw4u4qodTxoJECA7nG2erZLsYJoMwj43FDzJJ12hGRs4c7NEmj4pZbQ59b8qVOU8fruGDZYgAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:05.290667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17563b27583ee48f18d53f0b3d8c3f4d9902f7909fb4301683e254239c590284","sha256:dc8cbd3723ab860b46e83315c41887e3b849c306d4da81665c49acb11145cfc7"],"state_sha256":"c6ed0fea3117828f345d2256c66be1da99413f931035af6b2cd767e101ecb2cf"}