{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BJRITXWIR2BIHQYNMD6CMBYH5Q","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":"ce0b415cf4d5ea7ea58a735f2bf4943a39b3f0e03ed9bcf7e9b523a091812dec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-22T18:06:19Z","title_canon_sha256":"0972112d5a4e8dc07ef01a15fefe729a7540906603268f2a4ee99217c7e7b4fa"},"schema_version":"1.0","source":{"id":"1507.06275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06275","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06275v1","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06275","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"pith_short_12","alias_value":"BJRITXWIR2BI","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BJRITXWIR2BIHQYN","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BJRITXWI","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:67fb141e452bc05db419edbb96000d22b02c51222acc9731a9e08dfc3f564d0f","target":"graph","created_at":"2026-05-17T23:45:15Z","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 thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\\ldots X_{n},Y_{1},\\ldots Y_{n}$ be $2n$ independent random variables, with uniform distribution on $[0,1]$. We then say that the $i$th of the $n$ vertices is the interval $[X_{i},Y_{i}]$ if $X_{i}<Y_{i}$ and the interval $[Y_{i},X_{i}]$ if $Y_{i}<X_{i}$. We then say that two vertices are adjacent if and only if the corresponding intervals intersect.\n  We recall from our MA902 essay that fact that in such a graph, each edge arises with probability $2","authors_text":"Vasileios Iliopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-22T18:06:19Z","title":"Random Interval Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06275","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":"sha256:6e4e33be23d6d71a879048e43c63035ba2a916703f4e012b6455c1d7c6128d17","target":"record","created_at":"2026-05-17T23:45:15Z","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":"ce0b415cf4d5ea7ea58a735f2bf4943a39b3f0e03ed9bcf7e9b523a091812dec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-22T18:06:19Z","title_canon_sha256":"0972112d5a4e8dc07ef01a15fefe729a7540906603268f2a4ee99217c7e7b4fa"},"schema_version":"1.0","source":{"id":"1507.06275","kind":"arxiv","version":1}},"canonical_sha256":"0a6289dec88e8283c30d60fc260707ec18f75a64f3e339358341fed922458106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a6289dec88e8283c30d60fc260707ec18f75a64f3e339358341fed922458106","first_computed_at":"2026-05-17T23:45:15.875631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:15.875631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HtZe+5X/pZCGiZXQrjQpWnOaO59d9SXrji+HbMlrdI99whnN9y8lj8YEiLCPZONRmfv54yhGfdQX9AAV2TpAAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:15.876518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e4e33be23d6d71a879048e43c63035ba2a916703f4e012b6455c1d7c6128d17","sha256:67fb141e452bc05db419edbb96000d22b02c51222acc9731a9e08dfc3f564d0f"],"state_sha256":"9299ee98732cd170ded58a42937c97f1e98bdfe3d5b9a2308930a5efdfb0c545"}