{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:T5YOX2TOAJV5K2HNR6BJZWQNPF","short_pith_number":"pith:T5YOX2TO","canonical_record":{"source":{"id":"1604.00890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-04T14:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"45df04378117b91d50cc0e24abb61cebec23bb0206080c6fe7dd971ff150f457","abstract_canon_sha256":"3751f081f1ee128ffb343bf3bd4b9e83a68cd1c89db12e6c6524fcf9e941ab8b"},"schema_version":"1.0"},"canonical_sha256":"9f70ebea6e026bd568ed8f829cda0d797d4556693826507f4c00d6ac2b8ad7a8","source":{"kind":"arxiv","id":"1604.00890","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00890","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00890v2","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00890","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"T5YOX2TOAJV5","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T5YOX2TOAJV5K2HN","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T5YOX2TO","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:T5YOX2TOAJV5K2HNR6BJZWQNPF","target":"record","payload":{"canonical_record":{"source":{"id":"1604.00890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-04T14:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"45df04378117b91d50cc0e24abb61cebec23bb0206080c6fe7dd971ff150f457","abstract_canon_sha256":"3751f081f1ee128ffb343bf3bd4b9e83a68cd1c89db12e6c6524fcf9e941ab8b"},"schema_version":"1.0"},"canonical_sha256":"9f70ebea6e026bd568ed8f829cda0d797d4556693826507f4c00d6ac2b8ad7a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.722391Z","signature_b64":"DLYDxIdeXO6GjHtCA7/VSvxjl0VOZAmfDHzYjAYLqFpp5Sez96rHoJr9Od8DAi13ZOLwYzi50FR9ef5HlRn1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f70ebea6e026bd568ed8f829cda0d797d4556693826507f4c00d6ac2b8ad7a8","last_reissued_at":"2026-05-18T00:35:55.721936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.721936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.00890","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d23QBl+0oFNf1wn+b8gQG98d1svBB3vofVkiy6xtSDFliIbIqn4+NFRQqYe4qAfEIt4KwS8rhDFkQ6eO+lkEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:17:35.401634Z"},"content_sha256":"696944dcd9dcc664c5290b19e6acb4cb08822e7c0e36410b1ae1f406a3126887","schema_version":"1.0","event_id":"sha256:696944dcd9dcc664c5290b19e6acb4cb08822e7c0e36410b1ae1f406a3126887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:T5YOX2TOAJV5K2HNR6BJZWQNPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Perfect Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colin McDiarmid, Nikola Yolov","submitted_at":"2016-04-04T14:57:55Z","abstract_excerpt":"We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\\{1,\\ldots,n\\}$. Our approach is based on the result of Pr\\\"omel and Steger that almost all perfect graphs are generalised split graphs, together with a method to generate such graphs almost uniformly.\n  We show that the distribution of the maximum of the stability number $\\alpha(P_n)$ and clique number $\\omega(P_n)$ is close to a concentrated distribution $L(n)$ which plays an important role in our generation method. We also prove that the probability that $P_n$ con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00890","kind":"arxiv","version":2},"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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EMat59hWd8FYluFXqz3flP1w23frHK7cCOlIki6cl+fING5uqoZcpiohVgfqJGqMrqDH+9frg1s8gWT701/wDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:17:35.401969Z"},"content_sha256":"0249d638f961d9c60c683e5bdd5820efee2889d087d5c0df220ac7275917a8fc","schema_version":"1.0","event_id":"sha256:0249d638f961d9c60c683e5bdd5820efee2889d087d5c0df220ac7275917a8fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T5YOX2TOAJV5K2HNR6BJZWQNPF/bundle.json","state_url":"https://pith.science/pith/T5YOX2TOAJV5K2HNR6BJZWQNPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T5YOX2TOAJV5K2HNR6BJZWQNPF/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":"2026-06-27T20:17:35Z","links":{"resolver":"https://pith.science/pith/T5YOX2TOAJV5K2HNR6BJZWQNPF","bundle":"https://pith.science/pith/T5YOX2TOAJV5K2HNR6BJZWQNPF/bundle.json","state":"https://pith.science/pith/T5YOX2TOAJV5K2HNR6BJZWQNPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T5YOX2TOAJV5K2HNR6BJZWQNPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T5YOX2TOAJV5K2HNR6BJZWQNPF","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":"3751f081f1ee128ffb343bf3bd4b9e83a68cd1c89db12e6c6524fcf9e941ab8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-04T14:57:55Z","title_canon_sha256":"45df04378117b91d50cc0e24abb61cebec23bb0206080c6fe7dd971ff150f457"},"schema_version":"1.0","source":{"id":"1604.00890","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00890","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00890v2","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00890","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"T5YOX2TOAJV5","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T5YOX2TOAJV5K2HN","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T5YOX2TO","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:0249d638f961d9c60c683e5bdd5820efee2889d087d5c0df220ac7275917a8fc","target":"graph","created_at":"2026-05-18T00:35:55Z","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 asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\\{1,\\ldots,n\\}$. Our approach is based on the result of Pr\\\"omel and Steger that almost all perfect graphs are generalised split graphs, together with a method to generate such graphs almost uniformly.\n  We show that the distribution of the maximum of the stability number $\\alpha(P_n)$ and clique number $\\omega(P_n)$ is close to a concentrated distribution $L(n)$ which plays an important role in our generation method. We also prove that the probability that $P_n$ con","authors_text":"Colin McDiarmid, Nikola Yolov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-04T14:57:55Z","title":"Random Perfect Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00890","kind":"arxiv","version":2},"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":"sha256:696944dcd9dcc664c5290b19e6acb4cb08822e7c0e36410b1ae1f406a3126887","target":"record","created_at":"2026-05-18T00:35:55Z","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":"3751f081f1ee128ffb343bf3bd4b9e83a68cd1c89db12e6c6524fcf9e941ab8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-04T14:57:55Z","title_canon_sha256":"45df04378117b91d50cc0e24abb61cebec23bb0206080c6fe7dd971ff150f457"},"schema_version":"1.0","source":{"id":"1604.00890","kind":"arxiv","version":2}},"canonical_sha256":"9f70ebea6e026bd568ed8f829cda0d797d4556693826507f4c00d6ac2b8ad7a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f70ebea6e026bd568ed8f829cda0d797d4556693826507f4c00d6ac2b8ad7a8","first_computed_at":"2026-05-18T00:35:55.721936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.721936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DLYDxIdeXO6GjHtCA7/VSvxjl0VOZAmfDHzYjAYLqFpp5Sez96rHoJr9Od8DAi13ZOLwYzi50FR9ef5HlRn1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.722391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00890","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:696944dcd9dcc664c5290b19e6acb4cb08822e7c0e36410b1ae1f406a3126887","sha256:0249d638f961d9c60c683e5bdd5820efee2889d087d5c0df220ac7275917a8fc"],"state_sha256":"922d24c7b7336cd95295efe8bf1be2bac78d9fa140b9e603bd3037d56eb9be0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wKZwXF73UOGATTizL/6idQ7nssE57Jxj5wLV7FYvM8dwAI+L8iNwbPfB5TSZjbgiz1qs5lldMSnP4hlSEo4XAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:17:35.403771Z","bundle_sha256":"f6f90d1884cd7d0e930dcf17862abfb0248099dc6100f9a8a763d71ef19fd96a"}}