{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OSXZCPDZRD4YJ37E7WIS5FDZLD","short_pith_number":"pith:OSXZCPDZ","canonical_record":{"source":{"id":"1408.4257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-19T09:06:03Z","cross_cats_sorted":[],"title_canon_sha256":"fc05653c464e5135834359f86163b139f0f75b69e1c05bdaa01de512dc3ffa61","abstract_canon_sha256":"844534f1c3cf00be4785623c4dff33dab708f9463b0e1ca10be6b21fb4e07858"},"schema_version":"1.0"},"canonical_sha256":"74af913c7988f984efe4fd912e947958d904bbfcc63468486fb1ad64c1681dc5","source":{"kind":"arxiv","id":"1408.4257","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4257","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4257v2","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4257","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"OSXZCPDZRD4Y","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OSXZCPDZRD4YJ37E","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OSXZCPDZ","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OSXZCPDZRD4YJ37E7WIS5FDZLD","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-19T09:06:03Z","cross_cats_sorted":[],"title_canon_sha256":"fc05653c464e5135834359f86163b139f0f75b69e1c05bdaa01de512dc3ffa61","abstract_canon_sha256":"844534f1c3cf00be4785623c4dff33dab708f9463b0e1ca10be6b21fb4e07858"},"schema_version":"1.0"},"canonical_sha256":"74af913c7988f984efe4fd912e947958d904bbfcc63468486fb1ad64c1681dc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:53.421629Z","signature_b64":"i6L9MSqw1wvBdkEqdytAVln+50b+IxfHkO8h8BFYuKMfG7dZ2k409a9ufAKg/me9buQzwjt9+clzI6lG/+gGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74af913c7988f984efe4fd912e947958d904bbfcc63468486fb1ad64c1681dc5","last_reissued_at":"2026-05-18T01:14:53.421031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:53.421031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4257","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":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qRp8Tv6EOH4Hr+fWMbybUzAU+QbHpjyNO3TEj0hHgLO8E9gl6do9VL3qXKBJZ3tms+xQsR1s6/7HmTXOYUhqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:55:38.087239Z"},"content_sha256":"0f6544cb66b904e9e0f6ec0795253ce862a5a48d0f8a667206943240e9e73f74","schema_version":"1.0","event_id":"sha256:0f6544cb66b904e9e0f6ec0795253ce862a5a48d0f8a667206943240e9e73f74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OSXZCPDZRD4YJ37E7WIS5FDZLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random graphs from a block-stable class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Colin McDiarmid","submitted_at":"2014-08-19T09:06:03Z","abstract_excerpt":"A class of graphs is called block-stable when a graph is in the class if and only if each of its blocks is. We show that, as for trees, for most $n$-vertex graphs in such a class, each vertex is in at most $(1+o(1)) \\log n / \\log\\log n$ blocks, and each path passes through at most $5 (n \\log n)^{1/2}$ blocks. These results extend to `weakly block-stable' classes of graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4257","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":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vI7k2VIY/ICC5xzoMfR63Rdu5atcvy37dyE+BRGPEgwVsgEkUB/rNa6XyTnjq50wlAriv7sBIg1OWl/7jc5mAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:55:38.087595Z"},"content_sha256":"e2e3e85c5eb11041eae3639049aa4a05ad9725f73dd4edfd6b6210f58dc85ae0","schema_version":"1.0","event_id":"sha256:e2e3e85c5eb11041eae3639049aa4a05ad9725f73dd4edfd6b6210f58dc85ae0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSXZCPDZRD4YJ37E7WIS5FDZLD/bundle.json","state_url":"https://pith.science/pith/OSXZCPDZRD4YJ37E7WIS5FDZLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSXZCPDZRD4YJ37E7WIS5FDZLD/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":"2026-06-27T15:55:38Z","links":{"resolver":"https://pith.science/pith/OSXZCPDZRD4YJ37E7WIS5FDZLD","bundle":"https://pith.science/pith/OSXZCPDZRD4YJ37E7WIS5FDZLD/bundle.json","state":"https://pith.science/pith/OSXZCPDZRD4YJ37E7WIS5FDZLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSXZCPDZRD4YJ37E7WIS5FDZLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OSXZCPDZRD4YJ37E7WIS5FDZLD","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":"844534f1c3cf00be4785623c4dff33dab708f9463b0e1ca10be6b21fb4e07858","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-19T09:06:03Z","title_canon_sha256":"fc05653c464e5135834359f86163b139f0f75b69e1c05bdaa01de512dc3ffa61"},"schema_version":"1.0","source":{"id":"1408.4257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4257","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4257v2","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4257","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"OSXZCPDZRD4Y","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OSXZCPDZRD4YJ37E","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OSXZCPDZ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e2e3e85c5eb11041eae3639049aa4a05ad9725f73dd4edfd6b6210f58dc85ae0","target":"graph","created_at":"2026-05-18T01:14:53Z","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":"A class of graphs is called block-stable when a graph is in the class if and only if each of its blocks is. We show that, as for trees, for most $n$-vertex graphs in such a class, each vertex is in at most $(1+o(1)) \\log n / \\log\\log n$ blocks, and each path passes through at most $5 (n \\log n)^{1/2}$ blocks. These results extend to `weakly block-stable' classes of graphs.","authors_text":"Alex Scott, Colin McDiarmid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-19T09:06:03Z","title":"Random graphs from a block-stable class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4257","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":"sha256:0f6544cb66b904e9e0f6ec0795253ce862a5a48d0f8a667206943240e9e73f74","target":"record","created_at":"2026-05-18T01:14:53Z","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":"844534f1c3cf00be4785623c4dff33dab708f9463b0e1ca10be6b21fb4e07858","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-19T09:06:03Z","title_canon_sha256":"fc05653c464e5135834359f86163b139f0f75b69e1c05bdaa01de512dc3ffa61"},"schema_version":"1.0","source":{"id":"1408.4257","kind":"arxiv","version":2}},"canonical_sha256":"74af913c7988f984efe4fd912e947958d904bbfcc63468486fb1ad64c1681dc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74af913c7988f984efe4fd912e947958d904bbfcc63468486fb1ad64c1681dc5","first_computed_at":"2026-05-18T01:14:53.421031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:53.421031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6L9MSqw1wvBdkEqdytAVln+50b+IxfHkO8h8BFYuKMfG7dZ2k409a9ufAKg/me9buQzwjt9+clzI6lG/+gGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:53.421629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f6544cb66b904e9e0f6ec0795253ce862a5a48d0f8a667206943240e9e73f74","sha256:e2e3e85c5eb11041eae3639049aa4a05ad9725f73dd4edfd6b6210f58dc85ae0"],"state_sha256":"bcbea1da19861fba0b280e9738d446fdcc131c7d138fb12b5a1c69f49a425917"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rquf/ZQuQUdBLuc/TlmCvCnHvKxcXGIffjPs3cySJL0POQx/bccbRnhW9GuvoMkq2QN+4PetwIW/rK62Y0TOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:55:38.089786Z","bundle_sha256":"fb1085962da5d2d168f192eb67aeb8fe559103d87a11785f4c9f09f318834ab8"}}