{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:POZGXQ3AYOT3GKKT5WNBE3DIQL","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":"da5624c4fa6bb3880167f5c81dd0f60e31b809da52a232dd6d33c862a1bf671d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-27T17:17:16Z","title_canon_sha256":"69c3ef9cf94676f84f2201cac78eff05025553b2cfb9a82f26345f06c314f197"},"schema_version":"1.0","source":{"id":"1608.07727","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07727","created_at":"2026-05-18T00:13:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07727v2","created_at":"2026-05-18T00:13:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07727","created_at":"2026-05-18T00:13:19Z"},{"alias_kind":"pith_short_12","alias_value":"POZGXQ3AYOT3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"POZGXQ3AYOT3GKKT","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"POZGXQ3A","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:1b0d6f53e75360dfd9c55b430b8b3d437cb30fc1ec10d438c2e89bb5d58ae042","target":"graph","created_at":"2026-05-18T00:13:19Z","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":"The speed of a hereditary property $P$ is the number $P_n$ of $n$-vertex labelled graphs in $P$. It is known that the rates of growth of $P_n$ constitute discrete layers and the speed jumps, in particular, from constant to polynomial, from polynomial to exponential and from exponential to factorial. One more jump occurs when the entropy $\\lim_{n\\to\\infty}\\frac{\\log_2 P_n}{\\binom{n}{2}}$ changes from 0 to a nonzero value. In the present paper, for each of these jumps we identify a graph parameter responsible for it, i.e. we show that a jump of the speed coincides with a jump of the respective p","authors_text":"Vadim Lozin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-27T17:17:16Z","title":"Graph parameters, Ramsey theory and the speed of hereditary properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07727","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:afb848518337511921c021c2ea5e5aa3b4ce1d2e104b7e7c9df5e67cf48104c9","target":"record","created_at":"2026-05-18T00:13:19Z","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":"da5624c4fa6bb3880167f5c81dd0f60e31b809da52a232dd6d33c862a1bf671d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-27T17:17:16Z","title_canon_sha256":"69c3ef9cf94676f84f2201cac78eff05025553b2cfb9a82f26345f06c314f197"},"schema_version":"1.0","source":{"id":"1608.07727","kind":"arxiv","version":2}},"canonical_sha256":"7bb26bc360c3a7b32953ed9a126c6882fd00c96aec0a322044263802d324f652","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bb26bc360c3a7b32953ed9a126c6882fd00c96aec0a322044263802d324f652","first_computed_at":"2026-05-18T00:13:19.765063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:19.765063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LRH2oLLII8LVGVDiSv0eJ++TLUCDzV5DT1+xgqg2R8EswOD3dB+kRErV13IWLo+NpfliDrShUQBPH4h8CtCVBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:19.765760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07727","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afb848518337511921c021c2ea5e5aa3b4ce1d2e104b7e7c9df5e67cf48104c9","sha256:1b0d6f53e75360dfd9c55b430b8b3d437cb30fc1ec10d438c2e89bb5d58ae042"],"state_sha256":"c413ca01803feef0f3bd18d67b7131c6690a52118eec08fe1f0486396fe49568"}