{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:P3T7VFYVTAMAZBNDB5OPZOFQHD","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":"49a153f26e57c49f0c2d1e61829ed2e458e546b8c1c607a565b462457d08fa5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-21T17:45:29Z","title_canon_sha256":"4f5c723597eff05cba7a1a82575334d3abda60ec142d1af7a2ac4b49a77bfdd5"},"schema_version":"1.0","source":{"id":"1208.4319","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4319","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4319v3","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4319","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"pith_short_12","alias_value":"P3T7VFYVTAMA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P3T7VFYVTAMAZBND","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P3T7VFYV","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:857ab947f8e3f4a2d7dba6ecd5fc958a20ce3775d57afcba6198e726e706901e","target":"graph","created_at":"2026-05-18T01:00:10Z","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 \\emph{Tur\\'an function} $\\ex(n,F)$ of a graph $F$ is the maximum number of edges in an $F$-free graph with $n$ vertices. The classical results of Tur\\'an and Rademacher from 1941 led to the study of supersaturated graphs where the key question is to determine $h_F(n,q)$, the minimum number of copies of $F$ that a graph with $n$ vertices and $\\ex(n,F)+q$ edges can have.\n  We determine $h_F(n,q)$ asymptotically when $F$ is \\emph{color-critical} (that is, $F$ contains an edge whose deletion reduces its chromatic number) and $q=o(n^2)$.\n  Determining the exact value of $h_F(n,q)$ seems rather ","authors_text":"Oleg Pikhurko, Zelealem B. Yilma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-21T17:45:29Z","title":"Supersaturation Problem for Color-Critical Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4319","kind":"arxiv","version":3},"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":"sha256:1be5d0fa7686f6f22280e51f93d58b5a2155637cfb0c00cef64c8546631a3f0e","target":"record","created_at":"2026-05-18T01:00:10Z","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":"49a153f26e57c49f0c2d1e61829ed2e458e546b8c1c607a565b462457d08fa5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-21T17:45:29Z","title_canon_sha256":"4f5c723597eff05cba7a1a82575334d3abda60ec142d1af7a2ac4b49a77bfdd5"},"schema_version":"1.0","source":{"id":"1208.4319","kind":"arxiv","version":3}},"canonical_sha256":"7ee7fa971598180c85a30f5cfcb8b038c417ac06f626cba95ad21885fb0377b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ee7fa971598180c85a30f5cfcb8b038c417ac06f626cba95ad21885fb0377b0","first_computed_at":"2026-05-18T01:00:10.672257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:10.672257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fVlvUvr7wArmHlStdWUQ9/AXf5oS0V629ArCEQtFQmB1sLjGqHjosQ38Gv01x/u3QCPedoQW12uqWPx0bn+mAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:10.673021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4319","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be5d0fa7686f6f22280e51f93d58b5a2155637cfb0c00cef64c8546631a3f0e","sha256:857ab947f8e3f4a2d7dba6ecd5fc958a20ce3775d57afcba6198e726e706901e"],"state_sha256":"79669761217812e07b3d318865587c4747a4409e3cf81635f0c694f39290f527"}