{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QT2Q4ZI67W2XVPEORNJCFJHD5H","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":"a8defbbab8949d4d4ceeeb63ff6bb83dc1def6770aaa3110970197168104b2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-12T07:10:22Z","title_canon_sha256":"2cafd46cfe671970d6590c3a7bb2d127012c25c11821a1ae03d41ebb72f71672"},"schema_version":"1.0","source":{"id":"2310.08081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.08081","created_at":"2026-07-05T07:00:00Z"},{"alias_kind":"arxiv_version","alias_value":"2310.08081v1","created_at":"2026-07-05T07:00:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.08081","created_at":"2026-07-05T07:00:00Z"},{"alias_kind":"pith_short_12","alias_value":"QT2Q4ZI67W2X","created_at":"2026-07-05T07:00:00Z"},{"alias_kind":"pith_short_16","alias_value":"QT2Q4ZI67W2XVPEO","created_at":"2026-07-05T07:00:00Z"},{"alias_kind":"pith_short_8","alias_value":"QT2Q4ZI6","created_at":"2026-07-05T07:00:00Z"}],"graph_snapshots":[{"event_id":"sha256:b5afa9cb2c353f12061eba689c5edaa3fd9c417e35322f9a9b8b78845650cdd4","target":"graph","created_at":"2026-07-05T07:00:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.08081/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The supersaturation problem for a given graph $F$ asks for the minimum number $h_F(n,q)$ of copies of $F$ in an $n$-vertex graph with $ex(n,F)+q$ edges. Subsequent works by Rademacher, Erd\\H{o}s, and Lov\\'{a}sz and Simonovits determine the optimal range of $q$ (which is linear in $n$) for cliques $F$ such that $h_F(n,q)$ equals the minimum number $t_F(n,q)$ of copies of $F$ obtained from a maximum $F$-free $n$-vertex graph by adding $q$ new edges. A breakthrough result of Mubayi extends this line of research from cliques to color-critical graphs $F$, and this was further strengthened by Pikhur","authors_text":"Jie Ma, Long-tu Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-12T07:10:22Z","title":"Supersaturation beyond color-critical graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.08081","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":"sha256:8f3c5ebc634df425f8ba88821760fe4f34bb0d3ded4279098bceb4f08f575d51","target":"record","created_at":"2026-07-05T07:00:00Z","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":"a8defbbab8949d4d4ceeeb63ff6bb83dc1def6770aaa3110970197168104b2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-12T07:10:22Z","title_canon_sha256":"2cafd46cfe671970d6590c3a7bb2d127012c25c11821a1ae03d41ebb72f71672"},"schema_version":"1.0","source":{"id":"2310.08081","kind":"arxiv","version":1}},"canonical_sha256":"84f50e651efdb57abc8e8b5222a4e3e9e53265ccce8b11497fe150146d6f722f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84f50e651efdb57abc8e8b5222a4e3e9e53265ccce8b11497fe150146d6f722f","first_computed_at":"2026-07-05T07:00:00.691585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:00:00.691585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EMtr5ueircZYPmGHOskzIj2I5hyDXqcV4rMiaO/BcSvGxjQfSnJtquwLfgqTcU9XYG36KVk1pbWfHAEWVlEqAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:00:00.692020Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.08081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f3c5ebc634df425f8ba88821760fe4f34bb0d3ded4279098bceb4f08f575d51","sha256:b5afa9cb2c353f12061eba689c5edaa3fd9c417e35322f9a9b8b78845650cdd4"],"state_sha256":"d132ccddfaafdbea656bf9eda7fe7503a7367bbdd15f67208ceb42ebf6b448b8"}