{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CSCMVJSJMRYH4WOZRAFLGE74DI","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":"bbd84a425f8822c746bbc382f3e97b8211636421c7040f6fe5e639eb8b3fd3d3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-05-09T16:54:47Z","title_canon_sha256":"04f88572ba42da15f52dea2971cf76c0eeb6f69b0dde2455c985272bb4c382ae"},"schema_version":"1.0","source":{"id":"2405.05902","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05902","created_at":"2026-07-05T08:29:00Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05902v2","created_at":"2026-07-05T08:29:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05902","created_at":"2026-07-05T08:29:00Z"},{"alias_kind":"pith_short_12","alias_value":"CSCMVJSJMRYH","created_at":"2026-07-05T08:29:00Z"},{"alias_kind":"pith_short_16","alias_value":"CSCMVJSJMRYH4WOZ","created_at":"2026-07-05T08:29:00Z"},{"alias_kind":"pith_short_8","alias_value":"CSCMVJSJ","created_at":"2026-07-05T08:29:00Z"}],"graph_snapshots":[{"event_id":"sha256:6e0c76f7a8de736755e427502e95c50dcf960fdf382da7bdae1daa37f0a5f71b","target":"graph","created_at":"2026-07-05T08:29:00Z","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/2405.05902/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We initiate the systematic study of the following Tur\\'an-type question. Suppose $\\Gamma$ is a graph with $n$ vertices such that the edge density between any pair of subsets of vertices of size at least $t$ is at most $1 - c$, for some $t$ and $c > 0$. What is the largest number of edges in a subgraph $G \\subseteq \\Gamma$ which does not contain a fixed graph $H$ as an induced subgraph or, more generally, which belongs to a hereditary property $\\mathcal{P}$? This provides a common generalization of two recently studied cases, namely $\\Gamma$ being a (pseudo-)random graph and a graph without a l","authors_text":"Huy Tuan Pham, Jacob Fox, Rajko Nenadov","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-05-09T16:54:47Z","title":"The largest subgraph without a forbidden induced subgraph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05902","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:d37102854b2c61b564388bbfda915eb910df573c95399a6b951e85ee9fb0a6c4","target":"record","created_at":"2026-07-05T08:29:00Z","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":"bbd84a425f8822c746bbc382f3e97b8211636421c7040f6fe5e639eb8b3fd3d3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-05-09T16:54:47Z","title_canon_sha256":"04f88572ba42da15f52dea2971cf76c0eeb6f69b0dde2455c985272bb4c382ae"},"schema_version":"1.0","source":{"id":"2405.05902","kind":"arxiv","version":2}},"canonical_sha256":"1484caa64964707e59d9880ab313fc1a18aa41a99048193450911931fed65f01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1484caa64964707e59d9880ab313fc1a18aa41a99048193450911931fed65f01","first_computed_at":"2026-07-05T08:29:00.510889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:29:00.510889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ngmEC4eXj69HFdHrNjxNZmnfUY88Bnr968d6R4J3okSze42i8cTqqLWmmMw6bK6w/mSVTgqdFM2R7/JdaA2Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:29:00.511368Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.05902","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d37102854b2c61b564388bbfda915eb910df573c95399a6b951e85ee9fb0a6c4","sha256:6e0c76f7a8de736755e427502e95c50dcf960fdf382da7bdae1daa37f0a5f71b"],"state_sha256":"3a515a7a1b8ad5dcc332631a5382010afabe530af663adb30dafa091ed562fba"}