{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5SAZN5ATNDSCMGZ2AWIUEK5D5M","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":"dbf45698ac7b5688847f6eca925ed98b7c43745a110f030accfc4f40ca83c071","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-22T16:23:21Z","title_canon_sha256":"289f2ed0a8cfe21cd0dc1bf7a470bd54a18219da090c7d4d84e195b78f9f2bc2"},"schema_version":"1.0","source":{"id":"2306.13014","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.13014","created_at":"2026-07-05T08:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"2306.13014v2","created_at":"2026-07-05T08:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.13014","created_at":"2026-07-05T08:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"5SAZN5ATNDSC","created_at":"2026-07-05T08:58:19Z"},{"alias_kind":"pith_short_16","alias_value":"5SAZN5ATNDSCMGZ2","created_at":"2026-07-05T08:58:19Z"},{"alias_kind":"pith_short_8","alias_value":"5SAZN5AT","created_at":"2026-07-05T08:58:19Z"}],"graph_snapshots":[{"event_id":"sha256:a81c47a40e815e999557c53f2375dc751ed82604b525639c1c6968af0342757d","target":"graph","created_at":"2026-07-05T08:58:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.13014/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a finite graph $F$ and a value $p \\in [0,1]$, let $I(F,p)$ denote the largest $y$ for which there is a sequence of graphs of edge density approaching $p$ so that the induced $F$-density of the sequence approaches $y$. We show that for all $F$ on at least three vertices and all $p \\in (0,1)$, the binomial random graph $G(n,p)$ has induced $F$-density strictly less than $I(F,p).$ This provides a negative answer to a problem posed by Liu, Mubayi and Reiher.\n  Our approach is in the limiting setting of graphons, and we in fact show a stronger result: the binomial random graph is never a \\emph{","authors_text":"Fan Wei, Marcus Michelen, Vishesh Jain","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-22T16:23:21Z","title":"The binomial random graph is a bad inducer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.13014","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":"sha256:342d8610681e459570545e4400f000bbb7dcc7e6cc3284420692a0400bf54cc5","target":"record","created_at":"2026-07-05T08:58:19Z","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":"dbf45698ac7b5688847f6eca925ed98b7c43745a110f030accfc4f40ca83c071","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-22T16:23:21Z","title_canon_sha256":"289f2ed0a8cfe21cd0dc1bf7a470bd54a18219da090c7d4d84e195b78f9f2bc2"},"schema_version":"1.0","source":{"id":"2306.13014","kind":"arxiv","version":2}},"canonical_sha256":"ec8196f41368e4261b3a0591422ba3eb3e7b9cfd195f744caec5f556ff6e706d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec8196f41368e4261b3a0591422ba3eb3e7b9cfd195f744caec5f556ff6e706d","first_computed_at":"2026-07-05T08:58:19.680895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:19.680895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MWW0L0w4chuzVH77v+zPRopWD8Ey12i3K/eaT/XPOtFVJhgEn2Dy4tDjA5ml4yXCBlZEPbcm3MJnij6b2OcXAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:19.681378Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.13014","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:342d8610681e459570545e4400f000bbb7dcc7e6cc3284420692a0400bf54cc5","sha256:a81c47a40e815e999557c53f2375dc751ed82604b525639c1c6968af0342757d"],"state_sha256":"48f31cd5b8a8358a879c8071f1121c5eb31b32f68ce96e52359d1c2213ac5826"}