{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q4WZM462HNLOMCBETNHSLORDEP","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":"02dbcb8152ec8b9dc0260360bf959f95411197906a00a38c07948476688be629","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-05T06:46:41Z","title_canon_sha256":"30a3aa22fcb6a5acd360acc9e515028421cea729853c1e0cd1e2a360f860393e"},"schema_version":"1.0","source":{"id":"1809.01352","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01352","created_at":"2026-07-05T00:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01352v4","created_at":"2026-07-05T00:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01352","created_at":"2026-07-05T00:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"Q4WZM462HNLO","created_at":"2026-07-05T00:43:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q4WZM462HNLOMCBE","created_at":"2026-07-05T00:43:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q4WZM462","created_at":"2026-07-05T00:43:18Z"}],"graph_snapshots":[{"event_id":"sha256:1bc62fe06f3da42fd68a214bfe00723a9feb8d1ab42af784d69dc73e25815c84","target":"graph","created_at":"2026-07-05T00:43:18Z","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/1809.01352/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For given integers $k$ and $\\ell$ with $0<\\ell< {k \\choose 2}$, Alon, Hefetz, Krivelevich and Tyomkyn formulated the following conjecture: When sampling a $k$-vertex subset uniformly at random from a very large graph $G$, then the probability to have exactly $\\ell$ edges within the sampled $k$-vertex subset is at most $e^{-1}+o_k(1)$. This conjecture was proved in the case $\\Omega(k)\\leq \\ell\\leq {k \\choose 2}-\\Omega(k)$ by Kwan, Sudakov and Tran. In this paper, we complete the proof of the conjecture by resolving the remaining cases. We furthermore give nearly tight upper bounds for the proba","authors_text":"Jacob Fox, Lisa Sauermann","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-05T06:46:41Z","title":"A Completion of the Proof of the Edge-statistics Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01352","kind":"arxiv","version":4},"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":"sha256:76dddab835b9c27c9efdc63427e0909cb2261623a0146c6b28ae0292a890346f","target":"record","created_at":"2026-07-05T00:43:18Z","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":"02dbcb8152ec8b9dc0260360bf959f95411197906a00a38c07948476688be629","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-05T06:46:41Z","title_canon_sha256":"30a3aa22fcb6a5acd360acc9e515028421cea729853c1e0cd1e2a360f860393e"},"schema_version":"1.0","source":{"id":"1809.01352","kind":"arxiv","version":4}},"canonical_sha256":"872d9673da3b56e608249b4f25ba2323cc102170b0514282d72ddc10d452ee92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"872d9673da3b56e608249b4f25ba2323cc102170b0514282d72ddc10d452ee92","first_computed_at":"2026-07-05T00:43:18.144718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:43:18.144718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4dLmVr6uzCX2KayIAGvWGtftMRP3rXXtaBNzEL0T48INoArBFPUiSmYcP9VUT1sKXAT/eNPJsNos9biS6F3oCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:43:18.145128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01352","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76dddab835b9c27c9efdc63427e0909cb2261623a0146c6b28ae0292a890346f","sha256:1bc62fe06f3da42fd68a214bfe00723a9feb8d1ab42af784d69dc73e25815c84"],"state_sha256":"139c0b84e266f0a141063c99902d7b8144e52739a9ff4f44c470ff6ae0937e87"}