{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HKRRMO5DBPIUOY77ZU2DOIR4Q4","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":"f09cb136ddc720484215a256768eac60f61f6c2954ae293b458f07b1fdf1637b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-15T11:52:45Z","title_canon_sha256":"1785506c9c40e7a7a63edbd7fa13d1f63f399a8e453fd294dbd7d7d0a7d5fe7f"},"schema_version":"1.0","source":{"id":"1210.3989","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3989","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3989v4","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3989","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"HKRRMO5DBPIU","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HKRRMO5DBPIUOY77","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HKRRMO5D","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ee47d23b2080826c8b9239c83694cc38421468409ebbf62ab65543a97d777eef","target":"graph","created_at":"2026-05-18T00:41:13Z","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":"We prove that a balanced Boolean function on $S_{n}$ whose Fourier transform is highly concentrated on the first two irreducible representations of $S_{n}$, is close in structure to a dictatorship, a function which is determined by the image or pre-image of a single element. As a corollary, we obtain a stability result concerning extremal isoperimetric sets in the Cayley graph on $S_{n}$ generated by the transpositions. Our proof works in the case where the expectation of the function is bounded away from $0$ and $1$. In contrast, [Ellis, D., Filmus, Y., Friedgut, E., A quasi-stability result ","authors_text":"David Ellis, Ehud Friedgut, Yuval Filmus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-15T11:52:45Z","title":"A stability result for balanced dictatorships in $S_{n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3989","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":"sha256:7abae3e2c86d556d16ba4508a960e5e1378ae2e5e09b00b5f389be200d92c9a6","target":"record","created_at":"2026-05-18T00:41:13Z","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":"f09cb136ddc720484215a256768eac60f61f6c2954ae293b458f07b1fdf1637b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-15T11:52:45Z","title_canon_sha256":"1785506c9c40e7a7a63edbd7fa13d1f63f399a8e453fd294dbd7d7d0a7d5fe7f"},"schema_version":"1.0","source":{"id":"1210.3989","kind":"arxiv","version":4}},"canonical_sha256":"3aa3163ba30bd14763ffcd3437223c873ea4b2439b1ea528793fa8b41736c490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aa3163ba30bd14763ffcd3437223c873ea4b2439b1ea528793fa8b41736c490","first_computed_at":"2026-05-18T00:41:13.486054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:13.486054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xGkV/gujY59HH/08AZ2MzapdKyccX99DWH+mzZyRbHLseXhAW9OwsEXNCmlSO1yGyDQ+sTuH3vLR+NChosGSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:13.486806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3989","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7abae3e2c86d556d16ba4508a960e5e1378ae2e5e09b00b5f389be200d92c9a6","sha256:ee47d23b2080826c8b9239c83694cc38421468409ebbf62ab65543a97d777eef"],"state_sha256":"e31ef58b33bc173803b870f7d7b6329c31fa68ef0ff65963dacd6c191043ae4f"}