{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:C64HLHTX5YW4JUUIRBM5SBV3RB","short_pith_number":"pith:C64HLHTX","schema_version":"1.0","canonical_sha256":"17b8759e77ee2dc4d2888859d906bb8854ba92296fa34c434ca481afb3e3633e","source":{"kind":"arxiv","id":"1209.5557","version":8},"attestation_state":"computed","paper":{"title":"A quasi-stability result for dictatorships in $S_{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"David Ellis, Ehud Friedgut, Yuval Filmus","submitted_at":"2012-09-25T09:47:58Z","abstract_excerpt":"We prove that Boolean functions on $S_{n}$ whose Fourier transform is highly concentrated on the first two irreducible representations of $S_n$, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku, and first proved by the first author. We also use it to prove a `quasi-stability' result for an edge-isoperimetric inequality in the transposition graph on $S_n$, namely that subsets of $S_n$ with small edge-boundary in the transposition graph are close t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.5557","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-25T09:47:58Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f47f5410cc31d589abc2569d30d46a81b2c0f0dac32fd976eba98f3a984c4f78","abstract_canon_sha256":"e5fcff1dbcda6435dfb5962af98465e2b96a7371ec937ddcd77fc86f7167f991"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:13.497399Z","signature_b64":"+WsObRfxGPkcUjaA//ggtvDVmZd0r6h6RcwZjdkzrLcrpOElhwUdE8EpeuV7StqjDhs9GSn4KwZBCJ/MhE2VDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17b8759e77ee2dc4d2888859d906bb8854ba92296fa34c434ca481afb3e3633e","last_reissued_at":"2026-05-18T00:41:13.496677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:13.496677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A quasi-stability result for dictatorships in $S_{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"David Ellis, Ehud Friedgut, Yuval Filmus","submitted_at":"2012-09-25T09:47:58Z","abstract_excerpt":"We prove that Boolean functions on $S_{n}$ whose Fourier transform is highly concentrated on the first two irreducible representations of $S_n$, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku, and first proved by the first author. We also use it to prove a `quasi-stability' result for an edge-isoperimetric inequality in the transposition graph on $S_n$, namely that subsets of $S_n$ with small edge-boundary in the transposition graph are close t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5557","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.5557","created_at":"2026-05-18T00:41:13.496792+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.5557v8","created_at":"2026-05-18T00:41:13.496792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5557","created_at":"2026-05-18T00:41:13.496792+00:00"},{"alias_kind":"pith_short_12","alias_value":"C64HLHTX5YW4","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"C64HLHTX5YW4JUUI","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"C64HLHTX","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB","json":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB.json","graph_json":"https://pith.science/api/pith-number/C64HLHTX5YW4JUUIRBM5SBV3RB/graph.json","events_json":"https://pith.science/api/pith-number/C64HLHTX5YW4JUUIRBM5SBV3RB/events.json","paper":"https://pith.science/paper/C64HLHTX"},"agent_actions":{"view_html":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB","download_json":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB.json","view_paper":"https://pith.science/paper/C64HLHTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.5557&json=true","fetch_graph":"https://pith.science/api/pith-number/C64HLHTX5YW4JUUIRBM5SBV3RB/graph.json","fetch_events":"https://pith.science/api/pith-number/C64HLHTX5YW4JUUIRBM5SBV3RB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB/action/storage_attestation","attest_author":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB/action/author_attestation","sign_citation":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB/action/citation_signature","submit_replication":"https://pith.science/pith/C64HLHTX5YW4JUUIRBM5SBV3RB/action/replication_record"}},"created_at":"2026-05-18T00:41:13.496792+00:00","updated_at":"2026-05-18T00:41:13.496792+00:00"}