{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:CPEDG7XMW6FVGMJRV4I4UQEGBT","short_pith_number":"pith:CPEDG7XM","schema_version":"1.0","canonical_sha256":"13c8337eecb78b533131af11ca40860cf127ca79838eb391069fbb8fa78fe82b","source":{"kind":"arxiv","id":"2204.06686","version":4},"attestation_state":"computed","paper":{"title":"Isoperimetric Inequalities Made Simpler","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Dor Minzer, Guy Kindler, Noam Lifshitz, Ronen Eldan","submitted_at":"2022-04-14T01:11:05Z","abstract_excerpt":"We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show:\n  1. An elementary proof of classical isoperimetric inequalities of Talagrand, as well as a stronger isoperimetric result conjectured by Talagrand and recently proved by Eldan and Gross.\n  2. A strengthening of the Friedgut junta theorem, asserting that if the $p$-moment of the sensitivity of a function is constant for some $1/2 + \\varepsilon\\leq p\\leq 1$, then the function is close to a junta. In this language, Friedgut's theorem is the special case that $p=1$."},"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":"2204.06686","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-04-14T01:11:05Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b000d16db5e9e575f283267bc36b8f3209663147d7038bee498f791e7aecf67d","abstract_canon_sha256":"125cea35c036a2bb1bc109c21f0ae916563e521983fc00d6695d1f3f597ea04d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:28.786524Z","signature_b64":"XuXF34IFLNfz28NWfKQIe4QBhWLdeap6VKkGzxJgH6Z9kAnMGIr87bD7brDvNeQd+DvyyM44RPtg+CtTFBa1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13c8337eecb78b533131af11ca40860cf127ca79838eb391069fbb8fa78fe82b","last_reissued_at":"2026-07-05T11:40:28.786039Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:28.786039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isoperimetric Inequalities Made Simpler","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Dor Minzer, Guy Kindler, Noam Lifshitz, Ronen Eldan","submitted_at":"2022-04-14T01:11:05Z","abstract_excerpt":"We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show:\n  1. An elementary proof of classical isoperimetric inequalities of Talagrand, as well as a stronger isoperimetric result conjectured by Talagrand and recently proved by Eldan and Gross.\n  2. A strengthening of the Friedgut junta theorem, asserting that if the $p$-moment of the sensitivity of a function is constant for some $1/2 + \\varepsilon\\leq p\\leq 1$, then the function is close to a junta. In this language, Friedgut's theorem is the special case that $p=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.06686","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.06686/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2204.06686","created_at":"2026-07-05T11:40:28.786096+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.06686v4","created_at":"2026-07-05T11:40:28.786096+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.06686","created_at":"2026-07-05T11:40:28.786096+00:00"},{"alias_kind":"pith_short_12","alias_value":"CPEDG7XMW6FV","created_at":"2026-07-05T11:40:28.786096+00:00"},{"alias_kind":"pith_short_16","alias_value":"CPEDG7XMW6FVGMJR","created_at":"2026-07-05T11:40:28.786096+00:00"},{"alias_kind":"pith_short_8","alias_value":"CPEDG7XM","created_at":"2026-07-05T11:40:28.786096+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.31961","citing_title":"A Beckmann boundary form of Talagrand's conjecture on the discrete cube","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT","json":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT.json","graph_json":"https://pith.science/api/pith-number/CPEDG7XMW6FVGMJRV4I4UQEGBT/graph.json","events_json":"https://pith.science/api/pith-number/CPEDG7XMW6FVGMJRV4I4UQEGBT/events.json","paper":"https://pith.science/paper/CPEDG7XM"},"agent_actions":{"view_html":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT","download_json":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT.json","view_paper":"https://pith.science/paper/CPEDG7XM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.06686&json=true","fetch_graph":"https://pith.science/api/pith-number/CPEDG7XMW6FVGMJRV4I4UQEGBT/graph.json","fetch_events":"https://pith.science/api/pith-number/CPEDG7XMW6FVGMJRV4I4UQEGBT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT/action/storage_attestation","attest_author":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT/action/author_attestation","sign_citation":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT/action/citation_signature","submit_replication":"https://pith.science/pith/CPEDG7XMW6FVGMJRV4I4UQEGBT/action/replication_record"}},"created_at":"2026-07-05T11:40:28.786096+00:00","updated_at":"2026-07-05T11:40:28.786096+00:00"}