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We prove a stability version of this theorem, analogous to similar results of Dinur-Friedgut, Keevash-Mubayi and others for the Erd\\H{o}s-Ko-Rado theorem. The technique we use is a generalization of Katona's circle method, initially employed by Keevash, which uses expansion properties of a part"},"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":"1009.3973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-21T00:52:13Z","cross_cats_sorted":[],"title_canon_sha256":"f2db2e1bd68a811b8eb02830679c44bd4b2b0e38dea218dc7b5d1b002bc5ac6e","abstract_canon_sha256":"b455e47449d3778ab8455d408e01b309e0d019a44419cac3a5ee431adfef9c0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:16.575456Z","signature_b64":"y/b6zM7hMX8rJT0MFWvbosZLbcXFeLFrG7zWOlQoMtgTtnAjwvuK+qCJTDm1MfBuUiKF9qBeJNkJa/RPtIZmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e26e07eea13f8b421ec746958ddb159b9839cd05b4ad18964b0c5646d702e484","last_reissued_at":"2026-05-18T03:29:16.574833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:16.574833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability anaylsis for k-wise intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vikram Kamat","submitted_at":"2010-09-21T00:52:13Z","abstract_excerpt":"We consider the following generalization of the seminal Erd\\H{o}s-Ko-Rado theorem, due to Frankl. 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