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It is known that if $\\mathcal{F}$ is family of intersecting perfect matchings of $K_{2n}$, then $|\\mathcal{F}| \\leq (2n-3)!!$ and if equality holds, then $\\mathcal{F} = \\mathcal{F}_{ij}$ where $ \\mathcal{F}_{ij}$ is the family of all perfect matchings of $K_{2n}$ that contain some fixed edge $ij$. In this note, we show that the extremal families are stable, namely, that for any $\\epsilon \\in (0,1/\\sqrt{e})$ and $n > n(\\epsilon)$, any intersecting family of perfect matchings of size gre"},"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":"1808.03453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-10T08:40:14Z","cross_cats_sorted":[],"title_canon_sha256":"54bbf0a6b3e1e5d91970e8911e93205f44c803614ddc475460009f1b6b1aeb7a","abstract_canon_sha256":"2ce3dc105c1fba86f3f045ba34bb6cb3b89aa16ff769908d360b6979093c655b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:24.983581Z","signature_b64":"4HSvTHZfQ6K3VxoDm2D04fyKIlNxigZrNEm/+tF1kJlPvUDrioBPf3PQP8enrrQB41KWtyPtXsUkOhuryc7nAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b36af5ed646f214a08daeadea594907cb2de5b66d529a0667450df5117601e70","last_reissued_at":"2026-05-18T00:08:24.982978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:24.982978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability for Intersecting Families of Perfect Matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nathan Lindzey","submitted_at":"2018-08-10T08:40:14Z","abstract_excerpt":"A family of perfect matchings of $K_{2n}$ is $intersecting$ if any two of its members have an edge in common. 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