{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WNVPL3LEN4QUUCG25LPKLFEQPS","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":"2ce3dc105c1fba86f3f045ba34bb6cb3b89aa16ff769908d360b6979093c655b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-10T08:40:14Z","title_canon_sha256":"54bbf0a6b3e1e5d91970e8911e93205f44c803614ddc475460009f1b6b1aeb7a"},"schema_version":"1.0","source":{"id":"1808.03453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03453","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03453v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03453","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"WNVPL3LEN4QU","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WNVPL3LEN4QUUCG2","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WNVPL3LE","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:3376d810ab0551400a8f644a3a10a5a468c1cdfd6505b7f4341a5d8fd38484d9","target":"graph","created_at":"2026-05-18T00:08:24Z","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":"A family of perfect matchings of $K_{2n}$ is $intersecting$ if any two of its members have an edge in common. 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","authors_text":"Nathan Lindzey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-10T08:40:14Z","title":"Stability for Intersecting Families of Perfect Matchings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03453","kind":"arxiv","version":1},"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":"sha256:3085f232f17cf71d4ae9657a35283a9cf9c72484cd58be0fdc2867d9f4ff9d70","target":"record","created_at":"2026-05-18T00:08:24Z","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":"2ce3dc105c1fba86f3f045ba34bb6cb3b89aa16ff769908d360b6979093c655b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-10T08:40:14Z","title_canon_sha256":"54bbf0a6b3e1e5d91970e8911e93205f44c803614ddc475460009f1b6b1aeb7a"},"schema_version":"1.0","source":{"id":"1808.03453","kind":"arxiv","version":1}},"canonical_sha256":"b36af5ed646f214a08daeadea594907cb2de5b66d529a0667450df5117601e70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b36af5ed646f214a08daeadea594907cb2de5b66d529a0667450df5117601e70","first_computed_at":"2026-05-18T00:08:24.982978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:24.982978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4HSvTHZfQ6K3VxoDm2D04fyKIlNxigZrNEm/+tF1kJlPvUDrioBPf3PQP8enrrQB41KWtyPtXsUkOhuryc7nAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:24.983581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3085f232f17cf71d4ae9657a35283a9cf9c72484cd58be0fdc2867d9f4ff9d70","sha256:3376d810ab0551400a8f644a3a10a5a468c1cdfd6505b7f4341a5d8fd38484d9"],"state_sha256":"d432540c1b0f18b70139ecaa1e1e575f4e291de6cbf6b35537c6d3ccdd59b25a"}