{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VQORJY6IUJ56RF7UCXOSUDE3MK","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":"c2db915807d3a0edded8278e4c6cab8863fd7f390590d5d0ec3fd6b528283b18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-14T12:52:46Z","title_canon_sha256":"d82fdfc154bf602b3041e0bbcd9e87796506c7f1282f06b5184b0174a980f82f"},"schema_version":"1.0","source":{"id":"1607.04115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04115","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04115v2","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04115","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"VQORJY6IUJ56","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VQORJY6IUJ56RF7U","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VQORJY6I","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:95baecc5573530688cd8f69ab170c44c23dada703e8a82ced75d43b387541a7d","target":"graph","created_at":"2026-05-18T01:10:35Z","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":"We present an alternative proof to the Touchard-Kaplansky formula for the probl\\`eme des m\\'enages, which, we believe, is simpler than the extant ones and is in the spirit of the elegant original proof by Kaplansky (1943). About the latter proof, Bogart and Doyle (1986) argued that despite its cleverness, suffered from opting to give precedence to one of the genders for the couples involved (Bogart and Doyle supplied an elegant proof that avoided such gender-dependent bias).","authors_text":"Georgios Kontogeorgiou, Lefteris Kirousis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-14T12:52:46Z","title":"The probl\\`eme des m\\'enages revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04115","kind":"arxiv","version":2},"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":"sha256:78a14d9190ba1a86d6ff88a0fdcf57ec173e57e42ba058c334ae9813ba96710c","target":"record","created_at":"2026-05-18T01:10:35Z","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":"c2db915807d3a0edded8278e4c6cab8863fd7f390590d5d0ec3fd6b528283b18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-14T12:52:46Z","title_canon_sha256":"d82fdfc154bf602b3041e0bbcd9e87796506c7f1282f06b5184b0174a980f82f"},"schema_version":"1.0","source":{"id":"1607.04115","kind":"arxiv","version":2}},"canonical_sha256":"ac1d14e3c8a27be897f415dd2a0c9b62ad347c5c034b9655d59764fbfc19dc2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac1d14e3c8a27be897f415dd2a0c9b62ad347c5c034b9655d59764fbfc19dc2d","first_computed_at":"2026-05-18T01:10:35.842515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:35.842515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ugY2NIMWdDZYNV2KlODYL8wBcrg5qlRaK4BjDv+sZF4DaK2dWcmEYu3wFDMwJ3AdM9KNfzOIS/Yx4/jN4HnAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:35.843062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78a14d9190ba1a86d6ff88a0fdcf57ec173e57e42ba058c334ae9813ba96710c","sha256:95baecc5573530688cd8f69ab170c44c23dada703e8a82ced75d43b387541a7d"],"state_sha256":"0c688a77e0fbd64263783b7f976451e6589bd7ce11eb49ea49cd6062fa2e64cf"}