{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YQTH6D3DZJV3OX7NPRRO3VQUPD","short_pith_number":"pith:YQTH6D3D","canonical_record":{"source":{"id":"1710.03896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-11T04:01:46Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3127a5ab79a6971f0a8b95340226ca425a7112edcc72dc013953be7d741b2bd5","abstract_canon_sha256":"5a2047bb77c273400c82d3427c5c5745c2e0b5ec4c3b893ca7d225a0c734be0a"},"schema_version":"1.0"},"canonical_sha256":"c4267f0f63ca6bb75fed7c62edd61478d36867defceaa8be24f28774afa70817","source":{"kind":"arxiv","id":"1710.03896","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03896","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03896v1","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03896","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"YQTH6D3DZJV3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YQTH6D3DZJV3OX7N","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YQTH6D3D","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YQTH6D3DZJV3OX7NPRRO3VQUPD","target":"record","payload":{"canonical_record":{"source":{"id":"1710.03896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-11T04:01:46Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3127a5ab79a6971f0a8b95340226ca425a7112edcc72dc013953be7d741b2bd5","abstract_canon_sha256":"5a2047bb77c273400c82d3427c5c5745c2e0b5ec4c3b893ca7d225a0c734be0a"},"schema_version":"1.0"},"canonical_sha256":"c4267f0f63ca6bb75fed7c62edd61478d36867defceaa8be24f28774afa70817","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:05.667001Z","signature_b64":"9RdbkhgZ9yhXKOzjldkNxBWB8vfY5B6FfITtFKsr0/lkIVR7VihSzZ0Ivosp4xx+BKcnQPf/7sfhPctTqDfGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4267f0f63ca6bb75fed7c62edd61478d36867defceaa8be24f28774afa70817","last_reissued_at":"2026-05-18T00:33:05.666332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:05.666332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.03896","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ablBjjTm85iBi/Z29bDbNlgQSwk+jcnknNPa6T4EG24bdgHJK2D30xbH+qzN0V6x5bGfK61qkJtn/OVuM568AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T00:53:30.279942Z"},"content_sha256":"765f48362a5328ea8bba3d7799e6d8876b8c3a9261a12d56ab31e05dd635070b","schema_version":"1.0","event_id":"sha256:765f48362a5328ea8bba3d7799e6d8876b8c3a9261a12d56ab31e05dd635070b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YQTH6D3DZJV3OX7NPRRO3VQUPD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of descents in matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Gene B. Kim","submitted_at":"2017-10-11T04:01:46Z","abstract_excerpt":"The distribution of descents in a fixed conjugacy class of $S_n$ is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of interest is the class of matchings (also known as fixed point free involutions). This paper provides a bijective proof of the symmetry of the descents and major indices of matchings and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03896","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zLzjUAghcCI7K3Q4SFxbh9Fj0nLxcb+2/K5RLPwyflLI8shK/VuIeOljpLgcvVIfYuaqIqTdL/HYmwtJH4vgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T00:53:30.280285Z"},"content_sha256":"7644c32a0f8a27ec89c86853f3b50f1d717d4cb26c4d89ba71b3b6951bc5a892","schema_version":"1.0","event_id":"sha256:7644c32a0f8a27ec89c86853f3b50f1d717d4cb26c4d89ba71b3b6951bc5a892"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQTH6D3DZJV3OX7NPRRO3VQUPD/bundle.json","state_url":"https://pith.science/pith/YQTH6D3DZJV3OX7NPRRO3VQUPD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQTH6D3DZJV3OX7NPRRO3VQUPD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T00:53:30Z","links":{"resolver":"https://pith.science/pith/YQTH6D3DZJV3OX7NPRRO3VQUPD","bundle":"https://pith.science/pith/YQTH6D3DZJV3OX7NPRRO3VQUPD/bundle.json","state":"https://pith.science/pith/YQTH6D3DZJV3OX7NPRRO3VQUPD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQTH6D3DZJV3OX7NPRRO3VQUPD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YQTH6D3DZJV3OX7NPRRO3VQUPD","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":"5a2047bb77c273400c82d3427c5c5745c2e0b5ec4c3b893ca7d225a0c734be0a","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-11T04:01:46Z","title_canon_sha256":"3127a5ab79a6971f0a8b95340226ca425a7112edcc72dc013953be7d741b2bd5"},"schema_version":"1.0","source":{"id":"1710.03896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03896","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03896v1","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03896","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"YQTH6D3DZJV3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YQTH6D3DZJV3OX7N","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YQTH6D3D","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:7644c32a0f8a27ec89c86853f3b50f1d717d4cb26c4d89ba71b3b6951bc5a892","target":"graph","created_at":"2026-05-18T00:33:05Z","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":"The distribution of descents in a fixed conjugacy class of $S_n$ is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of interest is the class of matchings (also known as fixed point free involutions). This paper provides a bijective proof of the symmetry of the descents and major indices of matchings and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings.","authors_text":"Gene B. Kim","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-11T04:01:46Z","title":"Distribution of descents in matchings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03896","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":"sha256:765f48362a5328ea8bba3d7799e6d8876b8c3a9261a12d56ab31e05dd635070b","target":"record","created_at":"2026-05-18T00:33:05Z","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":"5a2047bb77c273400c82d3427c5c5745c2e0b5ec4c3b893ca7d225a0c734be0a","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-11T04:01:46Z","title_canon_sha256":"3127a5ab79a6971f0a8b95340226ca425a7112edcc72dc013953be7d741b2bd5"},"schema_version":"1.0","source":{"id":"1710.03896","kind":"arxiv","version":1}},"canonical_sha256":"c4267f0f63ca6bb75fed7c62edd61478d36867defceaa8be24f28774afa70817","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4267f0f63ca6bb75fed7c62edd61478d36867defceaa8be24f28774afa70817","first_computed_at":"2026-05-18T00:33:05.666332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:05.666332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9RdbkhgZ9yhXKOzjldkNxBWB8vfY5B6FfITtFKsr0/lkIVR7VihSzZ0Ivosp4xx+BKcnQPf/7sfhPctTqDfGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:05.667001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:765f48362a5328ea8bba3d7799e6d8876b8c3a9261a12d56ab31e05dd635070b","sha256:7644c32a0f8a27ec89c86853f3b50f1d717d4cb26c4d89ba71b3b6951bc5a892"],"state_sha256":"a339099f7c9881b5dca90115ca05c47bf50f6a5fe881a61df9f12ee897896e34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RIsx4OM8+dtuPWQnP1Pz044IhjrJ5J0fz09/9k1rodllYuPY0jIThtNQ1NEFErNUNGbNKBchrv5wGqfEe8IvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T00:53:30.282623Z","bundle_sha256":"5177254ee29ff662a7d2eeaaf6dc3f700c81f827b861dd3048d7a2102349827a"}}