{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:T6C7NYD2PPLTM6EOJNKEJZCKJ3","short_pith_number":"pith:T6C7NYD2","canonical_record":{"source":{"id":"0812.4091","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-22T04:49:05Z","cross_cats_sorted":[],"title_canon_sha256":"b666e17a542344754df08fbb60b7e7bed3dd8860a5259bfcf07aae7524dc32cd","abstract_canon_sha256":"5ed669ff6b0207ac829b6adb0d7d61fb9c57aaf876f05f10635bf5ff868ea7e1"},"schema_version":"1.0"},"canonical_sha256":"9f85f6e07a7bd736788e4b5444e44a4eecf2b5c95496e52e3c30c005f8b79be3","source":{"kind":"arxiv","id":"0812.4091","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4091","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4091v3","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4091","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"T6C7NYD2PPLT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"T6C7NYD2PPLTM6EO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"T6C7NYD2","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:T6C7NYD2PPLTM6EOJNKEJZCKJ3","target":"record","payload":{"canonical_record":{"source":{"id":"0812.4091","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-22T04:49:05Z","cross_cats_sorted":[],"title_canon_sha256":"b666e17a542344754df08fbb60b7e7bed3dd8860a5259bfcf07aae7524dc32cd","abstract_canon_sha256":"5ed669ff6b0207ac829b6adb0d7d61fb9c57aaf876f05f10635bf5ff868ea7e1"},"schema_version":"1.0"},"canonical_sha256":"9f85f6e07a7bd736788e4b5444e44a4eecf2b5c95496e52e3c30c005f8b79be3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:38.352837Z","signature_b64":"b62JtpXQBHMcvo7ykWgUpTiX1TJnGNMQTGfRuB5hXJUv7RprvHHAKCzPnU1yZQhZzHS9vFHJQBJfEFnRHZsBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f85f6e07a7bd736788e4b5444e44a4eecf2b5c95496e52e3c30c005f8b79be3","last_reissued_at":"2026-05-18T04:14:38.352299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:38.352299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.4091","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8hFyuKEevxiCe+omPk6byUt8IvPPtKE38tuMZRdH8WYcKJUpYlSJNV2tWxjUqhgoswhY2y5VZFGVj9JuB43CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:36:35.559038Z"},"content_sha256":"f51520098801ea893c4be8fe55f8c4ca176e6e7f8baff1bb29e94c2b5923970c","schema_version":"1.0","event_id":"sha256:f51520098801ea893c4be8fe55f8c4ca176e6e7f8baff1bb29e94c2b5923970c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:T6C7NYD2PPLTM6EOJNKEJZCKJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bijections on two variations of noncrossing partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jang Soo Kim","submitted_at":"2008-12-22T04:49:05Z","abstract_excerpt":"We find bijections on 2-distant noncrossing partitions, 12312-avoiding partitions, 3-Motzkin paths, UH-free Schr{\\\"o}der paths and Schr{\\\"o}der paths without peaks at even height. We also give a direct bijection between 2-distant noncrossing partitions and 12312-avoiding partitions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4091","kind":"arxiv","version":3},"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":"2026-05-18T04:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K6HG3HzgkYBWMVfbwy2jlDH6X4E4toQYdwJuv1SwY+6lDN8TV1bN0AlzszD/BbKyx20tiWyo/j5lvHhBDL+sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:36:35.559744Z"},"content_sha256":"3efb6f8677f486bac7926699a7c52467a06af31f03b6a32d9ddf5725007abad7","schema_version":"1.0","event_id":"sha256:3efb6f8677f486bac7926699a7c52467a06af31f03b6a32d9ddf5725007abad7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6C7NYD2PPLTM6EOJNKEJZCKJ3/bundle.json","state_url":"https://pith.science/pith/T6C7NYD2PPLTM6EOJNKEJZCKJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6C7NYD2PPLTM6EOJNKEJZCKJ3/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":"2026-05-25T23:36:35Z","links":{"resolver":"https://pith.science/pith/T6C7NYD2PPLTM6EOJNKEJZCKJ3","bundle":"https://pith.science/pith/T6C7NYD2PPLTM6EOJNKEJZCKJ3/bundle.json","state":"https://pith.science/pith/T6C7NYD2PPLTM6EOJNKEJZCKJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6C7NYD2PPLTM6EOJNKEJZCKJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:T6C7NYD2PPLTM6EOJNKEJZCKJ3","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":"5ed669ff6b0207ac829b6adb0d7d61fb9c57aaf876f05f10635bf5ff868ea7e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-22T04:49:05Z","title_canon_sha256":"b666e17a542344754df08fbb60b7e7bed3dd8860a5259bfcf07aae7524dc32cd"},"schema_version":"1.0","source":{"id":"0812.4091","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4091","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4091v3","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4091","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"T6C7NYD2PPLT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"T6C7NYD2PPLTM6EO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"T6C7NYD2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:3efb6f8677f486bac7926699a7c52467a06af31f03b6a32d9ddf5725007abad7","target":"graph","created_at":"2026-05-18T04:14:38Z","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 find bijections on 2-distant noncrossing partitions, 12312-avoiding partitions, 3-Motzkin paths, UH-free Schr{\\\"o}der paths and Schr{\\\"o}der paths without peaks at even height. We also give a direct bijection between 2-distant noncrossing partitions and 12312-avoiding partitions.","authors_text":"Jang Soo Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-22T04:49:05Z","title":"Bijections on two variations of noncrossing partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4091","kind":"arxiv","version":3},"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:f51520098801ea893c4be8fe55f8c4ca176e6e7f8baff1bb29e94c2b5923970c","target":"record","created_at":"2026-05-18T04:14:38Z","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":"5ed669ff6b0207ac829b6adb0d7d61fb9c57aaf876f05f10635bf5ff868ea7e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-22T04:49:05Z","title_canon_sha256":"b666e17a542344754df08fbb60b7e7bed3dd8860a5259bfcf07aae7524dc32cd"},"schema_version":"1.0","source":{"id":"0812.4091","kind":"arxiv","version":3}},"canonical_sha256":"9f85f6e07a7bd736788e4b5444e44a4eecf2b5c95496e52e3c30c005f8b79be3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f85f6e07a7bd736788e4b5444e44a4eecf2b5c95496e52e3c30c005f8b79be3","first_computed_at":"2026-05-18T04:14:38.352299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:38.352299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b62JtpXQBHMcvo7ykWgUpTiX1TJnGNMQTGfRuB5hXJUv7RprvHHAKCzPnU1yZQhZzHS9vFHJQBJfEFnRHZsBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:38.352837Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4091","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f51520098801ea893c4be8fe55f8c4ca176e6e7f8baff1bb29e94c2b5923970c","sha256:3efb6f8677f486bac7926699a7c52467a06af31f03b6a32d9ddf5725007abad7"],"state_sha256":"9ae3b0c0de2db95dba3fbd412b94a0fde5a8f7f6d9673ba19c7209c127a34e6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3TPaK0t5dMGuDAyuXQJO61dsC3X4qDw3KuJapD8URAOytPbb3BB/eSy7sqGCsabiOviJvgfPKtrumne6ITjCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:36:35.563397Z","bundle_sha256":"3bf921824f2263c6eb180d7c1a90031c767a239d0e83700ee794877bdcbd8220"}}