{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3C4BRB4HVETISOJUBWX5CXS3U5","short_pith_number":"pith:3C4BRB4H","canonical_record":{"source":{"id":"1501.03880","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T05:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"b8206c53984334b22b8b8d989f2e25b7161084d6ec4f1f1296a431d049d6e826","abstract_canon_sha256":"8953051259654f16b2591786f329bb6b50a6c60116bf61d5f2d21bb7bce878a9"},"schema_version":"1.0"},"canonical_sha256":"d8b8188787a9268939340dafd15e5ba7736e4466085cf06340bc1416e71b9e41","source":{"kind":"arxiv","id":"1501.03880","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03880","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03880v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03880","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"3C4BRB4HVETI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3C4BRB4HVETISOJU","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3C4BRB4H","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3C4BRB4HVETISOJUBWX5CXS3U5","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03880","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T05:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"b8206c53984334b22b8b8d989f2e25b7161084d6ec4f1f1296a431d049d6e826","abstract_canon_sha256":"8953051259654f16b2591786f329bb6b50a6c60116bf61d5f2d21bb7bce878a9"},"schema_version":"1.0"},"canonical_sha256":"d8b8188787a9268939340dafd15e5ba7736e4466085cf06340bc1416e71b9e41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:20.362371Z","signature_b64":"2foev6vOLkh63klcsJxhh0R9M/SfqsnRuMCoZFE5WWrcXE1dbgNEJ+WecnFFX0RLnJKMnrTtVwQxoj1kQFtoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8b8188787a9268939340dafd15e5ba7736e4466085cf06340bc1416e71b9e41","last_reissued_at":"2026-05-18T02:16:20.361786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:20.361786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03880","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sKF1iBNBrpUZxDp7eBUjmvJcf+Om1Z7e9uPF33e0QT/30F1x0RGOORKPL4Hz7R8zr6rakLL84qYeXhRbkj30Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:03:24.222113Z"},"content_sha256":"348bfb7a930a1ff2f159160b64771c1825613388223fd8bfdd3b7558cd47a915","schema_version":"1.0","event_id":"sha256:348bfb7a930a1ff2f159160b64771c1825613388223fd8bfdd3b7558cd47a915"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3C4BRB4HVETISOJUBWX5CXS3U5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Combinatorics of Associated Laguerre Polynomials","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dennis Stanton, Jang Soo Kim","submitted_at":"2015-01-16T05:34:05Z","abstract_excerpt":"The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03880","kind":"arxiv","version":2},"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":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSVP/Ctu7R+9AOD+U+G3bVddduqi6Y+YbvWhm3DFXiKxWqKdzoxxeQXsOdlv0C6oBm1Y6lg8/CsgojLL0ZQhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:03:24.222836Z"},"content_sha256":"3450938c53e07a5592264a2cd06af534bcc730f8fb373e72fb5f7121576a0ba0","schema_version":"1.0","event_id":"sha256:3450938c53e07a5592264a2cd06af534bcc730f8fb373e72fb5f7121576a0ba0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3C4BRB4HVETISOJUBWX5CXS3U5/bundle.json","state_url":"https://pith.science/pith/3C4BRB4HVETISOJUBWX5CXS3U5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3C4BRB4HVETISOJUBWX5CXS3U5/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":"2026-05-26T10:03:24Z","links":{"resolver":"https://pith.science/pith/3C4BRB4HVETISOJUBWX5CXS3U5","bundle":"https://pith.science/pith/3C4BRB4HVETISOJUBWX5CXS3U5/bundle.json","state":"https://pith.science/pith/3C4BRB4HVETISOJUBWX5CXS3U5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3C4BRB4HVETISOJUBWX5CXS3U5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3C4BRB4HVETISOJUBWX5CXS3U5","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":"8953051259654f16b2591786f329bb6b50a6c60116bf61d5f2d21bb7bce878a9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T05:34:05Z","title_canon_sha256":"b8206c53984334b22b8b8d989f2e25b7161084d6ec4f1f1296a431d049d6e826"},"schema_version":"1.0","source":{"id":"1501.03880","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03880","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03880v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03880","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"3C4BRB4HVETI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3C4BRB4HVETISOJU","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3C4BRB4H","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:3450938c53e07a5592264a2cd06af534bcc730f8fb373e72fb5f7121576a0ba0","target":"graph","created_at":"2026-05-18T02:16:20Z","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 explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function.","authors_text":"Dennis Stanton, Jang Soo Kim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T05:34:05Z","title":"The Combinatorics of Associated Laguerre Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03880","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":"sha256:348bfb7a930a1ff2f159160b64771c1825613388223fd8bfdd3b7558cd47a915","target":"record","created_at":"2026-05-18T02:16:20Z","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":"8953051259654f16b2591786f329bb6b50a6c60116bf61d5f2d21bb7bce878a9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T05:34:05Z","title_canon_sha256":"b8206c53984334b22b8b8d989f2e25b7161084d6ec4f1f1296a431d049d6e826"},"schema_version":"1.0","source":{"id":"1501.03880","kind":"arxiv","version":2}},"canonical_sha256":"d8b8188787a9268939340dafd15e5ba7736e4466085cf06340bc1416e71b9e41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b8188787a9268939340dafd15e5ba7736e4466085cf06340bc1416e71b9e41","first_computed_at":"2026-05-18T02:16:20.361786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:20.361786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2foev6vOLkh63klcsJxhh0R9M/SfqsnRuMCoZFE5WWrcXE1dbgNEJ+WecnFFX0RLnJKMnrTtVwQxoj1kQFtoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:20.362371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03880","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:348bfb7a930a1ff2f159160b64771c1825613388223fd8bfdd3b7558cd47a915","sha256:3450938c53e07a5592264a2cd06af534bcc730f8fb373e72fb5f7121576a0ba0"],"state_sha256":"c1ea13d2234cf9ede9f29a34020d5101cc5b15b91871c04946ba163f1753e7ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AV6IGmcPzw16IRscHLsaD0jwimvt6Ye/+SEcuo14nzPjCbwY9Qvm8fQqwMmZz3pnFdVGqXVjOR8cIE+zUC+GAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T10:03:24.226879Z","bundle_sha256":"7356e9acfe8d5b654e59cda4bb0836200089a6143231ac4ccca1d1cac8f9123c"}}