{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PEIT5I6H3M77A4LC7GUTZ26VIV","short_pith_number":"pith:PEIT5I6H","canonical_record":{"source":{"id":"1708.09109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T04:33:42Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3d5a44fa510557c1dd1ca047e4f9b7c3e9ff5b9d8fe5b57e22fab11b85486421","abstract_canon_sha256":"b58bcc4c71182aeaf385b2fd209c31ba597105e9b7cf2dfc769c0925eca04323"},"schema_version":"1.0"},"canonical_sha256":"79113ea3c7db3ff07162f9a93cebd545446f17642f3eacf9b6e24f3f217ecd21","source":{"kind":"arxiv","id":"1708.09109","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09109","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09109v2","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09109","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"pith_short_12","alias_value":"PEIT5I6H3M77","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PEIT5I6H3M77A4LC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PEIT5I6H","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PEIT5I6H3M77A4LC7GUTZ26VIV","target":"record","payload":{"canonical_record":{"source":{"id":"1708.09109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T04:33:42Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3d5a44fa510557c1dd1ca047e4f9b7c3e9ff5b9d8fe5b57e22fab11b85486421","abstract_canon_sha256":"b58bcc4c71182aeaf385b2fd209c31ba597105e9b7cf2dfc769c0925eca04323"},"schema_version":"1.0"},"canonical_sha256":"79113ea3c7db3ff07162f9a93cebd545446f17642f3eacf9b6e24f3f217ecd21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:58.074544Z","signature_b64":"p65D1oQ94WlmGh1t7VS6bwgjqRz0993YnEmKf2UXSsjOpn4MGXlhYok6lGfNwUj01I7qLXr+ya1j9/tWV5g7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79113ea3c7db3ff07162f9a93cebd545446f17642f3eacf9b6e24f3f217ecd21","last_reissued_at":"2026-05-17T23:53:58.073850Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:58.073850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.09109","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":"2026-05-17T23:53:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8seyANmghCnQFXvMU06kqYMNX4je2aCohHXl1WiplPf24dV6j+7Ww7DzFC0gypKARi5j1lOLi9GRTg0t+EepBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:48:29.002712Z"},"content_sha256":"42bd85d64fea7640b39d38d077db5a5bf58ba430321fcbe871c063523c7ecb9f","schema_version":"1.0","event_id":"sha256:42bd85d64fea7640b39d38d077db5a5bf58ba430321fcbe871c063523c7ecb9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PEIT5I6H3M77A4LC7GUTZ26VIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hook length property of $d$-complete posets via $q$-integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Jang Soo Kim, Meesue Yoo","submitted_at":"2017-08-30T04:33:42Z","abstract_excerpt":"The hook length formula for $d$-complete posets states that the $P$-partition generating function for them is given by a product in terms of hook lengths. We give a new proof of the hook length formula using $q$-integrals. The proof is done by a case-by-case analysis consisting of two steps. First, we express the $P$-partition generating function for each case as a $q$-integral and then we evaluate the $q$-integrals. Several $q$-integrals are evaluated using partial fraction expansion identities and others are verified by computer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09109","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":"2026-05-17T23:53:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9cuawuqfBxm91x8pj9DZW8mIs/Y+JWvAvj930vdpJPuLV9bC1szYtKzZ52Fv0JV+9Z/uO0xJc2JUbZkpq/iFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:48:29.003063Z"},"content_sha256":"bbcc77307376f69dba23e146d2da945862eea9b949f56970e4606d8e69b7b5f2","schema_version":"1.0","event_id":"sha256:bbcc77307376f69dba23e146d2da945862eea9b949f56970e4606d8e69b7b5f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PEIT5I6H3M77A4LC7GUTZ26VIV/bundle.json","state_url":"https://pith.science/pith/PEIT5I6H3M77A4LC7GUTZ26VIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PEIT5I6H3M77A4LC7GUTZ26VIV/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":"2026-05-25T09:48:29Z","links":{"resolver":"https://pith.science/pith/PEIT5I6H3M77A4LC7GUTZ26VIV","bundle":"https://pith.science/pith/PEIT5I6H3M77A4LC7GUTZ26VIV/bundle.json","state":"https://pith.science/pith/PEIT5I6H3M77A4LC7GUTZ26VIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PEIT5I6H3M77A4LC7GUTZ26VIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PEIT5I6H3M77A4LC7GUTZ26VIV","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":"b58bcc4c71182aeaf385b2fd209c31ba597105e9b7cf2dfc769c0925eca04323","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T04:33:42Z","title_canon_sha256":"3d5a44fa510557c1dd1ca047e4f9b7c3e9ff5b9d8fe5b57e22fab11b85486421"},"schema_version":"1.0","source":{"id":"1708.09109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09109","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09109v2","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09109","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"pith_short_12","alias_value":"PEIT5I6H3M77","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PEIT5I6H3M77A4LC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PEIT5I6H","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:bbcc77307376f69dba23e146d2da945862eea9b949f56970e4606d8e69b7b5f2","target":"graph","created_at":"2026-05-17T23:53:58Z","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 hook length formula for $d$-complete posets states that the $P$-partition generating function for them is given by a product in terms of hook lengths. We give a new proof of the hook length formula using $q$-integrals. The proof is done by a case-by-case analysis consisting of two steps. First, we express the $P$-partition generating function for each case as a $q$-integral and then we evaluate the $q$-integrals. Several $q$-integrals are evaluated using partial fraction expansion identities and others are verified by computer.","authors_text":"Jang Soo Kim, Meesue Yoo","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T04:33:42Z","title":"Hook length property of $d$-complete posets via $q$-integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09109","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":"sha256:42bd85d64fea7640b39d38d077db5a5bf58ba430321fcbe871c063523c7ecb9f","target":"record","created_at":"2026-05-17T23:53:58Z","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":"b58bcc4c71182aeaf385b2fd209c31ba597105e9b7cf2dfc769c0925eca04323","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T04:33:42Z","title_canon_sha256":"3d5a44fa510557c1dd1ca047e4f9b7c3e9ff5b9d8fe5b57e22fab11b85486421"},"schema_version":"1.0","source":{"id":"1708.09109","kind":"arxiv","version":2}},"canonical_sha256":"79113ea3c7db3ff07162f9a93cebd545446f17642f3eacf9b6e24f3f217ecd21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79113ea3c7db3ff07162f9a93cebd545446f17642f3eacf9b6e24f3f217ecd21","first_computed_at":"2026-05-17T23:53:58.073850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:58.073850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p65D1oQ94WlmGh1t7VS6bwgjqRz0993YnEmKf2UXSsjOpn4MGXlhYok6lGfNwUj01I7qLXr+ya1j9/tWV5g7Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:58.074544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42bd85d64fea7640b39d38d077db5a5bf58ba430321fcbe871c063523c7ecb9f","sha256:bbcc77307376f69dba23e146d2da945862eea9b949f56970e4606d8e69b7b5f2"],"state_sha256":"123e21209adf0acb9844c6364410a712925fb3fe503aa87b409304ed9ea9174f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eIemIZS9EGYzclEk89FAW3+R4Cxv8DUeGtOBJqa5KVqqp7fUrx6svRp2lHDFY8qHQBnP0CFcWbmy/fm30tHFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:48:29.005403Z","bundle_sha256":"8e08ef2856252318ea242ddb844ca8879aab43a08b6d166487a2705ac6e703bd"}}