{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JXFJFW4BTDVCNKDYVCCUMNNUNJ","short_pith_number":"pith:JXFJFW4B","canonical_record":{"source":{"id":"1711.02337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-07T08:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"6f775327ede039ae6b4590007038298ccf6eee3413277dea1818149d929be4c7","abstract_canon_sha256":"7afa427d9b74fa14548114020abd9d6d2ef0db5782b11ebdc4562242a36407f6"},"schema_version":"1.0"},"canonical_sha256":"4dca92db8198ea26a878a8854635b46a59c0f8ac02fc17c9aaf9edaf0406ce64","source":{"kind":"arxiv","id":"1711.02337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02337","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02337v1","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02337","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"JXFJFW4BTDVC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JXFJFW4BTDVCNKDY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JXFJFW4B","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JXFJFW4BTDVCNKDYVCCUMNNUNJ","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-07T08:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"6f775327ede039ae6b4590007038298ccf6eee3413277dea1818149d929be4c7","abstract_canon_sha256":"7afa427d9b74fa14548114020abd9d6d2ef0db5782b11ebdc4562242a36407f6"},"schema_version":"1.0"},"canonical_sha256":"4dca92db8198ea26a878a8854635b46a59c0f8ac02fc17c9aaf9edaf0406ce64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:08.196572Z","signature_b64":"d+3wGCKJtOqGC1LooP8MBaR1HdSComGa9cT2OoS0qqyI083BxlxPGK5izWoG2fz6Z97a0XRQBIWULvBMmKGiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dca92db8198ea26a878a8854635b46a59c0f8ac02fc17c9aaf9edaf0406ce64","last_reissued_at":"2026-05-18T00:31:08.195838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:08.195838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02337","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":"2026-05-18T00:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ic506trq4quIlbBM9/EAy9VvP7VfdGYTKoV0jeXssCToGEUUgXv0KloCSMPej8kAzSqeOLxKO7vdtDZzqO5MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:25:33.165558Z"},"content_sha256":"85f29db6af330dbfc17cbb31ace10c3b5ca0d8af9bd38328e607f49b18ad2dad","schema_version":"1.0","event_id":"sha256:85f29db6af330dbfc17cbb31ace10c3b5ca0d8af9bd38328e607f49b18ad2dad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JXFJFW4BTDVCNKDYVCCUMNNUNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reverse plane partitions of skew staircase shapes and $q$-Euler numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Byung-Hak Hwang, Jang Soo Kim, Meesue Yoo, Sun-mi Yun","submitted_at":"2017-11-07T08:43:12Z","abstract_excerpt":"Recently, Naruse discovered a hook length formula for the number of standard Young tableaux of a skew shape. Morales, Pak and Panova found two $q$-analogs of Naruse's hook length formula over semistandard Young tableaux (SSYTs) and reverse plane partitions (RPPs). As an application of their formula, they expressed certain $q$-Euler numbers, which are generating functions for SSYTs and RPPs of a zigzag border strip, in terms of weighted Dyck paths. They found a determinantal formula for the generating function for SSYTs of a skew staircase shape and proposed two conjectures related to RPPs of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02337","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":"2026-05-18T00:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DvQqu/7ExQQ37A6CZk1+Cd6EKyJcZMO6wGvP25+9ZrGEOGoYTuvOLgFgczNq89R5n5hWCWsKDLCI3UTQKWeRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:25:33.166300Z"},"content_sha256":"7bf8b6eda7ec2d75369b8fa636a64b43b36d892bf9e4ddcff3b376974717b4bc","schema_version":"1.0","event_id":"sha256:7bf8b6eda7ec2d75369b8fa636a64b43b36d892bf9e4ddcff3b376974717b4bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JXFJFW4BTDVCNKDYVCCUMNNUNJ/bundle.json","state_url":"https://pith.science/pith/JXFJFW4BTDVCNKDYVCCUMNNUNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JXFJFW4BTDVCNKDYVCCUMNNUNJ/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":"2026-05-25T15:25:33Z","links":{"resolver":"https://pith.science/pith/JXFJFW4BTDVCNKDYVCCUMNNUNJ","bundle":"https://pith.science/pith/JXFJFW4BTDVCNKDYVCCUMNNUNJ/bundle.json","state":"https://pith.science/pith/JXFJFW4BTDVCNKDYVCCUMNNUNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JXFJFW4BTDVCNKDYVCCUMNNUNJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JXFJFW4BTDVCNKDYVCCUMNNUNJ","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":"7afa427d9b74fa14548114020abd9d6d2ef0db5782b11ebdc4562242a36407f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-07T08:43:12Z","title_canon_sha256":"6f775327ede039ae6b4590007038298ccf6eee3413277dea1818149d929be4c7"},"schema_version":"1.0","source":{"id":"1711.02337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02337","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02337v1","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02337","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"JXFJFW4BTDVC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JXFJFW4BTDVCNKDY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JXFJFW4B","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:7bf8b6eda7ec2d75369b8fa636a64b43b36d892bf9e4ddcff3b376974717b4bc","target":"graph","created_at":"2026-05-18T00:31:08Z","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":"Recently, Naruse discovered a hook length formula for the number of standard Young tableaux of a skew shape. Morales, Pak and Panova found two $q$-analogs of Naruse's hook length formula over semistandard Young tableaux (SSYTs) and reverse plane partitions (RPPs). As an application of their formula, they expressed certain $q$-Euler numbers, which are generating functions for SSYTs and RPPs of a zigzag border strip, in terms of weighted Dyck paths. They found a determinantal formula for the generating function for SSYTs of a skew staircase shape and proposed two conjectures related to RPPs of t","authors_text":"Byung-Hak Hwang, Jang Soo Kim, Meesue Yoo, Sun-mi Yun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-07T08:43:12Z","title":"Reverse plane partitions of skew staircase shapes and $q$-Euler numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02337","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":"sha256:85f29db6af330dbfc17cbb31ace10c3b5ca0d8af9bd38328e607f49b18ad2dad","target":"record","created_at":"2026-05-18T00:31:08Z","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":"7afa427d9b74fa14548114020abd9d6d2ef0db5782b11ebdc4562242a36407f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-07T08:43:12Z","title_canon_sha256":"6f775327ede039ae6b4590007038298ccf6eee3413277dea1818149d929be4c7"},"schema_version":"1.0","source":{"id":"1711.02337","kind":"arxiv","version":1}},"canonical_sha256":"4dca92db8198ea26a878a8854635b46a59c0f8ac02fc17c9aaf9edaf0406ce64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dca92db8198ea26a878a8854635b46a59c0f8ac02fc17c9aaf9edaf0406ce64","first_computed_at":"2026-05-18T00:31:08.195838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:08.195838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d+3wGCKJtOqGC1LooP8MBaR1HdSComGa9cT2OoS0qqyI083BxlxPGK5izWoG2fz6Z97a0XRQBIWULvBMmKGiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:08.196572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85f29db6af330dbfc17cbb31ace10c3b5ca0d8af9bd38328e607f49b18ad2dad","sha256:7bf8b6eda7ec2d75369b8fa636a64b43b36d892bf9e4ddcff3b376974717b4bc"],"state_sha256":"734fbccdd6dbc59560bdfd37820bad6e8d72ecbaeb7f64e34bcfdac1389b10e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ACKK8+qDojQGrEmcyYujGhiAEwGTGdLp7hKJwGJgpd+Ptvuc4m26/tMOez6bQbiOJ23HbETWoODX8Qvq7dxuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:25:33.170222Z","bundle_sha256":"02b436c052c3aa7a3a57561e9737238aacdfdbd1b2e5b469b20ec1f1531272dd"}}