{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BGDAHWW3P6YHEC4S7FRVEFPGI7","short_pith_number":"pith:BGDAHWW3","canonical_record":{"source":{"id":"1906.07146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-17T17:41:34Z","cross_cats_sorted":[],"title_canon_sha256":"482812fb33c2880223446d9eb1fe258037ece234053c6d186f029db7d94ca513","abstract_canon_sha256":"172f95172c8e6c641099bfe8e81065c6c1c800b3611c2e4475085f3ed77f9ba2"},"schema_version":"1.0"},"canonical_sha256":"098603dadb7fb0720b92f9635215e647da0dea411aabdbb9360da2296074b22b","source":{"kind":"arxiv","id":"1906.07146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.07146","created_at":"2026-05-17T23:43:11Z"},{"alias_kind":"arxiv_version","alias_value":"1906.07146v1","created_at":"2026-05-17T23:43:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07146","created_at":"2026-05-17T23:43:11Z"},{"alias_kind":"pith_short_12","alias_value":"BGDAHWW3P6YH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BGDAHWW3P6YHEC4S","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BGDAHWW3","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BGDAHWW3P6YHEC4S7FRVEFPGI7","target":"record","payload":{"canonical_record":{"source":{"id":"1906.07146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-17T17:41:34Z","cross_cats_sorted":[],"title_canon_sha256":"482812fb33c2880223446d9eb1fe258037ece234053c6d186f029db7d94ca513","abstract_canon_sha256":"172f95172c8e6c641099bfe8e81065c6c1c800b3611c2e4475085f3ed77f9ba2"},"schema_version":"1.0"},"canonical_sha256":"098603dadb7fb0720b92f9635215e647da0dea411aabdbb9360da2296074b22b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:11.740030Z","signature_b64":"zmitZ9anIVWurDynCKA/3eA/fWkHIOb8RQ017FEuDacLe9UasTe4CxMc8c0F9Aro2qEkU10sC0+lvrd1020kBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"098603dadb7fb0720b92f9635215e647da0dea411aabdbb9360da2296074b22b","last_reissued_at":"2026-05-17T23:43:11.739529Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:11.739529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.07146","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":"2026-05-17T23:43:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CptLtB8AaEE0bPIiKMmZNiVnPZsc+9GftRFX0HijTSwNzug8cpGx3Rc5Tz6mleHtsJQgJESO4wnZQrLLNCLbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:43:50.969871Z"},"content_sha256":"ce179676d75f3b7d91d888b1acccb9ce2060c9fce1bcf025310d4819862ff96c","schema_version":"1.0","event_id":"sha256:ce179676d75f3b7d91d888b1acccb9ce2060c9fce1bcf025310d4819862ff96c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BGDAHWW3P6YHEC4S7FRVEFPGI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolating between promotion and the long cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bruce W. Westbury","submitted_at":"2019-06-17T17:41:34Z","abstract_excerpt":"We give a new proof of the cyclic sieving phenomena for promotion on rectangular standard tableaux. This uses an action of the cactus groups in the seminormal bases of the irreducible representations of the Hecke algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07146","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":"2026-05-17T23:43:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCn1bHti+nOKgR4VFZSU52L2jFyeLXVIBVUUD9cl1/LiiYqkrIIkmDr7njT0IFw13OhiUigLuNEKTzQaBCqcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:43:50.970219Z"},"content_sha256":"a75ede0432fa692e690dc4139276132ae2828d79761cce6558dd6cf83639bba9","schema_version":"1.0","event_id":"sha256:a75ede0432fa692e690dc4139276132ae2828d79761cce6558dd6cf83639bba9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGDAHWW3P6YHEC4S7FRVEFPGI7/bundle.json","state_url":"https://pith.science/pith/BGDAHWW3P6YHEC4S7FRVEFPGI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGDAHWW3P6YHEC4S7FRVEFPGI7/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":"2026-06-04T22:43:50Z","links":{"resolver":"https://pith.science/pith/BGDAHWW3P6YHEC4S7FRVEFPGI7","bundle":"https://pith.science/pith/BGDAHWW3P6YHEC4S7FRVEFPGI7/bundle.json","state":"https://pith.science/pith/BGDAHWW3P6YHEC4S7FRVEFPGI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGDAHWW3P6YHEC4S7FRVEFPGI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BGDAHWW3P6YHEC4S7FRVEFPGI7","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":"172f95172c8e6c641099bfe8e81065c6c1c800b3611c2e4475085f3ed77f9ba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-17T17:41:34Z","title_canon_sha256":"482812fb33c2880223446d9eb1fe258037ece234053c6d186f029db7d94ca513"},"schema_version":"1.0","source":{"id":"1906.07146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.07146","created_at":"2026-05-17T23:43:11Z"},{"alias_kind":"arxiv_version","alias_value":"1906.07146v1","created_at":"2026-05-17T23:43:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07146","created_at":"2026-05-17T23:43:11Z"},{"alias_kind":"pith_short_12","alias_value":"BGDAHWW3P6YH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BGDAHWW3P6YHEC4S","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BGDAHWW3","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:a75ede0432fa692e690dc4139276132ae2828d79761cce6558dd6cf83639bba9","target":"graph","created_at":"2026-05-17T23:43:11Z","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 give a new proof of the cyclic sieving phenomena for promotion on rectangular standard tableaux. This uses an action of the cactus groups in the seminormal bases of the irreducible representations of the Hecke algebras.","authors_text":"Bruce W. Westbury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-17T17:41:34Z","title":"Interpolating between promotion and the long cycle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07146","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:ce179676d75f3b7d91d888b1acccb9ce2060c9fce1bcf025310d4819862ff96c","target":"record","created_at":"2026-05-17T23:43:11Z","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":"172f95172c8e6c641099bfe8e81065c6c1c800b3611c2e4475085f3ed77f9ba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-17T17:41:34Z","title_canon_sha256":"482812fb33c2880223446d9eb1fe258037ece234053c6d186f029db7d94ca513"},"schema_version":"1.0","source":{"id":"1906.07146","kind":"arxiv","version":1}},"canonical_sha256":"098603dadb7fb0720b92f9635215e647da0dea411aabdbb9360da2296074b22b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"098603dadb7fb0720b92f9635215e647da0dea411aabdbb9360da2296074b22b","first_computed_at":"2026-05-17T23:43:11.739529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:11.739529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zmitZ9anIVWurDynCKA/3eA/fWkHIOb8RQ017FEuDacLe9UasTe4CxMc8c0F9Aro2qEkU10sC0+lvrd1020kBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:11.740030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.07146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce179676d75f3b7d91d888b1acccb9ce2060c9fce1bcf025310d4819862ff96c","sha256:a75ede0432fa692e690dc4139276132ae2828d79761cce6558dd6cf83639bba9"],"state_sha256":"fb636d748e48a6c6c5de3f91bbe603a7c37ab51c84627267897f201331e34581"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nKrSU9pK3CUDbI7IVI6zv1SNKd5hafZXs1SZSnXXTfC2UWKshjNlxcyPw/95a+CVY4NLvOmgoY2btH4UKCzkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:43:50.972234Z","bundle_sha256":"618246306a6bc494737e40f248fa8266fb7e18f033abdf5781949158dcaadd67"}}