{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:MFLHPGSJTW2UI3XL2CU6TQYLL3","short_pith_number":"pith:MFLHPGSJ","canonical_record":{"source":{"id":"2208.09773","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-08-21T01:20:41Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"38b29c4f10772473460fd25ef71f13949de18c7522faec723b93d4670982df01","abstract_canon_sha256":"9a46ad363a42edfcd14c72732b6ec569d440eb12e59372949b6cceae360c751c"},"schema_version":"1.0"},"canonical_sha256":"6156779a499db5446eebd0a9e9c30b5ec0d8fcb98e6645c42498622869b6e33c","source":{"kind":"arxiv","id":"2208.09773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.09773","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"2208.09773v1","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.09773","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"MFLHPGSJTW2U","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"MFLHPGSJTW2UI3XL","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"MFLHPGSJ","created_at":"2026-07-05T04:50:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:MFLHPGSJTW2UI3XL2CU6TQYLL3","target":"record","payload":{"canonical_record":{"source":{"id":"2208.09773","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-08-21T01:20:41Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"38b29c4f10772473460fd25ef71f13949de18c7522faec723b93d4670982df01","abstract_canon_sha256":"9a46ad363a42edfcd14c72732b6ec569d440eb12e59372949b6cceae360c751c"},"schema_version":"1.0"},"canonical_sha256":"6156779a499db5446eebd0a9e9c30b5ec0d8fcb98e6645c42498622869b6e33c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:50:21.879357Z","signature_b64":"G6PZKw0fxt0Zr9z2g+xtul9x+ivCVt42JyxW77lzLF9mLNhmC7LvL8k5Da9Bc9/80zrYWvaHr22j8DWAfeWZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6156779a499db5446eebd0a9e9c30b5ec0d8fcb98e6645c42498622869b6e33c","last_reissued_at":"2026-07-05T04:50:21.878948Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:50:21.878948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.09773","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":"2026-07-05T04:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOBeURPZ/J9BStZ/BrE5i2UUUx75BcXEB5YPjqIF3TEfoHMiWlJQiwXJvDvWqpfroSU1IYBgiBAnK3RzOOVTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:52:20.492301Z"},"content_sha256":"bb4f831afb9f0cef6e6dd156fb6ee86ccaa3d8c8528f08735d31bc12bfb04050","schema_version":"1.0","event_id":"sha256:bb4f831afb9f0cef6e6dd156fb6ee86ccaa3d8c8528f08735d31bc12bfb04050"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:MFLHPGSJTW2UI3XL2CU6TQYLL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Skew Howe duality for Types $\\mathbf{BD}$ via $q$-Clifford algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Willie Aboumrad","submitted_at":"2022-08-21T01:20:41Z","abstract_excerpt":"We extend a quantized skew Howe duality result for Type $\\mathbf{A}$ algebras to orthogonal types via a seesaw. We develop an operator commutant version of the First Fundamental Theorem of invariant theory for $U_q(\\mathfrak{so}_n)$ using a double centralizer property inside a quantized Clifford algebra. We obtain a multiplicity-free decomposition of tensor powers of the $U_q(\\mathfrak{so}_{2n})$ spin representation by explicitly computing joint highest weights with respect to an action of $U_q(\\mathfrak{so}_{2n}) \\otimes U_q'(\\mathfrak{so}_m)$. Clifford algebras are an essential feature of ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09773","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.09773/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sDpEBgxoQo65dhZV6lEcWTLBpSR6RWF0WB7xSAtFM8UyBI0glw8qAG9+N7m+zg9aiJpV5IK2NyxdveeEF8x8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:52:20.492799Z"},"content_sha256":"4ccd51c1b5045bb7704a5395f20009d5a76b088b124c87be2b113198e5881ab3","schema_version":"1.0","event_id":"sha256:4ccd51c1b5045bb7704a5395f20009d5a76b088b124c87be2b113198e5881ab3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFLHPGSJTW2UI3XL2CU6TQYLL3/bundle.json","state_url":"https://pith.science/pith/MFLHPGSJTW2UI3XL2CU6TQYLL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFLHPGSJTW2UI3XL2CU6TQYLL3/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":"2026-08-16T15:52:20Z","links":{"resolver":"https://pith.science/pith/MFLHPGSJTW2UI3XL2CU6TQYLL3","bundle":"https://pith.science/pith/MFLHPGSJTW2UI3XL2CU6TQYLL3/bundle.json","state":"https://pith.science/pith/MFLHPGSJTW2UI3XL2CU6TQYLL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFLHPGSJTW2UI3XL2CU6TQYLL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:MFLHPGSJTW2UI3XL2CU6TQYLL3","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":"9a46ad363a42edfcd14c72732b6ec569d440eb12e59372949b6cceae360c751c","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-08-21T01:20:41Z","title_canon_sha256":"38b29c4f10772473460fd25ef71f13949de18c7522faec723b93d4670982df01"},"schema_version":"1.0","source":{"id":"2208.09773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.09773","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"2208.09773v1","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.09773","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"MFLHPGSJTW2U","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"MFLHPGSJTW2UI3XL","created_at":"2026-07-05T04:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"MFLHPGSJ","created_at":"2026-07-05T04:50:21Z"}],"graph_snapshots":[{"event_id":"sha256:4ccd51c1b5045bb7704a5395f20009d5a76b088b124c87be2b113198e5881ab3","target":"graph","created_at":"2026-07-05T04:50:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.09773/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend a quantized skew Howe duality result for Type $\\mathbf{A}$ algebras to orthogonal types via a seesaw. We develop an operator commutant version of the First Fundamental Theorem of invariant theory for $U_q(\\mathfrak{so}_n)$ using a double centralizer property inside a quantized Clifford algebra. We obtain a multiplicity-free decomposition of tensor powers of the $U_q(\\mathfrak{so}_{2n})$ spin representation by explicitly computing joint highest weights with respect to an action of $U_q(\\mathfrak{so}_{2n}) \\otimes U_q'(\\mathfrak{so}_m)$. Clifford algebras are an essential feature of ou","authors_text":"Willie Aboumrad","cross_cats":["math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-08-21T01:20:41Z","title":"Skew Howe duality for Types $\\mathbf{BD}$ via $q$-Clifford algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09773","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:bb4f831afb9f0cef6e6dd156fb6ee86ccaa3d8c8528f08735d31bc12bfb04050","target":"record","created_at":"2026-07-05T04:50:21Z","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":"9a46ad363a42edfcd14c72732b6ec569d440eb12e59372949b6cceae360c751c","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-08-21T01:20:41Z","title_canon_sha256":"38b29c4f10772473460fd25ef71f13949de18c7522faec723b93d4670982df01"},"schema_version":"1.0","source":{"id":"2208.09773","kind":"arxiv","version":1}},"canonical_sha256":"6156779a499db5446eebd0a9e9c30b5ec0d8fcb98e6645c42498622869b6e33c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6156779a499db5446eebd0a9e9c30b5ec0d8fcb98e6645c42498622869b6e33c","first_computed_at":"2026-07-05T04:50:21.878948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:50:21.878948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G6PZKw0fxt0Zr9z2g+xtul9x+ivCVt42JyxW77lzLF9mLNhmC7LvL8k5Da9Bc9/80zrYWvaHr22j8DWAfeWZAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:50:21.879357Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.09773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb4f831afb9f0cef6e6dd156fb6ee86ccaa3d8c8528f08735d31bc12bfb04050","sha256:4ccd51c1b5045bb7704a5395f20009d5a76b088b124c87be2b113198e5881ab3"],"state_sha256":"e074d8c08c9e04e2c371b62a972815128c2f52cf8936d14afdf57022cb271c51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/780X+xG+zNAZWEggcVjldWpod65IISlhWRz/0p5jMp7/yiqJ2nTgVLisSZzXzYfkHYOq5rL0y5yv9QEsmWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:52:20.496568Z","bundle_sha256":"a2c4e8c8ded9af6b81730f72c23bac174987d5e20bbfb75de09b014c1baafa53"}}