{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:PN5W4AEP54TDKGZZVTB5A6RCO2","short_pith_number":"pith:PN5W4AEP","canonical_record":{"source":{"id":"math/0008093","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2000-08-13T09:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"2b7dd1da389d8fe3eb88dfd1c7466a44053fe05b7b0ffcc1645b2c1a0715af46","abstract_canon_sha256":"229d23ec155a1c5b0c0b0a96e78635d28c9b645a746387d06d0cd40fceedf0d5"},"schema_version":"1.0"},"canonical_sha256":"7b7b6e008fef26351b39acc3d07a2276be9da23aeb3bbbedc25b481df8689101","source":{"kind":"arxiv","id":"math/0008093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0008093","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0008093v1","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0008093","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"PN5W4AEP54TD","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"pith_short_16","alias_value":"PN5W4AEP54TDKGZZ","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"pith_short_8","alias_value":"PN5W4AEP","created_at":"2026-07-04T14:34:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:PN5W4AEP54TDKGZZVTB5A6RCO2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0008093","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2000-08-13T09:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"2b7dd1da389d8fe3eb88dfd1c7466a44053fe05b7b0ffcc1645b2c1a0715af46","abstract_canon_sha256":"229d23ec155a1c5b0c0b0a96e78635d28c9b645a746387d06d0cd40fceedf0d5"},"schema_version":"1.0"},"canonical_sha256":"7b7b6e008fef26351b39acc3d07a2276be9da23aeb3bbbedc25b481df8689101","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:38.758435Z","signature_b64":"BI1lCipEsKDZ/+fXvhaX5ycZ1NetspTilOWdMtC8zC8f3ay1TBSPG99V3moPGmNya1BWVhtQ+lkHrWZW5t+kDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b7b6e008fef26351b39acc3d07a2276be9da23aeb3bbbedc25b481df8689101","last_reissued_at":"2026-07-04T14:34:38.758036Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:38.758036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0008093","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":"2026-07-04T14:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Xh2qSxa/Nxy5n2mMc4FSDgJUMCmku04Y6oNmiHsXmxfMbgYermSyXC4Zgo/yijwCda/NEEFd763hknKheMwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T19:44:50.265620Z"},"content_sha256":"2f26899d6b8e73494ef20b4c97532da9503b20931e9ea8574586b0790035157f","schema_version":"1.0","event_id":"sha256:2f26899d6b8e73494ef20b4c97532da9503b20931e9ea8574586b0790035157f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:PN5W4AEP54TDKGZZVTB5A6RCO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Howe Duality for Lie Superalgebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Shun-Jen Cheng, Weiqiang Wang","submitted_at":"2000-08-13T09:16:53Z","abstract_excerpt":"We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicity-free decomposition into irreducible $gl(m|n)$-modules of the symmetric and skew-symmetric algebras of the symmetric square of the natural representation of $gl(m|n)$. In the former case we find as well explicit formulas for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0008093","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/math/0008093/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":"2026-07-04T14:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0CyXe/YBkFhMOPkz6jQf4p4YWyCQT22K4gMUfxGARu5LbLQmJWz92SdAuu7MXa5Qcr+FLWxcxkq7p+8RqJ1YAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T19:44:50.265991Z"},"content_sha256":"8e3bb33f3216d871c1e33f59a177176894c2fd5e628dece8a82382efe95ca799","schema_version":"1.0","event_id":"sha256:8e3bb33f3216d871c1e33f59a177176894c2fd5e628dece8a82382efe95ca799"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PN5W4AEP54TDKGZZVTB5A6RCO2/bundle.json","state_url":"https://pith.science/pith/PN5W4AEP54TDKGZZVTB5A6RCO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PN5W4AEP54TDKGZZVTB5A6RCO2/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":"2026-07-17T19:44:50Z","links":{"resolver":"https://pith.science/pith/PN5W4AEP54TDKGZZVTB5A6RCO2","bundle":"https://pith.science/pith/PN5W4AEP54TDKGZZVTB5A6RCO2/bundle.json","state":"https://pith.science/pith/PN5W4AEP54TDKGZZVTB5A6RCO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PN5W4AEP54TDKGZZVTB5A6RCO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:PN5W4AEP54TDKGZZVTB5A6RCO2","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":"229d23ec155a1c5b0c0b0a96e78635d28c9b645a746387d06d0cd40fceedf0d5","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2000-08-13T09:16:53Z","title_canon_sha256":"2b7dd1da389d8fe3eb88dfd1c7466a44053fe05b7b0ffcc1645b2c1a0715af46"},"schema_version":"1.0","source":{"id":"math/0008093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0008093","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0008093v1","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0008093","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"PN5W4AEP54TD","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"pith_short_16","alias_value":"PN5W4AEP54TDKGZZ","created_at":"2026-07-04T14:34:38Z"},{"alias_kind":"pith_short_8","alias_value":"PN5W4AEP","created_at":"2026-07-04T14:34:38Z"}],"graph_snapshots":[{"event_id":"sha256:8e3bb33f3216d871c1e33f59a177176894c2fd5e628dece8a82382efe95ca799","target":"graph","created_at":"2026-07-04T14:34:38Z","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/math/0008093/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicity-free decomposition into irreducible $gl(m|n)$-modules of the symmetric and skew-symmetric algebras of the symmetric square of the natural representation of $gl(m|n)$. In the former case we find as well explicit formulas for","authors_text":"Shun-Jen Cheng, Weiqiang Wang","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2000-08-13T09:16:53Z","title":"Howe Duality for Lie Superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0008093","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":"sha256:2f26899d6b8e73494ef20b4c97532da9503b20931e9ea8574586b0790035157f","target":"record","created_at":"2026-07-04T14:34:38Z","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":"229d23ec155a1c5b0c0b0a96e78635d28c9b645a746387d06d0cd40fceedf0d5","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2000-08-13T09:16:53Z","title_canon_sha256":"2b7dd1da389d8fe3eb88dfd1c7466a44053fe05b7b0ffcc1645b2c1a0715af46"},"schema_version":"1.0","source":{"id":"math/0008093","kind":"arxiv","version":1}},"canonical_sha256":"7b7b6e008fef26351b39acc3d07a2276be9da23aeb3bbbedc25b481df8689101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b7b6e008fef26351b39acc3d07a2276be9da23aeb3bbbedc25b481df8689101","first_computed_at":"2026-07-04T14:34:38.758036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:38.758036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BI1lCipEsKDZ/+fXvhaX5ycZ1NetspTilOWdMtC8zC8f3ay1TBSPG99V3moPGmNya1BWVhtQ+lkHrWZW5t+kDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:38.758435Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0008093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f26899d6b8e73494ef20b4c97532da9503b20931e9ea8574586b0790035157f","sha256:8e3bb33f3216d871c1e33f59a177176894c2fd5e628dece8a82382efe95ca799"],"state_sha256":"491ccf814f25e2f432f9bd0a8d1b1d27d0f33d5341de080d4d922c68a15e5912"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4gVKdEIy8GuVOREZC82+agxAuiIH8T8JnpX7o00MjuheDl5HJ3UY4efc4PS2g4n+Vk3KMa4ZboW1DQPo3dfjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T19:44:50.268568Z","bundle_sha256":"62d69cad77397210fe16b66cf98d0d30c0b734d2d614f67f76fdc081199ef8c9"}}