{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YSEHVVRR3PMMSAZXMEWVUD6ZEI","short_pith_number":"pith:YSEHVVRR","canonical_record":{"source":{"id":"1403.5509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-21T16:22:43Z","cross_cats_sorted":[],"title_canon_sha256":"201afa1c44672b1a623ebc706b8804d65856a65e73c812df33b17e51f7b8d4c9","abstract_canon_sha256":"5c5d54fdc9581acf8608d7a364618829524a823efa7a90be4e25daec46ca8fc5"},"schema_version":"1.0"},"canonical_sha256":"c4887ad631dbd8c90337612d5a0fd922213a254b1f1a0153bbab1a2afe73ffcc","source":{"kind":"arxiv","id":"1403.5509","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5509","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5509v2","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5509","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"YSEHVVRR3PMM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YSEHVVRR3PMMSAZX","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YSEHVVRR","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YSEHVVRR3PMMSAZXMEWVUD6ZEI","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-21T16:22:43Z","cross_cats_sorted":[],"title_canon_sha256":"201afa1c44672b1a623ebc706b8804d65856a65e73c812df33b17e51f7b8d4c9","abstract_canon_sha256":"5c5d54fdc9581acf8608d7a364618829524a823efa7a90be4e25daec46ca8fc5"},"schema_version":"1.0"},"canonical_sha256":"c4887ad631dbd8c90337612d5a0fd922213a254b1f1a0153bbab1a2afe73ffcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:18.276809Z","signature_b64":"uSgpDnPsF0xxNPX1xL/hyopaV9PC5UMs2Oqqf929BcbHVAmZTBg1nHBjVYASZZtwB2qk4nUirFcdIk1lPlKGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4887ad631dbd8c90337612d5a0fd922213a254b1f1a0153bbab1a2afe73ffcc","last_reissued_at":"2026-05-18T00:42:18.276142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:18.276142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5509","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":"2026-05-18T00:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5B2Co4p6pMrVwRu6GX4yQPQ7Rd+sSMrxhJqAXXzp2OXeCbV9zbXng3Y3YcEXCsNTV4YuX7aITh5GKMCL22JDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:54:59.029149Z"},"content_sha256":"1c4c221b644561a909b03868583bbab34e87e82e2f3d5559e39d6bdcaaed3600","schema_version":"1.0","event_id":"sha256:1c4c221b644561a909b03868583bbab34e87e82e2f3d5559e39d6bdcaaed3600"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YSEHVVRR3PMMSAZXMEWVUD6ZEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schur-Weyl duality for Deligne categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Inna Entova-Aizenbud","submitted_at":"2014-03-21T16:22:43Z","abstract_excerpt":"This paper gives an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space V (i.e. a vector space V with a distinguished non-zero vector 1), we give a definition of a complex tensor power of V. This is an Ind-object of the Deligne category Rep(S_t), equipped with a natural action of gl(V).\n  This construction allows us to describe a duality between the abelian envelope of the category Rep(S_t) and a localization of the parabolic category O for gl(V) associated with the pair (V, 1).\n  In particular, we obtain an exact co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5509","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":"2026-05-18T00:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2y3QqyUNAKIgvyglnjgj05VjS/MiF1uDWUie1Tc+Rm5PG3+9EzdNr4sSNAW5pvJkcbq0QTX3EdX9ozaPvexRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:54:59.029510Z"},"content_sha256":"8c03b4472a7e1a3e62fbbe6a0c92d87eff9e3daa6691561676c08ce409c78e5c","schema_version":"1.0","event_id":"sha256:8c03b4472a7e1a3e62fbbe6a0c92d87eff9e3daa6691561676c08ce409c78e5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSEHVVRR3PMMSAZXMEWVUD6ZEI/bundle.json","state_url":"https://pith.science/pith/YSEHVVRR3PMMSAZXMEWVUD6ZEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSEHVVRR3PMMSAZXMEWVUD6ZEI/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":"2026-05-30T03:54:59Z","links":{"resolver":"https://pith.science/pith/YSEHVVRR3PMMSAZXMEWVUD6ZEI","bundle":"https://pith.science/pith/YSEHVVRR3PMMSAZXMEWVUD6ZEI/bundle.json","state":"https://pith.science/pith/YSEHVVRR3PMMSAZXMEWVUD6ZEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSEHVVRR3PMMSAZXMEWVUD6ZEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YSEHVVRR3PMMSAZXMEWVUD6ZEI","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":"5c5d54fdc9581acf8608d7a364618829524a823efa7a90be4e25daec46ca8fc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-21T16:22:43Z","title_canon_sha256":"201afa1c44672b1a623ebc706b8804d65856a65e73c812df33b17e51f7b8d4c9"},"schema_version":"1.0","source":{"id":"1403.5509","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5509","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5509v2","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5509","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"YSEHVVRR3PMM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YSEHVVRR3PMMSAZX","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YSEHVVRR","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:8c03b4472a7e1a3e62fbbe6a0c92d87eff9e3daa6691561676c08ce409c78e5c","target":"graph","created_at":"2026-05-18T00:42:18Z","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":"This paper gives an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space V (i.e. a vector space V with a distinguished non-zero vector 1), we give a definition of a complex tensor power of V. This is an Ind-object of the Deligne category Rep(S_t), equipped with a natural action of gl(V).\n  This construction allows us to describe a duality between the abelian envelope of the category Rep(S_t) and a localization of the parabolic category O for gl(V) associated with the pair (V, 1).\n  In particular, we obtain an exact co","authors_text":"Inna Entova-Aizenbud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-21T16:22:43Z","title":"Schur-Weyl duality for Deligne categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5509","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":"sha256:1c4c221b644561a909b03868583bbab34e87e82e2f3d5559e39d6bdcaaed3600","target":"record","created_at":"2026-05-18T00:42:18Z","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":"5c5d54fdc9581acf8608d7a364618829524a823efa7a90be4e25daec46ca8fc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-21T16:22:43Z","title_canon_sha256":"201afa1c44672b1a623ebc706b8804d65856a65e73c812df33b17e51f7b8d4c9"},"schema_version":"1.0","source":{"id":"1403.5509","kind":"arxiv","version":2}},"canonical_sha256":"c4887ad631dbd8c90337612d5a0fd922213a254b1f1a0153bbab1a2afe73ffcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4887ad631dbd8c90337612d5a0fd922213a254b1f1a0153bbab1a2afe73ffcc","first_computed_at":"2026-05-18T00:42:18.276142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:18.276142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uSgpDnPsF0xxNPX1xL/hyopaV9PC5UMs2Oqqf929BcbHVAmZTBg1nHBjVYASZZtwB2qk4nUirFcdIk1lPlKGBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:18.276809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5509","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c4c221b644561a909b03868583bbab34e87e82e2f3d5559e39d6bdcaaed3600","sha256:8c03b4472a7e1a3e62fbbe6a0c92d87eff9e3daa6691561676c08ce409c78e5c"],"state_sha256":"0f322c3d76662fbadef1f0315d916e7c91e17c9251832f7ade174f4d67484412"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/fHEqDD3gSa89eT6NT0XfidKrY7WHKBel452txt7tllyXo/Qnc2J2AdMZWnDai+AkZzGZuN8gx3Lav1GuBHCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:54:59.032565Z","bundle_sha256":"e7e7f8fb0b29c9179b55d2627b136f6d6a87f6f902185bd5ed5bb76ab8549e2d"}}