{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XOCT7HXJZOHSAP3JSWK7ZVLIJ3","short_pith_number":"pith:XOCT7HXJ","canonical_record":{"source":{"id":"1608.08273","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T22:30:27Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"4e89734d1285ab8af61f4c12590a21c1f39265024734fa2e074bc6fbe79f9141","abstract_canon_sha256":"e3f955c854da22793a74e163f191d65aa3625a89aa49541bea5860f56891637f"},"schema_version":"1.0"},"canonical_sha256":"bb853f9ee9cb8f203f699595fcd5684ef550e5adf0a28851b25702978ff1f07e","source":{"kind":"arxiv","id":"1608.08273","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08273","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08273v1","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08273","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"pith_short_12","alias_value":"XOCT7HXJZOHS","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XOCT7HXJZOHSAP3J","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XOCT7HXJ","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XOCT7HXJZOHSAP3JSWK7ZVLIJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08273","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T22:30:27Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"4e89734d1285ab8af61f4c12590a21c1f39265024734fa2e074bc6fbe79f9141","abstract_canon_sha256":"e3f955c854da22793a74e163f191d65aa3625a89aa49541bea5860f56891637f"},"schema_version":"1.0"},"canonical_sha256":"bb853f9ee9cb8f203f699595fcd5684ef550e5adf0a28851b25702978ff1f07e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:19.804560Z","signature_b64":"J8+NnFVaXzvVXh3zBxCndFoKyNhpjydlctbhgeDFKeyoD/Z72Fv76gb8iW+Ls/aNLdQ3O5BIh54PoD9hyrk+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb853f9ee9cb8f203f699595fcd5684ef550e5adf0a28851b25702978ff1f07e","last_reissued_at":"2026-05-18T01:07:19.804062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:19.804062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08273","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":"2026-05-18T01:07:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qX5uOhVqw9EZDrXZsp/eJvm1d9iYWd9yy/MI6VqvObm94Ds6KcAzDJi6eCw/q1mhqpluiT/ggaC4MUgz2BThDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:30:29.402919Z"},"content_sha256":"b7d5e162e0d0979959aa71531c1e45457b86919a84e132683708dd6f04c45476","schema_version":"1.0","event_id":"sha256:b7d5e162e0d0979959aa71531c1e45457b86919a84e132683708dd6f04c45476"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XOCT7HXJZOHSAP3JSWK7ZVLIJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Highest Weights for Categorical Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"David Ben-Zvi, Hendrik Orem, Sam Gunningham","submitted_at":"2016-08-29T22:30:27Z","abstract_excerpt":"We present a criterion for establishing Morita equivalence of monoidal categories, and apply it to the categorical representation theory of reductive groups $G$. We show that the \"de Rham group algebra\" $\\mathcal D(G)$ (the monoidal category of $\\mathcal D$-modules on $G$) is Morita equivalent to the universal Hecke category $\\mathcal D(N \\backslash G/N)$ and to its monodromic variant $\\widetilde{\\mathcal D}(B \\backslash G / B)$. In other words, de Rham $G$-categories, i.e., module categories for $\\mathcal D(G)$, satisfy a \"highest weight theorem\" - they all appear in the decomposition of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08273","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":"2026-05-18T01:07:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yDhIs/JYAdARWV3TJQaxf6hzWy2JsNo8uNzRVNGTxe0uJ1A5j72iGcJs/X6+megSeyYhvYEteV/hZ11cv8/mDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:30:29.403262Z"},"content_sha256":"f8fb087bdcf96e2842c7eef126d64549fb647bfee49f95bdf47d55f30adc3142","schema_version":"1.0","event_id":"sha256:f8fb087bdcf96e2842c7eef126d64549fb647bfee49f95bdf47d55f30adc3142"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XOCT7HXJZOHSAP3JSWK7ZVLIJ3/bundle.json","state_url":"https://pith.science/pith/XOCT7HXJZOHSAP3JSWK7ZVLIJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XOCT7HXJZOHSAP3JSWK7ZVLIJ3/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":"2026-06-08T23:30:29Z","links":{"resolver":"https://pith.science/pith/XOCT7HXJZOHSAP3JSWK7ZVLIJ3","bundle":"https://pith.science/pith/XOCT7HXJZOHSAP3JSWK7ZVLIJ3/bundle.json","state":"https://pith.science/pith/XOCT7HXJZOHSAP3JSWK7ZVLIJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XOCT7HXJZOHSAP3JSWK7ZVLIJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XOCT7HXJZOHSAP3JSWK7ZVLIJ3","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":"e3f955c854da22793a74e163f191d65aa3625a89aa49541bea5860f56891637f","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T22:30:27Z","title_canon_sha256":"4e89734d1285ab8af61f4c12590a21c1f39265024734fa2e074bc6fbe79f9141"},"schema_version":"1.0","source":{"id":"1608.08273","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08273","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08273v1","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08273","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"pith_short_12","alias_value":"XOCT7HXJZOHS","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XOCT7HXJZOHSAP3J","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XOCT7HXJ","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:f8fb087bdcf96e2842c7eef126d64549fb647bfee49f95bdf47d55f30adc3142","target":"graph","created_at":"2026-05-18T01:07:19Z","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 present a criterion for establishing Morita equivalence of monoidal categories, and apply it to the categorical representation theory of reductive groups $G$. We show that the \"de Rham group algebra\" $\\mathcal D(G)$ (the monoidal category of $\\mathcal D$-modules on $G$) is Morita equivalent to the universal Hecke category $\\mathcal D(N \\backslash G/N)$ and to its monodromic variant $\\widetilde{\\mathcal D}(B \\backslash G / B)$. In other words, de Rham $G$-categories, i.e., module categories for $\\mathcal D(G)$, satisfy a \"highest weight theorem\" - they all appear in the decomposition of the ","authors_text":"David Ben-Zvi, Hendrik Orem, Sam Gunningham","cross_cats":["math.AG","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T22:30:27Z","title":"Highest Weights for Categorical Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08273","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:b7d5e162e0d0979959aa71531c1e45457b86919a84e132683708dd6f04c45476","target":"record","created_at":"2026-05-18T01:07:19Z","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":"e3f955c854da22793a74e163f191d65aa3625a89aa49541bea5860f56891637f","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T22:30:27Z","title_canon_sha256":"4e89734d1285ab8af61f4c12590a21c1f39265024734fa2e074bc6fbe79f9141"},"schema_version":"1.0","source":{"id":"1608.08273","kind":"arxiv","version":1}},"canonical_sha256":"bb853f9ee9cb8f203f699595fcd5684ef550e5adf0a28851b25702978ff1f07e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb853f9ee9cb8f203f699595fcd5684ef550e5adf0a28851b25702978ff1f07e","first_computed_at":"2026-05-18T01:07:19.804062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:19.804062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J8+NnFVaXzvVXh3zBxCndFoKyNhpjydlctbhgeDFKeyoD/Z72Fv76gb8iW+Ls/aNLdQ3O5BIh54PoD9hyrk+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:19.804560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08273","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7d5e162e0d0979959aa71531c1e45457b86919a84e132683708dd6f04c45476","sha256:f8fb087bdcf96e2842c7eef126d64549fb647bfee49f95bdf47d55f30adc3142"],"state_sha256":"09431c73d0c4cc0c34fca61d6effb2ede1ccf7a8e5d2851f608726c90e2ee819"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mF+lNkllyGJK/ln3sZNLixxX2i4ldD36quRzUeMFcnbl+qf15j2NcEbhgVmA9ChPH2m5DPZh3WR2oYYAy2XuDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:30:29.405096Z","bundle_sha256":"12387892ee3d72d3329545ddb09421a012bd040229fb7cfde06c9e45132b7c8b"}}