{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KL5RVRXFCH3ESHYVXZYFRN4F5Q","short_pith_number":"pith:KL5RVRXF","canonical_record":{"source":{"id":"1108.4999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-25T03:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"b01477dafaae7423d04ed1e23ccbbb1a118a1cb4d4b6a6b02e5018e80705f0f5","abstract_canon_sha256":"65fc6f56875fc84987a36d82ebc843175d7bba6836db7cb831d1f514291a7014"},"schema_version":"1.0"},"canonical_sha256":"52fb1ac6e511f6491f15be7058b785ec0d11309781a24e24aa24676249e059ea","source":{"kind":"arxiv","id":"1108.4999","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4999","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4999v2","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4999","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"KL5RVRXFCH3E","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KL5RVRXFCH3ESHYV","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KL5RVRXF","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KL5RVRXFCH3ESHYVXZYFRN4F5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-25T03:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"b01477dafaae7423d04ed1e23ccbbb1a118a1cb4d4b6a6b02e5018e80705f0f5","abstract_canon_sha256":"65fc6f56875fc84987a36d82ebc843175d7bba6836db7cb831d1f514291a7014"},"schema_version":"1.0"},"canonical_sha256":"52fb1ac6e511f6491f15be7058b785ec0d11309781a24e24aa24676249e059ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:38.776900Z","signature_b64":"+vOFLBwHbxn7QN8PEcMJRzpgsJaB3CTndJpOGsRdCghYKU30fFm4PYUtLiNdUXcEI18gPOxTvDQ+bIj5ReBaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52fb1ac6e511f6491f15be7058b785ec0d11309781a24e24aa24676249e059ea","last_reissued_at":"2026-05-18T03:04:38.776023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:38.776023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4999","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":"2026-05-18T03:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QN7AWmWUuSTfTshH9QvHZerytctF6N06RVvX13ieIztkoa59Ocw2yW7v9YDZgqtWMyqOBeHlkEtm7QH0G85iBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:27:55.647356Z"},"content_sha256":"f993cc1dc04a8dde0ad22cffa6ea0fc185cf681779bde11d88177b2e5d41495b","schema_version":"1.0","event_id":"sha256:f993cc1dc04a8dde0ad22cffa6ea0fc185cf681779bde11d88177b2e5d41495b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KL5RVRXFCH3ESHYVXZYFRN4F5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Satake, Springer correspondence, and small representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anthony Henderson, Pramod N. Achar","submitted_at":"2011-08-25T03:05:55Z","abstract_excerpt":"For a simply-connected simple algebraic group $G$ over $\\C$, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$, generalizing a well-known fact about $GL_n$. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number of known facts (mostly due to Broer and Reeder) about small representations of the dual group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4999","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":"2026-05-18T03:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PcTH7vLsJNh+fpN4hC64fY1lFHNP/J0A2gywh7NwLZQMp6ZPbORMtT29oElfwIbUJ9164IHUNCAuepN/HslCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:27:55.648072Z"},"content_sha256":"9651f2e90760f7d3eb950f874ef845a7c3be72616f7bebf5a21c6437df07d76f","schema_version":"1.0","event_id":"sha256:9651f2e90760f7d3eb950f874ef845a7c3be72616f7bebf5a21c6437df07d76f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KL5RVRXFCH3ESHYVXZYFRN4F5Q/bundle.json","state_url":"https://pith.science/pith/KL5RVRXFCH3ESHYVXZYFRN4F5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KL5RVRXFCH3ESHYVXZYFRN4F5Q/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":"2026-06-06T20:27:55Z","links":{"resolver":"https://pith.science/pith/KL5RVRXFCH3ESHYVXZYFRN4F5Q","bundle":"https://pith.science/pith/KL5RVRXFCH3ESHYVXZYFRN4F5Q/bundle.json","state":"https://pith.science/pith/KL5RVRXFCH3ESHYVXZYFRN4F5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KL5RVRXFCH3ESHYVXZYFRN4F5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KL5RVRXFCH3ESHYVXZYFRN4F5Q","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":"65fc6f56875fc84987a36d82ebc843175d7bba6836db7cb831d1f514291a7014","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-25T03:05:55Z","title_canon_sha256":"b01477dafaae7423d04ed1e23ccbbb1a118a1cb4d4b6a6b02e5018e80705f0f5"},"schema_version":"1.0","source":{"id":"1108.4999","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4999","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4999v2","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4999","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"KL5RVRXFCH3E","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KL5RVRXFCH3ESHYV","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KL5RVRXF","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:9651f2e90760f7d3eb950f874ef845a7c3be72616f7bebf5a21c6437df07d76f","target":"graph","created_at":"2026-05-18T03:04:38Z","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"},"paper":{"abstract_excerpt":"For a simply-connected simple algebraic group $G$ over $\\C$, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$, generalizing a well-known fact about $GL_n$. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number of known facts (mostly due to Broer and Reeder) about small representations of the dual group.","authors_text":"Anthony Henderson, Pramod N. Achar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-25T03:05:55Z","title":"Geometric Satake, Springer correspondence, and small representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4999","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:f993cc1dc04a8dde0ad22cffa6ea0fc185cf681779bde11d88177b2e5d41495b","target":"record","created_at":"2026-05-18T03:04:38Z","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":"65fc6f56875fc84987a36d82ebc843175d7bba6836db7cb831d1f514291a7014","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-25T03:05:55Z","title_canon_sha256":"b01477dafaae7423d04ed1e23ccbbb1a118a1cb4d4b6a6b02e5018e80705f0f5"},"schema_version":"1.0","source":{"id":"1108.4999","kind":"arxiv","version":2}},"canonical_sha256":"52fb1ac6e511f6491f15be7058b785ec0d11309781a24e24aa24676249e059ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52fb1ac6e511f6491f15be7058b785ec0d11309781a24e24aa24676249e059ea","first_computed_at":"2026-05-18T03:04:38.776023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:38.776023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vOFLBwHbxn7QN8PEcMJRzpgsJaB3CTndJpOGsRdCghYKU30fFm4PYUtLiNdUXcEI18gPOxTvDQ+bIj5ReBaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:38.776900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4999","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f993cc1dc04a8dde0ad22cffa6ea0fc185cf681779bde11d88177b2e5d41495b","sha256:9651f2e90760f7d3eb950f874ef845a7c3be72616f7bebf5a21c6437df07d76f"],"state_sha256":"75b299abf5f923551b75b7b068d7e7a5d4c6a69f85322f33128369ddb5321215"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pf5Xq6nINYEwBCjpG0Z0bW/lz2XlklsIVrCL5HIdi7SqSJbjycKTz8YktOjN0nVRUzTlzm6f6Amu9Tv0k9E1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:27:55.651600Z","bundle_sha256":"9888164b0c3ec2d0693df62774e6f7c98b689b831fb6a439e3daff3431d36261"}}