{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6PR7HV2LUGAFDCS3DEGBONKGK6","short_pith_number":"pith:6PR7HV2L","canonical_record":{"source":{"id":"1211.0042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-31T21:47:59Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e44720fd9fba22c9ed9eb5ea670e7fb786cf5162bd1a4053e4d7b860cdff9270","abstract_canon_sha256":"266432441c2ea7feb8a0f9ec354985571a8f0a108f1ac676b4e32ca1d81e6c87"},"schema_version":"1.0"},"canonical_sha256":"f3e3f3d74ba180518a5b190c173546579b2999ca1ab73c809eee5ade236b6651","source":{"kind":"arxiv","id":"1211.0042","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0042","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0042v2","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0042","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"6PR7HV2LUGAF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6PR7HV2LUGAFDCS3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6PR7HV2L","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6PR7HV2LUGAFDCS3DEGBONKGK6","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-31T21:47:59Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e44720fd9fba22c9ed9eb5ea670e7fb786cf5162bd1a4053e4d7b860cdff9270","abstract_canon_sha256":"266432441c2ea7feb8a0f9ec354985571a8f0a108f1ac676b4e32ca1d81e6c87"},"schema_version":"1.0"},"canonical_sha256":"f3e3f3d74ba180518a5b190c173546579b2999ca1ab73c809eee5ade236b6651","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:04.755703Z","signature_b64":"Bj3/EWp98Gn+zBqkE9OHuOd5O547dGMgEeIa/B4/zHir0wDyBkE1AvOdaopUTahd6EuwQEiUw8XYFPouua0ZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3e3f3d74ba180518a5b190c173546579b2999ca1ab73c809eee5ade236b6651","last_reissued_at":"2026-05-18T03:39:04.755195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:04.755195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0042","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":"2026-05-18T03:39:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VRW1cTHwrRZNmd+NHAf73UPri8f613aXa3RnN75mQy61CLg9vSVAUtNPYLariTYlsk75KCrDQFfkLa2igsE9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:10:26.730255Z"},"content_sha256":"1dde98124236b15b1b1a77586edf9b8ddd4b54565c98c4adc7c6b8ba6da82fa4","schema_version":"1.0","event_id":"sha256:1dde98124236b15b1b1a77586edf9b8ddd4b54565c98c4adc7c6b8ba6da82fa4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6PR7HV2LUGAFDCS3DEGBONKGK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted Satake Category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Bhairav Singh","submitted_at":"2012-10-31T21:47:59Z","abstract_excerpt":"We extend Bezrukavnikov and Finkelberg's description of the G(\\C[[t]])-equivariant derived category on the affine Grassmannian to the twisted setting of Finkelberg and Lysenko. Our description is in terms of coherent sheaves on the twisted dual Lie algebra. We also extend their computation of the corresponding loop rotation equivariant derived category, which is described in terms of Harish-Chandra bimodules for the twisted dual Lie algebra. To carry this out, we have to find a substitute for the functor of global equivariant cohomology. We describe such a functor, and show as in Bezrukavnikov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0042","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":"2026-05-18T03:39:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCD4qZyeoqH/3Y3GTugMkYn9rUamqcLovpfa1w+guHBXe8msGjLXrnn30jUbjS9o9t/WWtgTmImWKQpmI+R5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:10:26.730634Z"},"content_sha256":"3f8d6f7b44cfd2b779987177b0afc962b74a4edfac26e7326ba6199df2da7ec4","schema_version":"1.0","event_id":"sha256:3f8d6f7b44cfd2b779987177b0afc962b74a4edfac26e7326ba6199df2da7ec4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PR7HV2LUGAFDCS3DEGBONKGK6/bundle.json","state_url":"https://pith.science/pith/6PR7HV2LUGAFDCS3DEGBONKGK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PR7HV2LUGAFDCS3DEGBONKGK6/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":"2026-05-28T11:10:26Z","links":{"resolver":"https://pith.science/pith/6PR7HV2LUGAFDCS3DEGBONKGK6","bundle":"https://pith.science/pith/6PR7HV2LUGAFDCS3DEGBONKGK6/bundle.json","state":"https://pith.science/pith/6PR7HV2LUGAFDCS3DEGBONKGK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PR7HV2LUGAFDCS3DEGBONKGK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6PR7HV2LUGAFDCS3DEGBONKGK6","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":"266432441c2ea7feb8a0f9ec354985571a8f0a108f1ac676b4e32ca1d81e6c87","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-31T21:47:59Z","title_canon_sha256":"e44720fd9fba22c9ed9eb5ea670e7fb786cf5162bd1a4053e4d7b860cdff9270"},"schema_version":"1.0","source":{"id":"1211.0042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0042","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0042v2","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0042","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"6PR7HV2LUGAF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6PR7HV2LUGAFDCS3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6PR7HV2L","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:3f8d6f7b44cfd2b779987177b0afc962b74a4edfac26e7326ba6199df2da7ec4","target":"graph","created_at":"2026-05-18T03:39:04Z","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 extend Bezrukavnikov and Finkelberg's description of the G(\\C[[t]])-equivariant derived category on the affine Grassmannian to the twisted setting of Finkelberg and Lysenko. Our description is in terms of coherent sheaves on the twisted dual Lie algebra. We also extend their computation of the corresponding loop rotation equivariant derived category, which is described in terms of Harish-Chandra bimodules for the twisted dual Lie algebra. To carry this out, we have to find a substitute for the functor of global equivariant cohomology. We describe such a functor, and show as in Bezrukavnikov","authors_text":"Bhairav Singh","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-31T21:47:59Z","title":"Twisted Satake Category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0042","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":"sha256:1dde98124236b15b1b1a77586edf9b8ddd4b54565c98c4adc7c6b8ba6da82fa4","target":"record","created_at":"2026-05-18T03:39:04Z","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":"266432441c2ea7feb8a0f9ec354985571a8f0a108f1ac676b4e32ca1d81e6c87","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-31T21:47:59Z","title_canon_sha256":"e44720fd9fba22c9ed9eb5ea670e7fb786cf5162bd1a4053e4d7b860cdff9270"},"schema_version":"1.0","source":{"id":"1211.0042","kind":"arxiv","version":2}},"canonical_sha256":"f3e3f3d74ba180518a5b190c173546579b2999ca1ab73c809eee5ade236b6651","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3e3f3d74ba180518a5b190c173546579b2999ca1ab73c809eee5ade236b6651","first_computed_at":"2026-05-18T03:39:04.755195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:04.755195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bj3/EWp98Gn+zBqkE9OHuOd5O547dGMgEeIa/B4/zHir0wDyBkE1AvOdaopUTahd6EuwQEiUw8XYFPouua0ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:04.755703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dde98124236b15b1b1a77586edf9b8ddd4b54565c98c4adc7c6b8ba6da82fa4","sha256:3f8d6f7b44cfd2b779987177b0afc962b74a4edfac26e7326ba6199df2da7ec4"],"state_sha256":"903585aeb0fecb62c923dd00cd37d391d86e7ba559c0137c933316355eed1f93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2ba8ZTWNh9UzYEP0zqPiN/BSlKF2dzypzWxhqBjtf98rIISF2V9hGglB8iorY1q5xeAzNuDwPMqAgBMYsdYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:10:26.732629Z","bundle_sha256":"5642143b30c5ac3c4f788f4cb069f8fa2ca2384712858d4ac2c230843464620e"}}