{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:X2JR74I6QZLL5ZCJOGDOVLMMT2","short_pith_number":"pith:X2JR74I6","canonical_record":{"source":{"id":"2501.14156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-24T00:56:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9caa637304a63593a0494ab926dbeb73f961d6f81d03be00bd0566f90a902dea","abstract_canon_sha256":"a9ced1350e9534c126142a90edb8423db60f7e6ba3960b00842d812a03d3f8cb"},"schema_version":"1.0"},"canonical_sha256":"be931ff11e8656bee4497186eaad8c9e9808b0669981e46f9ca5e7e995c81483","source":{"kind":"arxiv","id":"2501.14156","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.14156","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"2501.14156v1","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.14156","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"X2JR74I6QZLL","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"pith_short_16","alias_value":"X2JR74I6QZLL5ZCJ","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"pith_short_8","alias_value":"X2JR74I6","created_at":"2026-07-05T10:04:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:X2JR74I6QZLL5ZCJOGDOVLMMT2","target":"record","payload":{"canonical_record":{"source":{"id":"2501.14156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-24T00:56:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9caa637304a63593a0494ab926dbeb73f961d6f81d03be00bd0566f90a902dea","abstract_canon_sha256":"a9ced1350e9534c126142a90edb8423db60f7e6ba3960b00842d812a03d3f8cb"},"schema_version":"1.0"},"canonical_sha256":"be931ff11e8656bee4497186eaad8c9e9808b0669981e46f9ca5e7e995c81483","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:04:46.267892Z","signature_b64":"5PpZJN4BAdVwOJ/zw9mhlGcmLkV347dHtDcVqW44zibqPLeScVejpCC2HfSDTxCQcs2EqE72wMfKso40fpC5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be931ff11e8656bee4497186eaad8c9e9808b0669981e46f9ca5e7e995c81483","last_reissued_at":"2026-07-05T10:04:46.267360Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:04:46.267360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.14156","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":"2026-07-05T10:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nwudMe7Ht6uAZZB0+KhdOi56K5qf0zQ1jeatpTwW50yJFBFlCiaKnoDYCp/L04Rfbwldal96+u+0uA+tIMlaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:47:48.407791Z"},"content_sha256":"c2d91c068720a47fb1ad1258682e756e8a1dbc32bdffb33e43eb49a36d7bf831","schema_version":"1.0","event_id":"sha256:c2d91c068720a47fb1ad1258682e756e8a1dbc32bdffb33e43eb49a36d7bf831"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:X2JR74I6QZLL5ZCJOGDOVLMMT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The universal monodromic Arkhipov--Bezrukavnikov equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Gurbir Dhillon, Jeremy Taylor","submitted_at":"2025-01-24T00:56:03Z","abstract_excerpt":"We identify equivariant quasicoherent sheaves on the Grothendieck alteration of a reductive group $\\mathsf{G}$ with universal monodromic Iwahori--Whittaker sheaves on the enhanced affine flag variety of the Langlands dual group $G$. This extends a similar result for equivariant quasicoherent sheaves on the Springer resolution due to Arkhipov--Bezrukavnikov. We further give a monoidal identification between adjoint equivariant coherent sheaves on the group $\\mathsf{G}$ itself and bi-Iwahori--Whittaker sheaves on the loop group of $G$. These results are used in the sequel to this paper to prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.14156","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/2501.14156/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":"2026-07-05T10:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3RBRJ+S2LtJmI28djsztr3YXvo0UKeqVYvgeeVmO8dnRpqP/CYTaWoq5O3wkoQkqm5OEgLDn1J1xi0/LwddvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:47:48.408165Z"},"content_sha256":"a1ceed344c828e380b29a3ea2884de1648f7b3b4571123d5aa96ace2fc9de10a","schema_version":"1.0","event_id":"sha256:a1ceed344c828e380b29a3ea2884de1648f7b3b4571123d5aa96ace2fc9de10a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2JR74I6QZLL5ZCJOGDOVLMMT2/bundle.json","state_url":"https://pith.science/pith/X2JR74I6QZLL5ZCJOGDOVLMMT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2JR74I6QZLL5ZCJOGDOVLMMT2/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":"2026-07-06T13:47:48Z","links":{"resolver":"https://pith.science/pith/X2JR74I6QZLL5ZCJOGDOVLMMT2","bundle":"https://pith.science/pith/X2JR74I6QZLL5ZCJOGDOVLMMT2/bundle.json","state":"https://pith.science/pith/X2JR74I6QZLL5ZCJOGDOVLMMT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2JR74I6QZLL5ZCJOGDOVLMMT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X2JR74I6QZLL5ZCJOGDOVLMMT2","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":"a9ced1350e9534c126142a90edb8423db60f7e6ba3960b00842d812a03d3f8cb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-24T00:56:03Z","title_canon_sha256":"9caa637304a63593a0494ab926dbeb73f961d6f81d03be00bd0566f90a902dea"},"schema_version":"1.0","source":{"id":"2501.14156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.14156","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"2501.14156v1","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.14156","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"X2JR74I6QZLL","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"pith_short_16","alias_value":"X2JR74I6QZLL5ZCJ","created_at":"2026-07-05T10:04:46Z"},{"alias_kind":"pith_short_8","alias_value":"X2JR74I6","created_at":"2026-07-05T10:04:46Z"}],"graph_snapshots":[{"event_id":"sha256:a1ceed344c828e380b29a3ea2884de1648f7b3b4571123d5aa96ace2fc9de10a","target":"graph","created_at":"2026-07-05T10:04:46Z","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/2501.14156/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We identify equivariant quasicoherent sheaves on the Grothendieck alteration of a reductive group $\\mathsf{G}$ with universal monodromic Iwahori--Whittaker sheaves on the enhanced affine flag variety of the Langlands dual group $G$. This extends a similar result for equivariant quasicoherent sheaves on the Springer resolution due to Arkhipov--Bezrukavnikov. We further give a monoidal identification between adjoint equivariant coherent sheaves on the group $\\mathsf{G}$ itself and bi-Iwahori--Whittaker sheaves on the loop group of $G$. These results are used in the sequel to this paper to prove ","authors_text":"Gurbir Dhillon, Jeremy Taylor","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-24T00:56:03Z","title":"The universal monodromic Arkhipov--Bezrukavnikov equivalence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.14156","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:c2d91c068720a47fb1ad1258682e756e8a1dbc32bdffb33e43eb49a36d7bf831","target":"record","created_at":"2026-07-05T10:04:46Z","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":"a9ced1350e9534c126142a90edb8423db60f7e6ba3960b00842d812a03d3f8cb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-24T00:56:03Z","title_canon_sha256":"9caa637304a63593a0494ab926dbeb73f961d6f81d03be00bd0566f90a902dea"},"schema_version":"1.0","source":{"id":"2501.14156","kind":"arxiv","version":1}},"canonical_sha256":"be931ff11e8656bee4497186eaad8c9e9808b0669981e46f9ca5e7e995c81483","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be931ff11e8656bee4497186eaad8c9e9808b0669981e46f9ca5e7e995c81483","first_computed_at":"2026-07-05T10:04:46.267360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:46.267360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5PpZJN4BAdVwOJ/zw9mhlGcmLkV347dHtDcVqW44zibqPLeScVejpCC2HfSDTxCQcs2EqE72wMfKso40fpC5AA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:46.267892Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.14156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2d91c068720a47fb1ad1258682e756e8a1dbc32bdffb33e43eb49a36d7bf831","sha256:a1ceed344c828e380b29a3ea2884de1648f7b3b4571123d5aa96ace2fc9de10a"],"state_sha256":"550a6f2aecd97dced2ff24d22959742e523a3b618e911a1c6575f522199d6031"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sfAAZoPzleKv1eKReCS+7XIDF2gE5riTXE+nUggqFNoMApKIW7FLcCKd7hr6iVZOhQma/KKIXk+1B60obWG3CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T13:47:48.410241Z","bundle_sha256":"cdc8eaaa4ee0405c718bf7f707aa3ab2a6e13c6d2f0d1509a15214c2cd533af9"}}