{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YUJUM5K4CGIXMCYEWXWCXBBWAL","short_pith_number":"pith:YUJUM5K4","canonical_record":{"source":{"id":"2104.13123","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-04-27T11:55:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"61164871215a361aa096e13d73297953693ddded612d0a795888f4826c7797d6","abstract_canon_sha256":"c338d79a75e4970874962d860d8af0ffdd09a234858695310f09cf55512376f2"},"schema_version":"1.0"},"canonical_sha256":"c51346755c1191760b04b5ec2b843602ecc5e4823e068ad5bf05dcb7b245ca0f","source":{"kind":"arxiv","id":"2104.13123","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.13123","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"2104.13123v3","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.13123","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"YUJUM5K4CGIX","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"pith_short_16","alias_value":"YUJUM5K4CGIXMCYE","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"pith_short_8","alias_value":"YUJUM5K4","created_at":"2026-07-05T11:50:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YUJUM5K4CGIXMCYEWXWCXBBWAL","target":"record","payload":{"canonical_record":{"source":{"id":"2104.13123","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-04-27T11:55:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"61164871215a361aa096e13d73297953693ddded612d0a795888f4826c7797d6","abstract_canon_sha256":"c338d79a75e4970874962d860d8af0ffdd09a234858695310f09cf55512376f2"},"schema_version":"1.0"},"canonical_sha256":"c51346755c1191760b04b5ec2b843602ecc5e4823e068ad5bf05dcb7b245ca0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:50:23.386178Z","signature_b64":"1rzLvnxNh0hCwnqJgEROE5A4xQjvOI5u8bGPuUNh+6ezyr0Iv3hlCjApTdaxacx9kYYATn3VyIQQNn9PDVqLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c51346755c1191760b04b5ec2b843602ecc5e4823e068ad5bf05dcb7b245ca0f","last_reissued_at":"2026-07-05T11:50:23.385709Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:50:23.385709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.13123","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYF2o643PaVwWkmkrBxphmui0QVFxiTfXBXds/sulx1tsIbKiuhVk5KdnpMy1aH7snNHyNMbemKaNmyKt4QFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:41:11.421641Z"},"content_sha256":"3eccec9a018e199cdd4e5be9785f126e4d3841336acf7bf29de891b4347ef22f","schema_version":"1.0","event_id":"sha256:3eccec9a018e199cdd4e5be9785f126e4d3841336acf7bf29de891b4347ef22f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YUJUM5K4CGIXMCYEWXWCXBBWAL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Affine Springer fibers and depth zero L-packets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Roman Bezrukavnikov, Yakov Varshavsky","submitted_at":"2021-04-27T11:55:54Z","abstract_excerpt":"Let $G$ be a connected reductive group over a field $F=\\mathbb{F}_q((t))$ splitting over $\\overline{\\mathbb{F}}_q((t))$. Following [KV,DR], a tamely unramified Langlands parameter $\\lambda:W_F\\to{}^L G(\\overline{\\mathbb{Q}}_{\\ell})$ in general position gives rise to a finite set $\\Pi_{\\lambda}$ of irreducible admissible representations of $G(F)$, called the $L$-packet.\n  The main goal of this work is to provide a geometric description of characters $\\chi_{\\pi}$ of $\\pi\\in\\Pi_{\\lambda}$ and of their endoscopic linear combinations $\\chi_{\\lambda}^{\\kappa}$ in terms of homology of affine Springer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.13123","kind":"arxiv","version":3},"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/2104.13123/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":"2026-07-05T11:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o0CyTed4Q2rbP3kKnXQufcvUhB+YhLzew0DIvR39ut+hxFo7QEyolpk33ZPmEf81YbfMmggGuRUZz1LmcjfbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:41:11.421978Z"},"content_sha256":"fbcc6c6feced178f434be11121009761786f3c41136311d85e47df88bd9fd123","schema_version":"1.0","event_id":"sha256:fbcc6c6feced178f434be11121009761786f3c41136311d85e47df88bd9fd123"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUJUM5K4CGIXMCYEWXWCXBBWAL/bundle.json","state_url":"https://pith.science/pith/YUJUM5K4CGIXMCYEWXWCXBBWAL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUJUM5K4CGIXMCYEWXWCXBBWAL/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":"2026-08-11T20:41:11Z","links":{"resolver":"https://pith.science/pith/YUJUM5K4CGIXMCYEWXWCXBBWAL","bundle":"https://pith.science/pith/YUJUM5K4CGIXMCYEWXWCXBBWAL/bundle.json","state":"https://pith.science/pith/YUJUM5K4CGIXMCYEWXWCXBBWAL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUJUM5K4CGIXMCYEWXWCXBBWAL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YUJUM5K4CGIXMCYEWXWCXBBWAL","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":"c338d79a75e4970874962d860d8af0ffdd09a234858695310f09cf55512376f2","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-04-27T11:55:54Z","title_canon_sha256":"61164871215a361aa096e13d73297953693ddded612d0a795888f4826c7797d6"},"schema_version":"1.0","source":{"id":"2104.13123","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.13123","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"2104.13123v3","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.13123","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"YUJUM5K4CGIX","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"pith_short_16","alias_value":"YUJUM5K4CGIXMCYE","created_at":"2026-07-05T11:50:23Z"},{"alias_kind":"pith_short_8","alias_value":"YUJUM5K4","created_at":"2026-07-05T11:50:23Z"}],"graph_snapshots":[{"event_id":"sha256:fbcc6c6feced178f434be11121009761786f3c41136311d85e47df88bd9fd123","target":"graph","created_at":"2026-07-05T11:50:23Z","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/2104.13123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a connected reductive group over a field $F=\\mathbb{F}_q((t))$ splitting over $\\overline{\\mathbb{F}}_q((t))$. Following [KV,DR], a tamely unramified Langlands parameter $\\lambda:W_F\\to{}^L G(\\overline{\\mathbb{Q}}_{\\ell})$ in general position gives rise to a finite set $\\Pi_{\\lambda}$ of irreducible admissible representations of $G(F)$, called the $L$-packet.\n  The main goal of this work is to provide a geometric description of characters $\\chi_{\\pi}$ of $\\pi\\in\\Pi_{\\lambda}$ and of their endoscopic linear combinations $\\chi_{\\lambda}^{\\kappa}$ in terms of homology of affine Springer","authors_text":"Roman Bezrukavnikov, Yakov Varshavsky","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-04-27T11:55:54Z","title":"Affine Springer fibers and depth zero L-packets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.13123","kind":"arxiv","version":3},"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":"sha256:3eccec9a018e199cdd4e5be9785f126e4d3841336acf7bf29de891b4347ef22f","target":"record","created_at":"2026-07-05T11:50:23Z","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":"c338d79a75e4970874962d860d8af0ffdd09a234858695310f09cf55512376f2","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-04-27T11:55:54Z","title_canon_sha256":"61164871215a361aa096e13d73297953693ddded612d0a795888f4826c7797d6"},"schema_version":"1.0","source":{"id":"2104.13123","kind":"arxiv","version":3}},"canonical_sha256":"c51346755c1191760b04b5ec2b843602ecc5e4823e068ad5bf05dcb7b245ca0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c51346755c1191760b04b5ec2b843602ecc5e4823e068ad5bf05dcb7b245ca0f","first_computed_at":"2026-07-05T11:50:23.385709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:23.385709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1rzLvnxNh0hCwnqJgEROE5A4xQjvOI5u8bGPuUNh+6ezyr0Iv3hlCjApTdaxacx9kYYATn3VyIQQNn9PDVqLDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:23.386178Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.13123","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eccec9a018e199cdd4e5be9785f126e4d3841336acf7bf29de891b4347ef22f","sha256:fbcc6c6feced178f434be11121009761786f3c41136311d85e47df88bd9fd123"],"state_sha256":"b043bfa8a7450c0f206cd38a4005486c30ecd9313ba18efabe192635a621e529"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lB3xqdcE6um7+S4cNaIb8G3CvlwkFqr4ghdgTr1Y0pElqlf2BXQO+mTlFgC29lu/dtrB0fsMBfLbKVo9MUBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T20:41:11.425170Z","bundle_sha256":"619bc76923e33517d8b6c50562d5f7e0de7df7b50d60316c6386401d8e4fc365"}}