{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LR3X2TXQ3IESIDBU32VOU2YRJZ","short_pith_number":"pith:LR3X2TXQ","canonical_record":{"source":{"id":"1710.11243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-30T21:14:22Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"373b589796dac16559a1fc67d16511b996b12552818e790e76ff32629599cdfa","abstract_canon_sha256":"2f611deaf94c209f819286f275fbdc1129c28b3819ce5359024d5359fd0362e0"},"schema_version":"1.0"},"canonical_sha256":"5c777d4ef0da09240c34deaaea6b114e7ab36972c77d1103fb18967ec59aef53","source":{"kind":"arxiv","id":"1710.11243","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11243","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11243v3","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11243","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"LR3X2TXQ3IES","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LR3X2TXQ3IESIDBU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LR3X2TXQ","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LR3X2TXQ3IESIDBU32VOU2YRJZ","target":"record","payload":{"canonical_record":{"source":{"id":"1710.11243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-30T21:14:22Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"373b589796dac16559a1fc67d16511b996b12552818e790e76ff32629599cdfa","abstract_canon_sha256":"2f611deaf94c209f819286f275fbdc1129c28b3819ce5359024d5359fd0362e0"},"schema_version":"1.0"},"canonical_sha256":"5c777d4ef0da09240c34deaaea6b114e7ab36972c77d1103fb18967ec59aef53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:10.029313Z","signature_b64":"qjclaSPp7VIxwcYlTrEj6RIGWUXUk3UvTFvMbvtu8V3eCgyNhU+v60aPBPZ9l029/kKrripJYQ/ezTztisqZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c777d4ef0da09240c34deaaea6b114e7ab36972c77d1103fb18967ec59aef53","last_reissued_at":"2026-05-18T00:15:10.028479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:10.028479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.11243","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":"2026-05-18T00:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+K3jbsYsJtSb6G1AQ0/kPPeiSBRkXByrp2chS40nJUzDVKk1WcyyYYe+KMGnr1f1UDhoy0vgiBj6sA5N3RuLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:00:28.096333Z"},"content_sha256":"637e962a63e2368c9090cc2e2e5d63fb249850f94c31f66e8a1c7a9f60e1aa6d","schema_version":"1.0","event_id":"sha256:637e962a63e2368c9090cc2e2e5d63fb249850f94c31f66e8a1c7a9f60e1aa6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LR3X2TXQ3IESIDBU32VOU2YRJZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometry of some generalized affine Springer fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Jingren Chi","submitted_at":"2017-10-30T21:14:22Z","abstract_excerpt":"We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible components of such varieties for a reductive group $G$ to certain weight multiplicities defined by the Langlands dual group $\\hat{G}$. We prove our conjecture in the case of unramified conjugacy class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11243","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":""},"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":"2026-05-18T00:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TWYi35xD4Ho+kYNmUbf4HpquiJIdrQpShC/SIhSPPTWiCyLckMfNlHz/13VsMGAAGm6XR8ovz6dBqtEtvMddCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:00:28.096803Z"},"content_sha256":"39fad7edbc8aa7978cd3caa19b9f431a79e40188532124ec6a8f50011b953e31","schema_version":"1.0","event_id":"sha256:39fad7edbc8aa7978cd3caa19b9f431a79e40188532124ec6a8f50011b953e31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LR3X2TXQ3IESIDBU32VOU2YRJZ/bundle.json","state_url":"https://pith.science/pith/LR3X2TXQ3IESIDBU32VOU2YRJZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LR3X2TXQ3IESIDBU32VOU2YRJZ/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":"2026-08-21T01:00:28Z","links":{"resolver":"https://pith.science/pith/LR3X2TXQ3IESIDBU32VOU2YRJZ","bundle":"https://pith.science/pith/LR3X2TXQ3IESIDBU32VOU2YRJZ/bundle.json","state":"https://pith.science/pith/LR3X2TXQ3IESIDBU32VOU2YRJZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LR3X2TXQ3IESIDBU32VOU2YRJZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LR3X2TXQ3IESIDBU32VOU2YRJZ","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":"2f611deaf94c209f819286f275fbdc1129c28b3819ce5359024d5359fd0362e0","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-30T21:14:22Z","title_canon_sha256":"373b589796dac16559a1fc67d16511b996b12552818e790e76ff32629599cdfa"},"schema_version":"1.0","source":{"id":"1710.11243","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11243","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11243v3","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11243","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"LR3X2TXQ3IES","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LR3X2TXQ3IESIDBU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LR3X2TXQ","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:39fad7edbc8aa7978cd3caa19b9f431a79e40188532124ec6a8f50011b953e31","target":"graph","created_at":"2026-05-18T00:15:10Z","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 study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible components of such varieties for a reductive group $G$ to certain weight multiplicities defined by the Langlands dual group $\\hat{G}$. We prove our conjecture in the case of unramified conjugacy class.","authors_text":"Jingren Chi","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-30T21:14:22Z","title":"The geometry of some generalized affine Springer fibers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11243","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":"sha256:637e962a63e2368c9090cc2e2e5d63fb249850f94c31f66e8a1c7a9f60e1aa6d","target":"record","created_at":"2026-05-18T00:15:10Z","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":"2f611deaf94c209f819286f275fbdc1129c28b3819ce5359024d5359fd0362e0","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-30T21:14:22Z","title_canon_sha256":"373b589796dac16559a1fc67d16511b996b12552818e790e76ff32629599cdfa"},"schema_version":"1.0","source":{"id":"1710.11243","kind":"arxiv","version":3}},"canonical_sha256":"5c777d4ef0da09240c34deaaea6b114e7ab36972c77d1103fb18967ec59aef53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c777d4ef0da09240c34deaaea6b114e7ab36972c77d1103fb18967ec59aef53","first_computed_at":"2026-05-18T00:15:10.028479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:10.028479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qjclaSPp7VIxwcYlTrEj6RIGWUXUk3UvTFvMbvtu8V3eCgyNhU+v60aPBPZ9l029/kKrripJYQ/ezTztisqZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:10.029313Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.11243","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:637e962a63e2368c9090cc2e2e5d63fb249850f94c31f66e8a1c7a9f60e1aa6d","sha256:39fad7edbc8aa7978cd3caa19b9f431a79e40188532124ec6a8f50011b953e31"],"state_sha256":"6b72e42123ea143977727d7fb82bd71bc02fa74daa99aa967a94d739d619cd30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3L18C6yrHBLfFHh8nlYdCJzbnVsb95c9zu2YSqLsHVDRgxXiaOLIo9LahfML8xs3vBXM8pjEz21viZy2/sejDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T01:00:28.108340Z","bundle_sha256":"f0d7c2df7e5c892966058709d4cae2cc3c20bf2f44eb13b42c851f0ec10e73ad"}}