{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U6SKEERVIBLNO55LCSVBPJREMA","short_pith_number":"pith:U6SKEERV","canonical_record":{"source":{"id":"1810.05556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-12T14:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"ff0ad6df4c859e7221d425b8983c785becbe31029fb0f38f6f4b273a991d2e86","abstract_canon_sha256":"9683778d77a6438d657663acd8bdf26019d5fa78413126aaa139e3c1a892a48c"},"schema_version":"1.0"},"canonical_sha256":"a7a4a212354056d777ab14aa17a6246025acdef8035c143247bacfea05e086b0","source":{"kind":"arxiv","id":"1810.05556","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05556","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05556v1","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05556","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"U6SKEERVIBLN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U6SKEERVIBLNO55L","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U6SKEERV","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U6SKEERVIBLNO55LCSVBPJREMA","target":"record","payload":{"canonical_record":{"source":{"id":"1810.05556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-12T14:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"ff0ad6df4c859e7221d425b8983c785becbe31029fb0f38f6f4b273a991d2e86","abstract_canon_sha256":"9683778d77a6438d657663acd8bdf26019d5fa78413126aaa139e3c1a892a48c"},"schema_version":"1.0"},"canonical_sha256":"a7a4a212354056d777ab14aa17a6246025acdef8035c143247bacfea05e086b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:30.065035Z","signature_b64":"mERYvYsHnWpkEZsr8BkxL4KCZLseykRZ7lqNhw4/gH4SbPK0DLgvzM6UONQsE7wcZIC3hs6AGf/kFaLpISuOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7a4a212354056d777ab14aa17a6246025acdef8035c143247bacfea05e086b0","last_reissued_at":"2026-05-18T00:03:30.064355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:30.064355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.05556","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":"2026-05-18T00:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yMGHcijtMKoNpVZtNFTKlbcjXBwTPrgSyc/mbbA89RmRENKIz1zU46CA5yhZWjK23PtByKTMuT6qK2Q4e4H3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:40:28.420334Z"},"content_sha256":"a5552e293dacbe65eb1ca5487957126ec98a085cce74a54bbb904ff5c3ed4214","schema_version":"1.0","event_id":"sha256:a5552e293dacbe65eb1ca5487957126ec98a085cce74a54bbb904ff5c3ed4214"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U6SKEERVIBLNO55LCSVBPJREMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tau Signatures and Characters of Weyl Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alfred G. No\\\"el, Steven Glenn Jackson, Thomas Folz-Donahue, Todor Milev","submitted_at":"2018-10-12T14:47:04Z","abstract_excerpt":"Let $G_{\\mathbb R}$ be the set of real points of a complex linear reductive group and $\\hat G_\\lambda$ its classes of irreducible admissible representations with infinitesimal integral regular character $\\lambda$. In this case each cell of representations is associated to a \\emph{special} nilpotent orbit. This helps organize the corresponding set of irreducible Harish-Chandra modules. The goal of this paper is to is to describe algorithms for identifying the special nilpotent orbit attached to a cell in terms of descent sets appearing in the cell."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05556","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":""},"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":"2026-05-18T00:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3cGNuUMizyvbG6orBAXcNkhwD6kDANCFnxCFr3iB+AX5ZSaShiRfOYPEAX7qWC9aI86tQEPUZwrgv3BVMXzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:40:28.420681Z"},"content_sha256":"7e80069cb073ebc0ae919189091c71429e4fd0a871ca0311bae43ca1d14efd97","schema_version":"1.0","event_id":"sha256:7e80069cb073ebc0ae919189091c71429e4fd0a871ca0311bae43ca1d14efd97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6SKEERVIBLNO55LCSVBPJREMA/bundle.json","state_url":"https://pith.science/pith/U6SKEERVIBLNO55LCSVBPJREMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6SKEERVIBLNO55LCSVBPJREMA/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":"2026-06-09T00:40:28Z","links":{"resolver":"https://pith.science/pith/U6SKEERVIBLNO55LCSVBPJREMA","bundle":"https://pith.science/pith/U6SKEERVIBLNO55LCSVBPJREMA/bundle.json","state":"https://pith.science/pith/U6SKEERVIBLNO55LCSVBPJREMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6SKEERVIBLNO55LCSVBPJREMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U6SKEERVIBLNO55LCSVBPJREMA","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":"9683778d77a6438d657663acd8bdf26019d5fa78413126aaa139e3c1a892a48c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-12T14:47:04Z","title_canon_sha256":"ff0ad6df4c859e7221d425b8983c785becbe31029fb0f38f6f4b273a991d2e86"},"schema_version":"1.0","source":{"id":"1810.05556","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05556","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05556v1","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05556","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"U6SKEERVIBLN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U6SKEERVIBLNO55L","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U6SKEERV","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:7e80069cb073ebc0ae919189091c71429e4fd0a871ca0311bae43ca1d14efd97","target":"graph","created_at":"2026-05-18T00:03:30Z","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":"Let $G_{\\mathbb R}$ be the set of real points of a complex linear reductive group and $\\hat G_\\lambda$ its classes of irreducible admissible representations with infinitesimal integral regular character $\\lambda$. In this case each cell of representations is associated to a \\emph{special} nilpotent orbit. This helps organize the corresponding set of irreducible Harish-Chandra modules. The goal of this paper is to is to describe algorithms for identifying the special nilpotent orbit attached to a cell in terms of descent sets appearing in the cell.","authors_text":"Alfred G. No\\\"el, Steven Glenn Jackson, Thomas Folz-Donahue, Todor Milev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-12T14:47:04Z","title":"Tau Signatures and Characters of Weyl Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05556","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:a5552e293dacbe65eb1ca5487957126ec98a085cce74a54bbb904ff5c3ed4214","target":"record","created_at":"2026-05-18T00:03:30Z","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":"9683778d77a6438d657663acd8bdf26019d5fa78413126aaa139e3c1a892a48c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-12T14:47:04Z","title_canon_sha256":"ff0ad6df4c859e7221d425b8983c785becbe31029fb0f38f6f4b273a991d2e86"},"schema_version":"1.0","source":{"id":"1810.05556","kind":"arxiv","version":1}},"canonical_sha256":"a7a4a212354056d777ab14aa17a6246025acdef8035c143247bacfea05e086b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7a4a212354056d777ab14aa17a6246025acdef8035c143247bacfea05e086b0","first_computed_at":"2026-05-18T00:03:30.064355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:30.064355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mERYvYsHnWpkEZsr8BkxL4KCZLseykRZ7lqNhw4/gH4SbPK0DLgvzM6UONQsE7wcZIC3hs6AGf/kFaLpISuOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:30.065035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05556","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5552e293dacbe65eb1ca5487957126ec98a085cce74a54bbb904ff5c3ed4214","sha256:7e80069cb073ebc0ae919189091c71429e4fd0a871ca0311bae43ca1d14efd97"],"state_sha256":"4cf607988d5073cd4303419cb3b2e732c36ceba95fbfc04aa2fae33cf4f0d5f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmNBaS4mEx6QubE1niWKIeqRKyx+/cmRTpKPyrO2KHzUeoxeV9+VWyMMSDlyHnjCDbS8ukyLitNtCLQY4upxCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:40:28.422552Z","bundle_sha256":"52f74427857ce24679f77adaa5330f34413dcb375f8d60139207c6b169c833bb"}}