{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z5QBVRVISAHGJZIIUVAGOPWZH7","short_pith_number":"pith:Z5QBVRVI","canonical_record":{"source":{"id":"1502.06483","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-23T16:17:11Z","cross_cats_sorted":[],"title_canon_sha256":"7066dbc4df19f8e8cf98d45f7fdb1d8e488ab0299c5c2cd7f3baacd8dd468695","abstract_canon_sha256":"504881968fb851df12773e0400c855a664c725c2cbf2abfccdacb8757988fdac"},"schema_version":"1.0"},"canonical_sha256":"cf601ac6a8900e64e508a540673ed93fdf9e79359b89e5f097cad204e4d6150a","source":{"kind":"arxiv","id":"1502.06483","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06483","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06483v5","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06483","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"Z5QBVRVISAHG","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z5QBVRVISAHGJZII","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z5QBVRVI","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z5QBVRVISAHGJZIIUVAGOPWZH7","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06483","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-23T16:17:11Z","cross_cats_sorted":[],"title_canon_sha256":"7066dbc4df19f8e8cf98d45f7fdb1d8e488ab0299c5c2cd7f3baacd8dd468695","abstract_canon_sha256":"504881968fb851df12773e0400c855a664c725c2cbf2abfccdacb8757988fdac"},"schema_version":"1.0"},"canonical_sha256":"cf601ac6a8900e64e508a540673ed93fdf9e79359b89e5f097cad204e4d6150a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:13.938651Z","signature_b64":"dLB9l3Z3VskqglRbBPLpqgIc7R+cP5uDSQmruxxHyQvRNzI3snuwsZ+T17GR5W6JBu758tfac87QPxQkWFhDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf601ac6a8900e64e508a540673ed93fdf9e79359b89e5f097cad204e4d6150a","last_reissued_at":"2026-05-17T23:53:13.938099Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:13.938099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06483","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ANOA13N5ciRZ/HhSVRYolTyMECpkvKmO6Q84DCAGJxX2TxranQ410m9W42600xKC3NMA1R7tm8/Nk2fXjaBiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T16:53:48.130418Z"},"content_sha256":"46fe48d9440bd63dd4b7eb967048cce86cf0bb72321beadc4a8a103c493c5db6","schema_version":"1.0","event_id":"sha256:46fe48d9440bd63dd4b7eb967048cce86cf0bb72321beadc4a8a103c493c5db6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z5QBVRVISAHGJZIIUVAGOPWZH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized and degenerate Whittaker models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitry Gourevitch, Raul Gomez, Siddhartha Sahi","submitted_at":"2015-02-23T16:17:11Z","abstract_excerpt":"We study generalized and degenerate Whittaker models for reductive groups over local fields of characteristic zero (archimedean or non-archimedean). Our main result is the construction of epimorphisms from the generalized Whittaker model corresponding to a nilpotent orbit to any degenerate Whittaker model corresponding to the same orbit, and to certain degenerate Whittaker models corresponding to bigger orbits. We also give choice-free definitions of generalized and degenerate Whittaker models. Finally, we explain how our methods imply analogous results for Whittaker-Fourier coefficients of au"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06483","kind":"arxiv","version":5},"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":"2026-05-17T23:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"udyk5mFhvvGyyjnkKGcbfNFxkYPOB4QGSm2JOLA6g8QYiQQ1d+XNFiS6LpJD3TLyzwz6IQryxzqwAT9Xx/NdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T16:53:48.130958Z"},"content_sha256":"a57fe60a486c746394fbdb23049dd410f93109a85daa9943fa728faa107693fd","schema_version":"1.0","event_id":"sha256:a57fe60a486c746394fbdb23049dd410f93109a85daa9943fa728faa107693fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5QBVRVISAHGJZIIUVAGOPWZH7/bundle.json","state_url":"https://pith.science/pith/Z5QBVRVISAHGJZIIUVAGOPWZH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5QBVRVISAHGJZIIUVAGOPWZH7/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":"2026-06-04T16:53:48Z","links":{"resolver":"https://pith.science/pith/Z5QBVRVISAHGJZIIUVAGOPWZH7","bundle":"https://pith.science/pith/Z5QBVRVISAHGJZIIUVAGOPWZH7/bundle.json","state":"https://pith.science/pith/Z5QBVRVISAHGJZIIUVAGOPWZH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5QBVRVISAHGJZIIUVAGOPWZH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z5QBVRVISAHGJZIIUVAGOPWZH7","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":"504881968fb851df12773e0400c855a664c725c2cbf2abfccdacb8757988fdac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-23T16:17:11Z","title_canon_sha256":"7066dbc4df19f8e8cf98d45f7fdb1d8e488ab0299c5c2cd7f3baacd8dd468695"},"schema_version":"1.0","source":{"id":"1502.06483","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06483","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06483v5","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06483","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"Z5QBVRVISAHG","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z5QBVRVISAHGJZII","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z5QBVRVI","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:a57fe60a486c746394fbdb23049dd410f93109a85daa9943fa728faa107693fd","target":"graph","created_at":"2026-05-17T23:53:13Z","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 generalized and degenerate Whittaker models for reductive groups over local fields of characteristic zero (archimedean or non-archimedean). Our main result is the construction of epimorphisms from the generalized Whittaker model corresponding to a nilpotent orbit to any degenerate Whittaker model corresponding to the same orbit, and to certain degenerate Whittaker models corresponding to bigger orbits. We also give choice-free definitions of generalized and degenerate Whittaker models. Finally, we explain how our methods imply analogous results for Whittaker-Fourier coefficients of au","authors_text":"Dmitry Gourevitch, Raul Gomez, Siddhartha Sahi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-23T16:17:11Z","title":"Generalized and degenerate Whittaker models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06483","kind":"arxiv","version":5},"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":"sha256:46fe48d9440bd63dd4b7eb967048cce86cf0bb72321beadc4a8a103c493c5db6","target":"record","created_at":"2026-05-17T23:53:13Z","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":"504881968fb851df12773e0400c855a664c725c2cbf2abfccdacb8757988fdac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-23T16:17:11Z","title_canon_sha256":"7066dbc4df19f8e8cf98d45f7fdb1d8e488ab0299c5c2cd7f3baacd8dd468695"},"schema_version":"1.0","source":{"id":"1502.06483","kind":"arxiv","version":5}},"canonical_sha256":"cf601ac6a8900e64e508a540673ed93fdf9e79359b89e5f097cad204e4d6150a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf601ac6a8900e64e508a540673ed93fdf9e79359b89e5f097cad204e4d6150a","first_computed_at":"2026-05-17T23:53:13.938099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:13.938099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLB9l3Z3VskqglRbBPLpqgIc7R+cP5uDSQmruxxHyQvRNzI3snuwsZ+T17GR5W6JBu758tfac87QPxQkWFhDDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:13.938651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06483","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46fe48d9440bd63dd4b7eb967048cce86cf0bb72321beadc4a8a103c493c5db6","sha256:a57fe60a486c746394fbdb23049dd410f93109a85daa9943fa728faa107693fd"],"state_sha256":"465163f0fd80fbdc8508a1cb106578ae3eeee8d211aeaeadd9d5e2886cec4a86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6yB+En56gqtqbCSH1aXS/p9Uu5g9NbpM/Yl1O5f+UalglsCve5qyviHCSmMcdy5OkJMfnGpIuEVK/OR9d1TfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T16:53:48.133576Z","bundle_sha256":"c284fd45e86336919aadf32221e173d1f36ffbd91fd5fca085a8ba13a91d720b"}}