{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YYBP7JZL5JXMNTU4FV335JZ7AB","short_pith_number":"pith:YYBP7JZL","canonical_record":{"source":{"id":"1403.6055","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T17:41:53Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"f94f9bec5d747dce5d8afea09a8059c23c57e71da4a2c6627924f117a70703d9","abstract_canon_sha256":"346d51cd80cdb2e2ec3640c020914c8d2a9a829fc3bdae61751dc1e16094f613"},"schema_version":"1.0"},"canonical_sha256":"c602ffa72bea6ec6ce9c2d77bea73f005dda947e18d6fd2204df6a31652dc7ba","source":{"kind":"arxiv","id":"1403.6055","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6055","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6055v3","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6055","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"YYBP7JZL5JXM","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YYBP7JZL5JXMNTU4","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YYBP7JZL","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YYBP7JZL5JXMNTU4FV335JZ7AB","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6055","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T17:41:53Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"f94f9bec5d747dce5d8afea09a8059c23c57e71da4a2c6627924f117a70703d9","abstract_canon_sha256":"346d51cd80cdb2e2ec3640c020914c8d2a9a829fc3bdae61751dc1e16094f613"},"schema_version":"1.0"},"canonical_sha256":"c602ffa72bea6ec6ce9c2d77bea73f005dda947e18d6fd2204df6a31652dc7ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:19.464935Z","signature_b64":"JbbIpKcTRVM1PPuVhoUobLH9Ls3AeozQOgAcb9S9LHDkhrue29/UwX4jnaqsF/VJrgFcrU5gK/yoylkrTyhrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c602ffa72bea6ec6ce9c2d77bea73f005dda947e18d6fd2204df6a31652dc7ba","last_reissued_at":"2026-05-18T01:24:19.464471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:19.464471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6055","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":"2026-05-18T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SeGa+DCT2J6ezqa5Rosjg0CLYwdHryIe6uRXMgKQiGXBJR8p46jZnX8LEL5o2WcXzuy+ZPPf/yVOy+0L6GjPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:58.517196Z"},"content_sha256":"9f891ba52f4b01e5b96415ab0fdc870528891f186f98734eb33f7c850e35fab3","schema_version":"1.0","event_id":"sha256:9f891ba52f4b01e5b96415ab0fdc870528891f186f98734eb33f7c850e35fab3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YYBP7JZL5JXMNTU4FV335JZ7AB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Whittaker Coefficients of Metaplectic Eisenstein Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.NT","authors_text":"Benjamin Brubaker, Solomon Friedberg","submitted_at":"2014-03-24T17:41:53Z","abstract_excerpt":"We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However they are not Eulerian and the standard methods to compute them in the reductive case do not apply to covers. For \"cominuscule\" maximal parabolics, we give an explicit description of the coefficients as Dirichlet series whose arithmetic content is expressed in an exponential sum. The exponential sum is then shown to satisfy a twisted multiplicativity, reducing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6055","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":"2026-05-18T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6AC1u84xmYY5sHAXhbrerFVMam6iOG+6gLw0sN47ecwryWZPBs6WTYtJUuiG2hbHpAoNMJTQN99tRsXKcPJSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:58.517567Z"},"content_sha256":"ab700377a90b0f7beba1e465598e42d270dcf4bfe5bed10a77f235e62b6dc2ac","schema_version":"1.0","event_id":"sha256:ab700377a90b0f7beba1e465598e42d270dcf4bfe5bed10a77f235e62b6dc2ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYBP7JZL5JXMNTU4FV335JZ7AB/bundle.json","state_url":"https://pith.science/pith/YYBP7JZL5JXMNTU4FV335JZ7AB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYBP7JZL5JXMNTU4FV335JZ7AB/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":"2026-06-02T23:02:58Z","links":{"resolver":"https://pith.science/pith/YYBP7JZL5JXMNTU4FV335JZ7AB","bundle":"https://pith.science/pith/YYBP7JZL5JXMNTU4FV335JZ7AB/bundle.json","state":"https://pith.science/pith/YYBP7JZL5JXMNTU4FV335JZ7AB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYBP7JZL5JXMNTU4FV335JZ7AB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YYBP7JZL5JXMNTU4FV335JZ7AB","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":"346d51cd80cdb2e2ec3640c020914c8d2a9a829fc3bdae61751dc1e16094f613","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T17:41:53Z","title_canon_sha256":"f94f9bec5d747dce5d8afea09a8059c23c57e71da4a2c6627924f117a70703d9"},"schema_version":"1.0","source":{"id":"1403.6055","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6055","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6055v3","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6055","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"YYBP7JZL5JXM","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YYBP7JZL5JXMNTU4","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YYBP7JZL","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:ab700377a90b0f7beba1e465598e42d270dcf4bfe5bed10a77f235e62b6dc2ac","target":"graph","created_at":"2026-05-18T01:24:19Z","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 Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However they are not Eulerian and the standard methods to compute them in the reductive case do not apply to covers. For \"cominuscule\" maximal parabolics, we give an explicit description of the coefficients as Dirichlet series whose arithmetic content is expressed in an exponential sum. The exponential sum is then shown to satisfy a twisted multiplicativity, reducing ","authors_text":"Benjamin Brubaker, Solomon Friedberg","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T17:41:53Z","title":"Whittaker Coefficients of Metaplectic Eisenstein Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6055","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":"sha256:9f891ba52f4b01e5b96415ab0fdc870528891f186f98734eb33f7c850e35fab3","target":"record","created_at":"2026-05-18T01:24:19Z","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":"346d51cd80cdb2e2ec3640c020914c8d2a9a829fc3bdae61751dc1e16094f613","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T17:41:53Z","title_canon_sha256":"f94f9bec5d747dce5d8afea09a8059c23c57e71da4a2c6627924f117a70703d9"},"schema_version":"1.0","source":{"id":"1403.6055","kind":"arxiv","version":3}},"canonical_sha256":"c602ffa72bea6ec6ce9c2d77bea73f005dda947e18d6fd2204df6a31652dc7ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c602ffa72bea6ec6ce9c2d77bea73f005dda947e18d6fd2204df6a31652dc7ba","first_computed_at":"2026-05-18T01:24:19.464471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:19.464471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JbbIpKcTRVM1PPuVhoUobLH9Ls3AeozQOgAcb9S9LHDkhrue29/UwX4jnaqsF/VJrgFcrU5gK/yoylkrTyhrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:19.464935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6055","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f891ba52f4b01e5b96415ab0fdc870528891f186f98734eb33f7c850e35fab3","sha256:ab700377a90b0f7beba1e465598e42d270dcf4bfe5bed10a77f235e62b6dc2ac"],"state_sha256":"cf682b278664599723b38f7dfaf3ccd6bda94123fd48e29d4d72e8c55c595192"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1N2rcwybQ/Q4iDgE3QOl7tLoggU7wop2jgC6Tg0JgD0tyRXWJxmwLmK1kgaoE/UeM7bUKgyX0KXxhRZa+ljzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:02:58.519577Z","bundle_sha256":"e84e6189fdc8bf31ef40fe3791eeeffaac633bdb8ae553697a26405bedf9e956"}}