{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XSF2UTVOVKOTIF6VK7RCX3OWNR","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":"e6b628a405ab9a10180a7c06760b9513b22d656300d7c8d22e0e7813e10be555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-29T00:24:22Z","title_canon_sha256":"c686288cbcefb40e37c46ff72508f61888c63a13e3eb4469b6070297932e3a4e"},"schema_version":"1.0","source":{"id":"1512.08566","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08566","created_at":"2026-07-05T04:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08566v4","created_at":"2026-07-05T04:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08566","created_at":"2026-07-05T04:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"XSF2UTVOVKOT","created_at":"2026-07-05T04:40:41Z"},{"alias_kind":"pith_short_16","alias_value":"XSF2UTVOVKOTIF6V","created_at":"2026-07-05T04:40:41Z"},{"alias_kind":"pith_short_8","alias_value":"XSF2UTVO","created_at":"2026-07-05T04:40:41Z"}],"graph_snapshots":[{"event_id":"sha256:2f0d38674592f857424d9bc7f9bed5f924b22fbb32ccc8736a66dd3fabf1c0ca","target":"graph","created_at":"2026-07-05T04:40:41Z","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/1512.08566/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For an unramified connected reductive group $G$ defined over a number field $F$, consider the part of the spherical automorphic spectrum with cuspidal support $[T,\\mathcal{O}(\\chi)]$, where $T$ is a maximal torus and $\\chi$ is an unramified automorphic character. We define a normalization of the Eisenstein series and we give the precise spectral decomposition of the closure of the subspace spanned by the normalized pseudo-Eiseinstein series. The proof uses residue distributions which were introduced by the third author (in joint work with G. Heckman) in the study of graded affine Hecke algebra","authors_text":"Eric Opdam, Marcelo De Martino, Volker Heiermann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-29T00:24:22Z","title":"On the unramified spherical automorphic spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08566","kind":"arxiv","version":4},"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:c3c3452221dbeb9866d0aa0b61ed531bb254f0707c2b250bac2b22d3ac15d4cb","target":"record","created_at":"2026-07-05T04:40:41Z","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":"e6b628a405ab9a10180a7c06760b9513b22d656300d7c8d22e0e7813e10be555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-29T00:24:22Z","title_canon_sha256":"c686288cbcefb40e37c46ff72508f61888c63a13e3eb4469b6070297932e3a4e"},"schema_version":"1.0","source":{"id":"1512.08566","kind":"arxiv","version":4}},"canonical_sha256":"bc8baa4eaeaa9d3417d557e22bedd66c57986c43ca3b4d397dacc82bab26ea91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc8baa4eaeaa9d3417d557e22bedd66c57986c43ca3b4d397dacc82bab26ea91","first_computed_at":"2026-07-05T04:40:41.188828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:40:41.188828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BFzDNzoIXYSNhHnG1UjV08swCBDNRFOLWgOWv2WxUKYTOyOu28KLFz3vLXhK4Tvtrhh2yE9YP28tYx9KNf6NAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:40:41.189291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08566","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3c3452221dbeb9866d0aa0b61ed531bb254f0707c2b250bac2b22d3ac15d4cb","sha256:2f0d38674592f857424d9bc7f9bed5f924b22fbb32ccc8736a66dd3fabf1c0ca"],"state_sha256":"917b0bf9ef638410e7960482036b9136cfe14d694da963ae05ef180acfb40e16"}