{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QXBGR2EQQLRBKN7YMFATRALH57","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":"7467ad754fe222358cdc408aa3bd3b6596751a8b96fa3204d2a092427a790b3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-27T21:02:31Z","title_canon_sha256":"4e2dc0b808b1f9325898bbbf39702393aa9a28afb50e612ffdd4f9dfa89c1cb5"},"schema_version":"1.0","source":{"id":"1508.07032","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07032","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07032v2","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07032","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"QXBGR2EQQLRB","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QXBGR2EQQLRBKN7Y","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QXBGR2EQ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:171c945aa2e8a064a53bed42c1df03a858ac21633eb10ba15b3d0b81bb5515e1","target":"graph","created_at":"2026-05-18T01:25:46Z","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 $X=X_1 \\times X_2$ be a direct product of two rank-one Riemannian symmetric spaces of the noncompact type. We show that when at least one of the two spaces is isomorphic to a real hyperbolic space of odd dimension, the resolvent of the Laplacian of $X$ can be lifted to a holomorphic function on a Riemann surface which is a branched covering of $\\mathbb C$. In all other cases, the resolvent of the Laplacian of $X$ admits a singular meromorphic lift. The poles of this function are called the resonances of the Laplacian. We determine all resonances and show that the corresponding residue oper","authors_text":"A. Pasquale, J. Hilgert, T. Przebinda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-27T21:02:31Z","title":"Resonances for the Laplacian on products of two rank one Riemannian symmetric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07032","kind":"arxiv","version":2},"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:ae45a92a52ed1359a4a3699ea1b3ed7e9d9117eab82e904e4d6c6a37a8291f64","target":"record","created_at":"2026-05-18T01:25:46Z","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":"7467ad754fe222358cdc408aa3bd3b6596751a8b96fa3204d2a092427a790b3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-27T21:02:31Z","title_canon_sha256":"4e2dc0b808b1f9325898bbbf39702393aa9a28afb50e612ffdd4f9dfa89c1cb5"},"schema_version":"1.0","source":{"id":"1508.07032","kind":"arxiv","version":2}},"canonical_sha256":"85c268e89082e21537f86141388167effe26eeb56442926b05ec91e969a8c1c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85c268e89082e21537f86141388167effe26eeb56442926b05ec91e969a8c1c1","first_computed_at":"2026-05-18T01:25:46.699499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:46.699499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gZ0+F535NqR4QNd9NPjkNhHRkx4LT/M9dwgn/oTSkZ2RKLF7sRu8feiiIANiW9crmkeI06o5YF/xiG/UovCVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:46.699997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07032","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae45a92a52ed1359a4a3699ea1b3ed7e9d9117eab82e904e4d6c6a37a8291f64","sha256:171c945aa2e8a064a53bed42c1df03a858ac21633eb10ba15b3d0b81bb5515e1"],"state_sha256":"319fc4730400685281d2d12e3fdf17184587abb5961bc6a71b9306e0e2d5e4ed"}