{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CPSW5OKMIDTCV4Q6YEN4LDSNKT","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":"0cd368d0e8be1c409a24c131a250c8ed48f5145f0b745084170fb2f7fb6f4f15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-06T12:35:53Z","title_canon_sha256":"a9dc58277386845c66b6b83d2c4dffe5c97a323d2c4e302c545c1c2dfc3aa322"},"schema_version":"1.0","source":{"id":"1407.1489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1489","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1489v2","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1489","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"CPSW5OKMIDTC","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CPSW5OKMIDTCV4Q6","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CPSW5OKM","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:6c1c3eed0c9a9230ba322075331d7592fc59aaf6970711e0e6fdae1114f6589a","target":"graph","created_at":"2026-05-18T01:25:47Z","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":"Paley-Wiener type theorems describe the image of a given space of functions, often compactly supported functions, under an integral transform, usually a Fourier transform on a group or homogeneous space. Several authors have studied Paley-Wiener type theorems for Euclidean spaces, Riemannian symmetric spaces of compact or non-compact type as well as affine Riemannian symmetric spaces. In this article we prove a Paley-Wiener theorem for homogeneous line bundles over a compact symmetric space $U/K$. The Paley-Wiener theorem characterizes f with sufficiently small support in terms of holomorphic ","authors_text":"Gestur Olafsson, Vivian M. Ho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-06T12:35:53Z","title":"Paley-Wiener Theorem for Line Bundles over Compact Symmetric Spaces and New Estimates for the Heckman-Opdam Hypergeometric Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1489","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":"sha256:4653a9d0f5a23bde8740487ed0c471c5f3950e15f3a92cd76924746328c70f35","target":"record","created_at":"2026-05-18T01:25:47Z","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":"0cd368d0e8be1c409a24c131a250c8ed48f5145f0b745084170fb2f7fb6f4f15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-06T12:35:53Z","title_canon_sha256":"a9dc58277386845c66b6b83d2c4dffe5c97a323d2c4e302c545c1c2dfc3aa322"},"schema_version":"1.0","source":{"id":"1407.1489","kind":"arxiv","version":2}},"canonical_sha256":"13e56eb94c40e62af21ec11bc58e4d54f22156023d7ce5b0b140086e0beff5fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13e56eb94c40e62af21ec11bc58e4d54f22156023d7ce5b0b140086e0beff5fb","first_computed_at":"2026-05-18T01:25:47.617624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:47.617624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9Omzsn46eErddSTSW3PF4oTUd2vD98bmhTt9z3mfbPQ2kdI806P1VSLvIF+yFnRYq4VNrTiFJqkSYNsZeN5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:47.618132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4653a9d0f5a23bde8740487ed0c471c5f3950e15f3a92cd76924746328c70f35","sha256:6c1c3eed0c9a9230ba322075331d7592fc59aaf6970711e0e6fdae1114f6589a"],"state_sha256":"eefc715a6e6db55d04826cb0252c7c9f49aba3bfa38b25ead7ba9ff289816cef"}