{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:O6ZV55CCVDAOR6EVFARHKPI22S","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":"ce3b1c4d466ca937bbc0aa28454ad41e458139b41bfd97ce85790f8c73f3438e","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.CA","submitted_at":"2001-04-03T11:58:53Z","title_canon_sha256":"376ada3ecd7b2e70049c8bb867df982ddfeadf9d42f3f46c20d2c924256e57a3"},"schema_version":"1.0","source":{"id":"math/0104035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0104035","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0104035v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0104035","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"O6ZV55CCVDAO","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"O6ZV55CCVDAOR6EV","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"O6ZV55CC","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:113dbe937faed2c47981c2ac66028c197c48db965fa8a8d011461e1df183237a","target":"graph","created_at":"2026-05-18T03:36:27Z","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 discuss properties of the index hypergeometric transform (it is named also the Jacobi transform or the Olevsky transform) interpolating analysis of Berezin kernels on rank 1 symmetric spaces. We discuss a unitary intertwining operator from $L^2$ on symmetric space to Berezin deformation of $L^2$. We also find images of some differential operators under the index transform.","authors_text":"Yurii Neretin","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2001-04-03T11:58:53Z","title":"Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104035","kind":"arxiv","version":1},"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:a0dcf612fc0fc217ca7f49925f6c1dfe348c735198851c38255ee7508ed1bdc6","target":"record","created_at":"2026-05-18T03:36:27Z","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":"ce3b1c4d466ca937bbc0aa28454ad41e458139b41bfd97ce85790f8c73f3438e","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.CA","submitted_at":"2001-04-03T11:58:53Z","title_canon_sha256":"376ada3ecd7b2e70049c8bb867df982ddfeadf9d42f3f46c20d2c924256e57a3"},"schema_version":"1.0","source":{"id":"math/0104035","kind":"arxiv","version":1}},"canonical_sha256":"77b35ef442a8c0e8f8952822753d1ad4a9600df4ba59de8b3098bce6f1c85d37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77b35ef442a8c0e8f8952822753d1ad4a9600df4ba59de8b3098bce6f1c85d37","first_computed_at":"2026-05-18T03:36:27.363944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:27.363944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5h71t4Fg/dy/o+7lo5xYN+RyhSELWXyfSTzxE2lveANe0w8wRDuIcRVUBQrxCw9oGrGJujB47GqOss05uEKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:27.364394Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0104035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0dcf612fc0fc217ca7f49925f6c1dfe348c735198851c38255ee7508ed1bdc6","sha256:113dbe937faed2c47981c2ac66028c197c48db965fa8a8d011461e1df183237a"],"state_sha256":"14153bde1deaad14b5c5f9003f03d5716ee14cc5dd55665d39f6c8dde19fdfdd"}