{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DMRENIYHOESDCODQMR42ST7N4Z","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":"ce471208ac3bde07b2a4fbb4a6fe8d04781aa864a47d0278b8ee854bbb9ba1d3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-17T07:26:33Z","title_canon_sha256":"41b765228aab681b2e8f0d9c0c15f9b3f7ff1ca67e74ee946f8d4e7be962fb95"},"schema_version":"1.0","source":{"id":"1409.4882","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4882","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4882v3","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4882","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"DMRENIYHOESD","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DMRENIYHOESDCODQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DMRENIYH","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8f0b2e8cc8395bf6b3435c7c8dbc3dde9d39ca0acb5fffe85d5f5c7f364820a5","target":"graph","created_at":"2026-05-18T01:15:36Z","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":"The goal of this paper is to describe the $\\alpha$-cosine transform on functions on a Grassmannian of $i$-planes in an $n$-dimensional real vector space. in analytic terms as explicitly as possible. We show that for all but finitely many complex $\\alpha$ the $\\alpha$-cosine transform is a composition of the $(\\alpha+2)$-cosine transform with an explicitly written (though complicated) O(n)-invariant differential operator. For all exceptional values of $\\alpha$ except one we interpret the $\\alpha$-cosine transform explicitly as either the Radon transform or composition of two Radon transforms. E","authors_text":"Dmitry Gourevitch, Semyon Alesker, Siddhartha Sahi","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-17T07:26:33Z","title":"On an analytic description of the $\\alpha$-cosine transform on real Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4882","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":"sha256:251ed29b63a987cb3e2d07b59ec6095df3dc24ea05b234b46e8e2450313a402e","target":"record","created_at":"2026-05-18T01:15:36Z","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":"ce471208ac3bde07b2a4fbb4a6fe8d04781aa864a47d0278b8ee854bbb9ba1d3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-17T07:26:33Z","title_canon_sha256":"41b765228aab681b2e8f0d9c0c15f9b3f7ff1ca67e74ee946f8d4e7be962fb95"},"schema_version":"1.0","source":{"id":"1409.4882","kind":"arxiv","version":3}},"canonical_sha256":"1b2246a30771243138706479a94fede66b002e922841aeffacb4b892ff7424cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b2246a30771243138706479a94fede66b002e922841aeffacb4b892ff7424cd","first_computed_at":"2026-05-18T01:15:36.426728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:36.426728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZEjsLKTFn28I9CEzjm7LHTWi1/yjc93dWjeZVjGnNaOTRmRLt/Vy6o0asQ1AzG0tYL/dxl+O+1gzjK7h+4fAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:36.427288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4882","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:251ed29b63a987cb3e2d07b59ec6095df3dc24ea05b234b46e8e2450313a402e","sha256:8f0b2e8cc8395bf6b3435c7c8dbc3dde9d39ca0acb5fffe85d5f5c7f364820a5"],"state_sha256":"0bf1c26bcbaf11de58a73ae1b7aba9345e2817d9879be8a99a7f5e71d057bfe5"}