{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HY5CACNDGMWTHJAPPA432DYUIS","short_pith_number":"pith:HY5CACND","canonical_record":{"source":{"id":"1802.05147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-14T15:15:55Z","cross_cats_sorted":["math.CA","math.RT"],"title_canon_sha256":"48271f334c7f42d46bb2630c09bfc60afc9a6cb1518f38428d76084220796d2c","abstract_canon_sha256":"63761816c7137b6d2d20d3f1f648a3fd1d606a9fe900efb6656012e026adbff4"},"schema_version":"1.0"},"canonical_sha256":"3e3a2009a3332d33a40f7839bd0f1444a5788646b56a3502a6c99d61d31c9eff","source":{"kind":"arxiv","id":"1802.05147","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05147","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05147v2","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05147","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"HY5CACNDGMWT","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HY5CACNDGMWTHJAP","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HY5CACND","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HY5CACNDGMWTHJAPPA432DYUIS","target":"record","payload":{"canonical_record":{"source":{"id":"1802.05147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-14T15:15:55Z","cross_cats_sorted":["math.CA","math.RT"],"title_canon_sha256":"48271f334c7f42d46bb2630c09bfc60afc9a6cb1518f38428d76084220796d2c","abstract_canon_sha256":"63761816c7137b6d2d20d3f1f648a3fd1d606a9fe900efb6656012e026adbff4"},"schema_version":"1.0"},"canonical_sha256":"3e3a2009a3332d33a40f7839bd0f1444a5788646b56a3502a6c99d61d31c9eff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:13.309767Z","signature_b64":"hZPO6i2dwb0z45vJMQQofUZoyUJngdoCkAoDoIAZBimPS70NM3szOgrMzHtEsBc+8nmVTb3lnUG63ctIA7iyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e3a2009a3332d33a40f7839bd0f1444a5788646b56a3502a6c99d61d31c9eff","last_reissued_at":"2026-05-17T23:41:13.309258Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:13.309258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.05147","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3tMecEOTbigFl9bTWFEbn5wcS9H+mtWiUAZ8UAXraYOOL5KIa/5HeiwTXVQbbE/nGZFPGZNERVgeU4TXgr7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:19:10.378027Z"},"content_sha256":"569b5cc843392a303521c52af4b669964cd0d7ff398ca2321bdc9d861ee4d77b","schema_version":"1.0","event_id":"sha256:569b5cc843392a303521c52af4b669964cd0d7ff398ca2321bdc9d861ee4d77b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HY5CACNDGMWTHJAPPA432DYUIS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some central limit theorems for random walks associated with hypergeometric functions of type BC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.RT"],"primary_cat":"math.PR","authors_text":"Merdan Artykov, Michael Voit","submitted_at":"2018-02-14T15:15:55Z","abstract_excerpt":"The spherical functions of the noncompact Grassmann manifolds over the real or complex numbers or the quaternions with rank q and dimension parameter p can be seen as Heckman-Opdam hypergeometric functions of type BC, when the double coset space is identified with some Weyl chamber of type B. The associated double coset hypergroups may be embedded into a continuous family of commutative hypergroups with these hypergeometric functions as multiplicative functions with p in some continuous parameter range by a result of R\\\"osler. Several limit theorems for random walks associated with these hyper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05147","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aTKr8jCwDdROtEqprTNG/kPUCZsEPyvAvWu4I3E7q/y3TMNL2EjfXFkL4STOSbgrEhqP9znR92qpYdL+dDRnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:19:10.378411Z"},"content_sha256":"157248d6d0e1296fea64675115749aab1ce7a45b98a2b54c78103c25ef1e6379","schema_version":"1.0","event_id":"sha256:157248d6d0e1296fea64675115749aab1ce7a45b98a2b54c78103c25ef1e6379"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY5CACNDGMWTHJAPPA432DYUIS/bundle.json","state_url":"https://pith.science/pith/HY5CACNDGMWTHJAPPA432DYUIS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY5CACNDGMWTHJAPPA432DYUIS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T21:19:10Z","links":{"resolver":"https://pith.science/pith/HY5CACNDGMWTHJAPPA432DYUIS","bundle":"https://pith.science/pith/HY5CACNDGMWTHJAPPA432DYUIS/bundle.json","state":"https://pith.science/pith/HY5CACNDGMWTHJAPPA432DYUIS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY5CACNDGMWTHJAPPA432DYUIS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HY5CACNDGMWTHJAPPA432DYUIS","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":"63761816c7137b6d2d20d3f1f648a3fd1d606a9fe900efb6656012e026adbff4","cross_cats_sorted":["math.CA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-14T15:15:55Z","title_canon_sha256":"48271f334c7f42d46bb2630c09bfc60afc9a6cb1518f38428d76084220796d2c"},"schema_version":"1.0","source":{"id":"1802.05147","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05147","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05147v2","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05147","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"HY5CACNDGMWT","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HY5CACNDGMWTHJAP","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HY5CACND","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:157248d6d0e1296fea64675115749aab1ce7a45b98a2b54c78103c25ef1e6379","target":"graph","created_at":"2026-05-17T23:41:13Z","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 spherical functions of the noncompact Grassmann manifolds over the real or complex numbers or the quaternions with rank q and dimension parameter p can be seen as Heckman-Opdam hypergeometric functions of type BC, when the double coset space is identified with some Weyl chamber of type B. The associated double coset hypergroups may be embedded into a continuous family of commutative hypergroups with these hypergeometric functions as multiplicative functions with p in some continuous parameter range by a result of R\\\"osler. Several limit theorems for random walks associated with these hyper","authors_text":"Merdan Artykov, Michael Voit","cross_cats":["math.CA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-14T15:15:55Z","title":"Some central limit theorems for random walks associated with hypergeometric functions of type BC"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05147","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":"sha256:569b5cc843392a303521c52af4b669964cd0d7ff398ca2321bdc9d861ee4d77b","target":"record","created_at":"2026-05-17T23:41:13Z","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":"63761816c7137b6d2d20d3f1f648a3fd1d606a9fe900efb6656012e026adbff4","cross_cats_sorted":["math.CA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-14T15:15:55Z","title_canon_sha256":"48271f334c7f42d46bb2630c09bfc60afc9a6cb1518f38428d76084220796d2c"},"schema_version":"1.0","source":{"id":"1802.05147","kind":"arxiv","version":2}},"canonical_sha256":"3e3a2009a3332d33a40f7839bd0f1444a5788646b56a3502a6c99d61d31c9eff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e3a2009a3332d33a40f7839bd0f1444a5788646b56a3502a6c99d61d31c9eff","first_computed_at":"2026-05-17T23:41:13.309258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:13.309258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hZPO6i2dwb0z45vJMQQofUZoyUJngdoCkAoDoIAZBimPS70NM3szOgrMzHtEsBc+8nmVTb3lnUG63ctIA7iyBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:13.309767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.05147","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:569b5cc843392a303521c52af4b669964cd0d7ff398ca2321bdc9d861ee4d77b","sha256:157248d6d0e1296fea64675115749aab1ce7a45b98a2b54c78103c25ef1e6379"],"state_sha256":"d86e854500d1191f2a0f77e8d11e9d28c45dd79225ca85371d72b3cbb500104e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eXnzVFWbr5sAGERx9ZensrbcYxJ36G1DcRPty3MEP9qHDpElwh/kKvO8gNcVuuSdXV92njnIp3MNqmaYpYHJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:19:10.380591Z","bundle_sha256":"ba2ac9d4dc521c34093a246da2ce73161de14be4e4cbd30c893f0587d29c3d5c"}}