{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZBIZMC3B5YTS42722VMR4ICDKV","short_pith_number":"pith:ZBIZMC3B","canonical_record":{"source":{"id":"1310.7344","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T08:57:54Z","cross_cats_sorted":[],"title_canon_sha256":"7f01d5ca1f52531bfc78c0d08a70c3c7bcaea4d3acfa39d57b12da03a83cad8d","abstract_canon_sha256":"869ee44a95960f1808e87e9292fb875bcf08a53e4e5717492b44480dc9768873"},"schema_version":"1.0"},"canonical_sha256":"c851960b61ee272e6bfad5591e2043557339adcbb6e5132749d7b1c6daa1a66e","source":{"kind":"arxiv","id":"1310.7344","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7344","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7344v2","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7344","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZBIZMC3B5YTS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBIZMC3B5YTS4272","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBIZMC3B","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZBIZMC3B5YTS42722VMR4ICDKV","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7344","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T08:57:54Z","cross_cats_sorted":[],"title_canon_sha256":"7f01d5ca1f52531bfc78c0d08a70c3c7bcaea4d3acfa39d57b12da03a83cad8d","abstract_canon_sha256":"869ee44a95960f1808e87e9292fb875bcf08a53e4e5717492b44480dc9768873"},"schema_version":"1.0"},"canonical_sha256":"c851960b61ee272e6bfad5591e2043557339adcbb6e5132749d7b1c6daa1a66e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:08.487856Z","signature_b64":"g+nOgQyYk0+3HqBEFi59dB1ngFUXwiRl9iZLcPWDyFiR7T5DlSN7UWQSmKJwXjOEPu2KaStMXlR51bTmoDcnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c851960b61ee272e6bfad5591e2043557339adcbb6e5132749d7b1c6daa1a66e","last_reissued_at":"2026-05-18T02:59:08.487243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:08.487243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7344","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":"2026-05-18T02:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8Z5o0NzZS8Rr0uT1XT8snj7qS+ail5PzAi97zAUPV+cRwhjMDGWMeQUq8iAouBSe/8KB6TRKp5vhdM8vX2dDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:20:19.009875Z"},"content_sha256":"996dcb192c2dd8811ab45dc5dc2e5ef67fd717e02769cc7224916c1b9dcce75d","schema_version":"1.0","event_id":"sha256:996dcb192c2dd8811ab45dc5dc2e5ef67fd717e02769cc7224916c1b9dcce75d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZBIZMC3B5YTS42722VMR4ICDKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Luk\\'{a}cs--Olkin--Rubin theorem on symmetric cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eszter Gselmann","submitted_at":"2013-10-28T08:57:54Z","abstract_excerpt":"In this paper we prove a Luk\\'{a}cs type characterization theorem of the Wishart distribution on Euclidean simple Jordan algebras under weak regularity assumptions (e.g. measurability) on the densities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7344","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":"2026-05-18T02:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUHH6zGNDYyUM2xi3TqKqIpPO24bE9UVBeqWwt96seTpe4caVlqQ6QIGbLlCjml2wA2sjwWSBn83EaPH4jZBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:20:19.010541Z"},"content_sha256":"1ac10726a622fb710d2509e6e04ae7c6f56e583f63ffad53856e42d438a0b3fb","schema_version":"1.0","event_id":"sha256:1ac10726a622fb710d2509e6e04ae7c6f56e583f63ffad53856e42d438a0b3fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBIZMC3B5YTS42722VMR4ICDKV/bundle.json","state_url":"https://pith.science/pith/ZBIZMC3B5YTS42722VMR4ICDKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBIZMC3B5YTS42722VMR4ICDKV/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":"2026-06-06T21:20:19Z","links":{"resolver":"https://pith.science/pith/ZBIZMC3B5YTS42722VMR4ICDKV","bundle":"https://pith.science/pith/ZBIZMC3B5YTS42722VMR4ICDKV/bundle.json","state":"https://pith.science/pith/ZBIZMC3B5YTS42722VMR4ICDKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBIZMC3B5YTS42722VMR4ICDKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZBIZMC3B5YTS42722VMR4ICDKV","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":"869ee44a95960f1808e87e9292fb875bcf08a53e4e5717492b44480dc9768873","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T08:57:54Z","title_canon_sha256":"7f01d5ca1f52531bfc78c0d08a70c3c7bcaea4d3acfa39d57b12da03a83cad8d"},"schema_version":"1.0","source":{"id":"1310.7344","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7344","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7344v2","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7344","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZBIZMC3B5YTS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBIZMC3B5YTS4272","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBIZMC3B","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:1ac10726a622fb710d2509e6e04ae7c6f56e583f63ffad53856e42d438a0b3fb","target":"graph","created_at":"2026-05-18T02:59:08Z","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":"In this paper we prove a Luk\\'{a}cs type characterization theorem of the Wishart distribution on Euclidean simple Jordan algebras under weak regularity assumptions (e.g. measurability) on the densities.","authors_text":"Eszter Gselmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T08:57:54Z","title":"The Luk\\'{a}cs--Olkin--Rubin theorem on symmetric cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7344","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":"sha256:996dcb192c2dd8811ab45dc5dc2e5ef67fd717e02769cc7224916c1b9dcce75d","target":"record","created_at":"2026-05-18T02:59:08Z","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":"869ee44a95960f1808e87e9292fb875bcf08a53e4e5717492b44480dc9768873","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T08:57:54Z","title_canon_sha256":"7f01d5ca1f52531bfc78c0d08a70c3c7bcaea4d3acfa39d57b12da03a83cad8d"},"schema_version":"1.0","source":{"id":"1310.7344","kind":"arxiv","version":2}},"canonical_sha256":"c851960b61ee272e6bfad5591e2043557339adcbb6e5132749d7b1c6daa1a66e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c851960b61ee272e6bfad5591e2043557339adcbb6e5132749d7b1c6daa1a66e","first_computed_at":"2026-05-18T02:59:08.487243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:08.487243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g+nOgQyYk0+3HqBEFi59dB1ngFUXwiRl9iZLcPWDyFiR7T5DlSN7UWQSmKJwXjOEPu2KaStMXlR51bTmoDcnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:08.487856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7344","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:996dcb192c2dd8811ab45dc5dc2e5ef67fd717e02769cc7224916c1b9dcce75d","sha256:1ac10726a622fb710d2509e6e04ae7c6f56e583f63ffad53856e42d438a0b3fb"],"state_sha256":"b3b62d3013fc12e340f9e685a7db1d2fdb6bf1aeab7354c40353bc395d6505b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vqUz8tHtXVWphTdv4dJbPArd5G0gst9zvYikmIpcGK0hfCetrGdTGGWbA6MCzLCBi0XGsiuvLPBi/zA8eLUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:20:19.014345Z","bundle_sha256":"876209ca8da1ca34363b1d64ee44cbdaefb92839fe79cba282d480a1cdd0f657"}}