{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MVK5BC2VXOFH7OAZXKDWUUXLXZ","short_pith_number":"pith:MVK5BC2V","canonical_record":{"source":{"id":"1411.2110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-08T11:27:18Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"701ba41f40c5e1aebef4265fe717afdd4674ef5679ad2a00e8f17ddc168292c8","abstract_canon_sha256":"6019616c1c97b9eae4d5b29becf7cb704af35a0fb9cf0436d8c93de89fc5d52b"},"schema_version":"1.0"},"canonical_sha256":"6555d08b55bb8a7fb819ba876a52ebbe411e7cf2ef1f28d828262144e50a733c","source":{"kind":"arxiv","id":"1411.2110","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2110","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2110v2","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2110","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"MVK5BC2VXOFH","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MVK5BC2VXOFH7OAZ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MVK5BC2V","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MVK5BC2VXOFH7OAZXKDWUUXLXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-08T11:27:18Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"701ba41f40c5e1aebef4265fe717afdd4674ef5679ad2a00e8f17ddc168292c8","abstract_canon_sha256":"6019616c1c97b9eae4d5b29becf7cb704af35a0fb9cf0436d8c93de89fc5d52b"},"schema_version":"1.0"},"canonical_sha256":"6555d08b55bb8a7fb819ba876a52ebbe411e7cf2ef1f28d828262144e50a733c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:59.508884Z","signature_b64":"H2Fcp7NA2CsTqP6e37Vg+YeEjoc0ScwBq7LutNXT27qPIC0pJXBQ2jCPZsqCvuJ9yfocIUfmEOUxVH997wc/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6555d08b55bb8a7fb819ba876a52ebbe411e7cf2ef1f28d828262144e50a733c","last_reissued_at":"2026-05-18T00:47:59.508242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:59.508242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2110","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":"2026-05-18T00:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HCK75FnkkMdTU0Dt/5HlCHmO2CDVlP45cVPtxgnYHZ4kHDWFWvEdnnIZqWTlYO4kncI2tqqy2OktiWgbjQnJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:02:06.121566Z"},"content_sha256":"0d0f436ad1bba72e52863146fbf288fca9dea47881df04dc87ee26f2d0239281","schema_version":"1.0","event_id":"sha256:0d0f436ad1bba72e52863146fbf288fca9dea47881df04dc87ee26f2d0239281"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MVK5BC2VXOFH7OAZXKDWUUXLXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix beta-integrals: an overview","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.CA","authors_text":"Yury A. Neretin","submitted_at":"2014-11-08T11:27:18Z","abstract_excerpt":"First examples of matrix beta-integrals were discovered on 1930-50s by Siegel and Hua, in 60s Gindikin obtained multi-parametric series of such integrals. We discuss beta-integrals related to symmetric spaces, their interpolation with respect to the dimension of a ground field, and adelic analogs; also we discuss beta-integrals related to flag spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2110","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":"2026-05-18T00:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmVBrSr/KUcaki6te3v9q6yFQktbmuOOe6R7ZM1ToJqP/NVnvIi2hxjPhkRv154bBCdb6vAH+5f+EwblWmzZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:02:06.122146Z"},"content_sha256":"328b6830b2ad4fd8491f2c8e7e829ac1260b448ff176517934eb8af220cb6562","schema_version":"1.0","event_id":"sha256:328b6830b2ad4fd8491f2c8e7e829ac1260b448ff176517934eb8af220cb6562"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVK5BC2VXOFH7OAZXKDWUUXLXZ/bundle.json","state_url":"https://pith.science/pith/MVK5BC2VXOFH7OAZXKDWUUXLXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVK5BC2VXOFH7OAZXKDWUUXLXZ/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":"2026-06-11T02:02:06Z","links":{"resolver":"https://pith.science/pith/MVK5BC2VXOFH7OAZXKDWUUXLXZ","bundle":"https://pith.science/pith/MVK5BC2VXOFH7OAZXKDWUUXLXZ/bundle.json","state":"https://pith.science/pith/MVK5BC2VXOFH7OAZXKDWUUXLXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVK5BC2VXOFH7OAZXKDWUUXLXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MVK5BC2VXOFH7OAZXKDWUUXLXZ","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":"6019616c1c97b9eae4d5b29becf7cb704af35a0fb9cf0436d8c93de89fc5d52b","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-08T11:27:18Z","title_canon_sha256":"701ba41f40c5e1aebef4265fe717afdd4674ef5679ad2a00e8f17ddc168292c8"},"schema_version":"1.0","source":{"id":"1411.2110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2110","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2110v2","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2110","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"MVK5BC2VXOFH","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MVK5BC2VXOFH7OAZ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MVK5BC2V","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:328b6830b2ad4fd8491f2c8e7e829ac1260b448ff176517934eb8af220cb6562","target":"graph","created_at":"2026-05-18T00:47:59Z","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":"First examples of matrix beta-integrals were discovered on 1930-50s by Siegel and Hua, in 60s Gindikin obtained multi-parametric series of such integrals. We discuss beta-integrals related to symmetric spaces, their interpolation with respect to the dimension of a ground field, and adelic analogs; also we discuss beta-integrals related to flag spaces.","authors_text":"Yury A. Neretin","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-08T11:27:18Z","title":"Matrix beta-integrals: an overview"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2110","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":"sha256:0d0f436ad1bba72e52863146fbf288fca9dea47881df04dc87ee26f2d0239281","target":"record","created_at":"2026-05-18T00:47:59Z","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":"6019616c1c97b9eae4d5b29becf7cb704af35a0fb9cf0436d8c93de89fc5d52b","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-08T11:27:18Z","title_canon_sha256":"701ba41f40c5e1aebef4265fe717afdd4674ef5679ad2a00e8f17ddc168292c8"},"schema_version":"1.0","source":{"id":"1411.2110","kind":"arxiv","version":2}},"canonical_sha256":"6555d08b55bb8a7fb819ba876a52ebbe411e7cf2ef1f28d828262144e50a733c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6555d08b55bb8a7fb819ba876a52ebbe411e7cf2ef1f28d828262144e50a733c","first_computed_at":"2026-05-18T00:47:59.508242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:59.508242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H2Fcp7NA2CsTqP6e37Vg+YeEjoc0ScwBq7LutNXT27qPIC0pJXBQ2jCPZsqCvuJ9yfocIUfmEOUxVH997wc/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:59.508884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d0f436ad1bba72e52863146fbf288fca9dea47881df04dc87ee26f2d0239281","sha256:328b6830b2ad4fd8491f2c8e7e829ac1260b448ff176517934eb8af220cb6562"],"state_sha256":"e3d849408632e70a1428995c0a5d7f045b937c562f95ec080d92b9e577429118"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5f8+ctT1/GauMYpfy7TfL69pTJyvQ6qCrZHymeIyT6kNyTxQ2RbeLQgpFcxw9QZsAw6ynq7a51/KEUvzCpCyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:02:06.125763Z","bundle_sha256":"28bb73a0b24f85e7e2b271d26c93b4377c0817fd3a97e767891492ccef2d451c"}}