{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BDMSKL3LWM6CL2K7GAVG5PX64B","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":"89b40f256327b392f0c4f374c6c26da2f0c32686cc7f244efd71a7bd892b67b5","cross_cats_sorted":["gr-qc","math.CV","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-04T16:32:29Z","title_canon_sha256":"018543a6aeb2deda443ab50b8dbb5107d9fe275df534780c4a4f26883bc61098"},"schema_version":"1.0","source":{"id":"1511.01385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01385","created_at":"2026-05-18T01:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01385v1","created_at":"2026-05-18T01:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01385","created_at":"2026-05-18T01:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"BDMSKL3LWM6C","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BDMSKL3LWM6CL2K7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BDMSKL3L","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:f4075141b6daaa944db232e3f55b790d3e664a3ebd7475c96b599495f2aaa51f","target":"graph","created_at":"2026-05-18T01:10:09Z","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":"Some integrals of matrix spaces over a quaternionic field have been calculated in this work. The associated volume of hyperbolic matrix spaces over a quaternionic field has also been calculated by making use of these integrals, and it is of great significance in calculating related kernel functions of these spaces.","authors_text":"Fu-Wen Shu, You-Gen Shen","cross_cats":["gr-qc","math.CV","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-04T16:32:29Z","title":"Several integrals of quaternionic field on hyperbolic matrix space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01385","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":"sha256:108fdc72b1a5f7e5a5cdadbc7841327e6750548acb404d030a3435e1c82a38c5","target":"record","created_at":"2026-05-18T01:10:09Z","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":"89b40f256327b392f0c4f374c6c26da2f0c32686cc7f244efd71a7bd892b67b5","cross_cats_sorted":["gr-qc","math.CV","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-04T16:32:29Z","title_canon_sha256":"018543a6aeb2deda443ab50b8dbb5107d9fe275df534780c4a4f26883bc61098"},"schema_version":"1.0","source":{"id":"1511.01385","kind":"arxiv","version":1}},"canonical_sha256":"08d9252f6bb33c25e95f302a6ebefee07bf07d9cb02b5eb1fb6f07e0b434dfd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08d9252f6bb33c25e95f302a6ebefee07bf07d9cb02b5eb1fb6f07e0b434dfd1","first_computed_at":"2026-05-18T01:10:09.730959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:09.730959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/RDUNvdnuV8QNxL/QUzLfvdVvm4f9MASJua4dZoY6zlanJBecyqIH5IFOwMYxuCtGjugUY2SE7Jb1S/jmOGfCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:09.731516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:108fdc72b1a5f7e5a5cdadbc7841327e6750548acb404d030a3435e1c82a38c5","sha256:f4075141b6daaa944db232e3f55b790d3e664a3ebd7475c96b599495f2aaa51f"],"state_sha256":"852ca4ba6908fdfde8afe6b5d314fa30ded79eb324091ab0647b1110c5e7f866"}