{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JZMFCZQCNQFTJ7XRCYBZZK75Z2","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":"23fe42e64cfe2354cfb73be7ca9013f8f5e8685e39b96fb39ec36494dc7331c1","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-06T13:52:52Z","title_canon_sha256":"6da1744379895d42f57fb02e438af58178f6c57f8adf01a189f1099207a93da6"},"schema_version":"1.0","source":{"id":"2607.05094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05094","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05094v1","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05094","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"JZMFCZQCNQFT","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"JZMFCZQCNQFTJ7XR","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"JZMFCZQC","created_at":"2026-07-07T03:19:15Z"}],"graph_snapshots":[{"event_id":"sha256:9c8a902bac98fd64c6fad19f9c40d83e5e2266b00a414eb7d4da601aa6e09ccd","target":"graph","created_at":"2026-07-07T03:19:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.05094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Matrix Brownian motion provides a powerful framework for studying crossover ensembles in quantum chaos and quantum transport, as well as thermalization and information scrambling in many-body dynamics. Here, we develop a unified diagrammatic framework to characterize Brownian ensembles for orthogonal and symplectic random matrices, which describe systems with particle-hole symmetry. We compute polynomial averages up to fourth order and construct an orthogonally invariant interpolation for the disconnected $\\mathrm{SO}^-(q)$ sector of the orthogonal group. We consider applications relating to t","authors_text":"Piet W. Brouwer, Zhiyang Tan","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-06T13:52:52Z","title":"Brownian Motion in Orthogonal and Symplectic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05094","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:cd5da92832de64621385f3aafe7575fcc3bd6e65c815aac80f3b89c2fca1c840","target":"record","created_at":"2026-07-07T03:19:15Z","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":"23fe42e64cfe2354cfb73be7ca9013f8f5e8685e39b96fb39ec36494dc7331c1","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-06T13:52:52Z","title_canon_sha256":"6da1744379895d42f57fb02e438af58178f6c57f8adf01a189f1099207a93da6"},"schema_version":"1.0","source":{"id":"2607.05094","kind":"arxiv","version":1}},"canonical_sha256":"4e585166026c0b34fef116039cabfdceac90fecb6b69bdb370bd7c21d5907c22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e585166026c0b34fef116039cabfdceac90fecb6b69bdb370bd7c21d5907c22","first_computed_at":"2026-07-07T03:19:15.861281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T03:19:15.861281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y0G30qjDYXmDCXvJcvBSH8pB3mFyXxpgDZZvAKHLNiYMQ3/YdGS191VSMzXwk92CxtFAO5BnnIhLrqFdLBfBDQ==","signature_status":"signed_v1","signed_at":"2026-07-07T03:19:15.861697Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd5da92832de64621385f3aafe7575fcc3bd6e65c815aac80f3b89c2fca1c840","sha256:9c8a902bac98fd64c6fad19f9c40d83e5e2266b00a414eb7d4da601aa6e09ccd"],"state_sha256":"c66226fd08203c6412db84cf4e4b60bb5695ab256b4ed6cccaa628a10234caaa"}