{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:BICQXTXE7DDSKVMVUSHVGXZCB2","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":"58e12d05dea008ba8076d853e0f044fa61bbf3ed429ace23099366ca112cecfa","cross_cats_sorted":["math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2005-07-18T22:45:42Z","title_canon_sha256":"f57620d9c90c80f42dc87b18b3809aeec7cac5aed6f362b36ea49ef04dfd5bff"},"schema_version":"1.0","source":{"id":"math-ph/0507045","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0507045","created_at":"2026-07-04T14:50:33Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0507045v3","created_at":"2026-07-04T14:50:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0507045","created_at":"2026-07-04T14:50:33Z"},{"alias_kind":"pith_short_12","alias_value":"BICQXTXE7DDS","created_at":"2026-07-04T14:50:33Z"},{"alias_kind":"pith_short_16","alias_value":"BICQXTXE7DDSKVMV","created_at":"2026-07-04T14:50:33Z"},{"alias_kind":"pith_short_8","alias_value":"BICQXTXE","created_at":"2026-07-04T14:50:33Z"}],"graph_snapshots":[{"event_id":"sha256:6640618ece09d202cf36d95e7abce31ccd39035f337c19ccc9f5afc896f1ef4c","target":"graph","created_at":"2026-07-04T14:50:33Z","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/math-ph/0507045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Various problems concerning the geometry of the space $u^*(\\cH)$ of Hermitian operators on a Hilbert space $\\cH$ are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into K\\\"ahler submanifolds. It is also shown that the space $\\cD(\\cH)$ of density states on an $n$-dimensional Hilbert space $\\cH$ is naturally a manifold stratified space with the stratification induced by the the rank of the state. Thus the space $\\cD^k(\\cH)$ of rank-$k$ states, $k=1,...,n$, is a smooth manifold of (real) dimension $2nk-k^2-1$ and this stratific","authors_text":"Giuseppe Marmo, Janusz Grabowski, Marek Ku\\'s","cross_cats":["math.MP","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-07-18T22:45:42Z","title":"Geometry of quantum systems: density states and entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507045","kind":"arxiv","version":3},"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":"sha256:42e7ac7ca3a4a9e512f205e3d07271f834015a1889a75697a2375ee6f4349d5e","target":"record","created_at":"2026-07-04T14:50:33Z","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":"58e12d05dea008ba8076d853e0f044fa61bbf3ed429ace23099366ca112cecfa","cross_cats_sorted":["math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2005-07-18T22:45:42Z","title_canon_sha256":"f57620d9c90c80f42dc87b18b3809aeec7cac5aed6f362b36ea49ef04dfd5bff"},"schema_version":"1.0","source":{"id":"math-ph/0507045","kind":"arxiv","version":3}},"canonical_sha256":"0a050bcee4f8c7255595a48f535f220e80cc5d413218f40f8c648d0794005ec4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a050bcee4f8c7255595a48f535f220e80cc5d413218f40f8c648d0794005ec4","first_computed_at":"2026-07-04T14:50:33.907190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:50:33.907190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eb2zUN/+0P/pnV/l2Arai+gTzX/Gnxvx/jE9eTTgsXhR/IsiuTDB49yBnD7DUnfKsoZ+wa/XGNF8Be41wvCyCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:50:33.907563Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0507045","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42e7ac7ca3a4a9e512f205e3d07271f834015a1889a75697a2375ee6f4349d5e","sha256:6640618ece09d202cf36d95e7abce31ccd39035f337c19ccc9f5afc896f1ef4c"],"state_sha256":"02cb0bae60ae4af57925fc37a6d6335dd242ef535613646dddaba333e42be9dc"}