{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Q2OMYZDXROUTTDADKAWVBPAMZP","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":"b3950bc1ce6c742760a2044b3f32ca9f20e06ee7e979e0c6e052e924c745d4b4","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-09T12:36:22Z","title_canon_sha256":"66a754c1805e7ba374238de4c0cc52a4b84ce85a9ccf365e19d3b2dd739d1d4d"},"schema_version":"1.0","source":{"id":"2607.08411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08411","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08411v1","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08411","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q2OMYZDXROUT","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"pith_short_16","alias_value":"Q2OMYZDXROUTTDAD","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"pith_short_8","alias_value":"Q2OMYZDX","created_at":"2026-07-10T01:19:49Z"}],"graph_snapshots":[{"event_id":"sha256:891e93449d3a433830cc057054c94c02141b58140156b2d20cae98fc83d94650","target":"graph","created_at":"2026-07-10T01:19:49Z","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/2607.08411/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend Nielsen's geometric approach for quantum complexity from closed to open quantum systems, whose dynamics is governed by Lindbladian evolution. In this framework, complexity is defined through an optimal-control problem on the space of mixed states, with a cost assigned to both unitary and non-unitary generators. We show that the resulting geometric structure differs fundamentally from the Riemannian geometry that emerges in the case of unitary evolution. In the open-system setting, the natural geometry is typically sub-Finslerian. Dissipation makes the geodesics non-reversible, while ","authors_text":"Ezra Acalapati, Giuseppe Policastro, Kausik Ghosh","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-09T12:36:22Z","title":"The Geometry of Quantum Complexity in Open Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08411","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:fb574fc9a671625aaacbb69c0648abccf1273d48f9f200f3e1a30a27851a47a1","target":"record","created_at":"2026-07-10T01:19:49Z","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":"b3950bc1ce6c742760a2044b3f32ca9f20e06ee7e979e0c6e052e924c745d4b4","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-09T12:36:22Z","title_canon_sha256":"66a754c1805e7ba374238de4c0cc52a4b84ce85a9ccf365e19d3b2dd739d1d4d"},"schema_version":"1.0","source":{"id":"2607.08411","kind":"arxiv","version":1}},"canonical_sha256":"869ccc64778ba9398c03502d50bc0ccbcd375840f7decbd1c26c287a6877607c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"869ccc64778ba9398c03502d50bc0ccbcd375840f7decbd1c26c287a6877607c","first_computed_at":"2026-07-10T01:19:49.793484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T01:19:49.793484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKFKFj8BohM5OM0M7Uf6rm+8R/LB/Jpsfqb3s2RB3YNG/FrdzKbjHdfzmyMRyJ1ZRgZaJK/uvuft4uTK0kY2Dg==","signature_status":"signed_v1","signed_at":"2026-07-10T01:19:49.793904Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb574fc9a671625aaacbb69c0648abccf1273d48f9f200f3e1a30a27851a47a1","sha256:891e93449d3a433830cc057054c94c02141b58140156b2d20cae98fc83d94650"],"state_sha256":"d11f9524224f3e918c675bb64339aadabfff302fe1138677b1dbbaba2f8b8ca6"}