{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Q2OMYZDXROUTTDADKAWVBPAMZP","short_pith_number":"pith:Q2OMYZDX","canonical_record":{"source":{"id":"2607.08411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-09T12:36:22Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"66a754c1805e7ba374238de4c0cc52a4b84ce85a9ccf365e19d3b2dd739d1d4d","abstract_canon_sha256":"b3950bc1ce6c742760a2044b3f32ca9f20e06ee7e979e0c6e052e924c745d4b4"},"schema_version":"1.0"},"canonical_sha256":"869ccc64778ba9398c03502d50bc0ccbcd375840f7decbd1c26c287a6877607c","source":{"kind":"arxiv","id":"2607.08411","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Q2OMYZDXROUTTDADKAWVBPAMZP","target":"record","payload":{"canonical_record":{"source":{"id":"2607.08411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-09T12:36:22Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"66a754c1805e7ba374238de4c0cc52a4b84ce85a9ccf365e19d3b2dd739d1d4d","abstract_canon_sha256":"b3950bc1ce6c742760a2044b3f32ca9f20e06ee7e979e0c6e052e924c745d4b4"},"schema_version":"1.0"},"canonical_sha256":"869ccc64778ba9398c03502d50bc0ccbcd375840f7decbd1c26c287a6877607c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:49.793904Z","signature_b64":"aKFKFj8BohM5OM0M7Uf6rm+8R/LB/Jpsfqb3s2RB3YNG/FrdzKbjHdfzmyMRyJ1ZRgZaJK/uvuft4uTK0kY2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"869ccc64778ba9398c03502d50bc0ccbcd375840f7decbd1c26c287a6877607c","last_reissued_at":"2026-07-10T01:19:49.793484Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:49.793484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.08411","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-10T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Po0rs+a2r88dBzy57+6ci/Zu6UVp1jvGOnN+ZTP7wmUvPw74A3H0rEl4XFxTvU2fb3e/hioPNQTNaB+v483OBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T02:39:35.858560Z"},"content_sha256":"fb574fc9a671625aaacbb69c0648abccf1273d48f9f200f3e1a30a27851a47a1","schema_version":"1.0","event_id":"sha256:fb574fc9a671625aaacbb69c0648abccf1273d48f9f200f3e1a30a27851a47a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Q2OMYZDXROUTTDADKAWVBPAMZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Quantum Complexity in Open Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Ezra Acalapati, Giuseppe Policastro, Kausik Ghosh","submitted_at":"2026-07-09T12:36:22Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08411","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08411/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-10T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1QIaUg8M6wDix6tuHIv14gF+zZd7vbWloaI9qkfltUXgRsQZREChW471hpQfYQGwJeUY/iA8GwdiDKT80SXXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T02:39:35.859275Z"},"content_sha256":"891e93449d3a433830cc057054c94c02141b58140156b2d20cae98fc83d94650","schema_version":"1.0","event_id":"sha256:891e93449d3a433830cc057054c94c02141b58140156b2d20cae98fc83d94650"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2OMYZDXROUTTDADKAWVBPAMZP/bundle.json","state_url":"https://pith.science/pith/Q2OMYZDXROUTTDADKAWVBPAMZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2OMYZDXROUTTDADKAWVBPAMZP/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":"2026-07-11T02:39:35Z","links":{"resolver":"https://pith.science/pith/Q2OMYZDXROUTTDADKAWVBPAMZP","bundle":"https://pith.science/pith/Q2OMYZDXROUTTDADKAWVBPAMZP/bundle.json","state":"https://pith.science/pith/Q2OMYZDXROUTTDADKAWVBPAMZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2OMYZDXROUTTDADKAWVBPAMZP/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hmTOw77nDRCi0vHU0JMHVTfIhxoZH+GV2o3xfH/MTUDyGE1aDs70eqoxIvZ3toKYLhFPDKQL/wCq2Zvx5emBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T02:39:35.876066Z","bundle_sha256":"fbb65e122bdc3fb9fb53cd272b14d203899a72a73364a058585c34ac53cd700f"}}