{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:435U2LRDJAETYZ37TPXB33755S","short_pith_number":"pith:435U2LRD","canonical_record":{"source":{"id":"2504.12507","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-04-16T21:59:05Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"3a38df2c2a3fdbc51a19f98995f3f19d816b5deef5199c5efdd42722d55e5938","abstract_canon_sha256":"bcf95fedcdf0c597ddf5dad9daf28fa4321392c16c3c2ac40ac7b16c1fc86af8"},"schema_version":"1.0"},"canonical_sha256":"e6fb4d2e2348093c677f9bee1deffdecacc593a0a4309d58438b1be3277ca510","source":{"kind":"arxiv","id":"2504.12507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.12507","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"arxiv_version","alias_value":"2504.12507v1","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.12507","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"pith_short_12","alias_value":"435U2LRDJAET","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"pith_short_16","alias_value":"435U2LRDJAETYZ37","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"pith_short_8","alias_value":"435U2LRD","created_at":"2026-07-05T10:50:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:435U2LRDJAETYZ37TPXB33755S","target":"record","payload":{"canonical_record":{"source":{"id":"2504.12507","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-04-16T21:59:05Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"3a38df2c2a3fdbc51a19f98995f3f19d816b5deef5199c5efdd42722d55e5938","abstract_canon_sha256":"bcf95fedcdf0c597ddf5dad9daf28fa4321392c16c3c2ac40ac7b16c1fc86af8"},"schema_version":"1.0"},"canonical_sha256":"e6fb4d2e2348093c677f9bee1deffdecacc593a0a4309d58438b1be3277ca510","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:17.605360Z","signature_b64":"zhH/EHZfUyCTd7mR02oQDINkpy9Dw8hWst3nvH7W2CeBDFhJm9bQtzYZ7SRjlKOoueJsyt8Fa846VkHUPkEmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6fb4d2e2348093c677f9bee1deffdecacc593a0a4309d58438b1be3277ca510","last_reissued_at":"2026-07-05T10:50:17.604814Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:17.604814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.12507","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":"2026-07-05T10:50:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0Vzn6Ljtd1IXLo2COMDbVymmAHTc+BupYOQ0GodFA28i5JbSZu3GilR0pOhf5b0dnAFz3uAdC9ULSLkk4xHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:35:02.939928Z"},"content_sha256":"ee37995b8821c674309f954d7149e79b35c12feeada19d82d06b39959658f0f1","schema_version":"1.0","event_id":"sha256:ee37995b8821c674309f954d7149e79b35c12feeada19d82d06b39959658f0f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:435U2LRDJAETYZ37TPXB33755S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Berislav Buca, Martin Seltmann","submitted_at":"2025-04-16T21:59:05Z","abstract_excerpt":"The dimensionality of kernels for Lindbladian superoperators is of physical interest in various scenarios out of equilibrium, for example in mean-field methods for driven-dissipative spin lattice models that give rise to phase diagrams with a multitude of non-equilibrium stationary states in specific parameter regions. We show that known criteria established in the literature for unique fixpoints of the Lindblad master equation can be better treated in a graph-theoretic framework via a focus on the connectivity of directed graphs associated to the Hamiltonian and jump operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.12507","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/2504.12507/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":"2026-07-05T10:50:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQE0+G6zh+pSUGB6mj6bTsQFi7Q6tY0JrwDoTYsVgKSonwqyLtRjlIL3EW0NxgucOe80WILFsL8A+kStRQvrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:35:02.940424Z"},"content_sha256":"752b9ff83bd4310a9e349865dc20a25521fc1ed676ed3c827022bde0dbfa56c5","schema_version":"1.0","event_id":"sha256:752b9ff83bd4310a9e349865dc20a25521fc1ed676ed3c827022bde0dbfa56c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/435U2LRDJAETYZ37TPXB33755S/bundle.json","state_url":"https://pith.science/pith/435U2LRDJAETYZ37TPXB33755S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/435U2LRDJAETYZ37TPXB33755S/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":"2026-08-19T11:35:02Z","links":{"resolver":"https://pith.science/pith/435U2LRDJAETYZ37TPXB33755S","bundle":"https://pith.science/pith/435U2LRDJAETYZ37TPXB33755S/bundle.json","state":"https://pith.science/pith/435U2LRDJAETYZ37TPXB33755S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/435U2LRDJAETYZ37TPXB33755S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:435U2LRDJAETYZ37TPXB33755S","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":"bcf95fedcdf0c597ddf5dad9daf28fa4321392c16c3c2ac40ac7b16c1fc86af8","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-04-16T21:59:05Z","title_canon_sha256":"3a38df2c2a3fdbc51a19f98995f3f19d816b5deef5199c5efdd42722d55e5938"},"schema_version":"1.0","source":{"id":"2504.12507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.12507","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"arxiv_version","alias_value":"2504.12507v1","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.12507","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"pith_short_12","alias_value":"435U2LRDJAET","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"pith_short_16","alias_value":"435U2LRDJAETYZ37","created_at":"2026-07-05T10:50:17Z"},{"alias_kind":"pith_short_8","alias_value":"435U2LRD","created_at":"2026-07-05T10:50:17Z"}],"graph_snapshots":[{"event_id":"sha256:752b9ff83bd4310a9e349865dc20a25521fc1ed676ed3c827022bde0dbfa56c5","target":"graph","created_at":"2026-07-05T10:50:17Z","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/2504.12507/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The dimensionality of kernels for Lindbladian superoperators is of physical interest in various scenarios out of equilibrium, for example in mean-field methods for driven-dissipative spin lattice models that give rise to phase diagrams with a multitude of non-equilibrium stationary states in specific parameter regions. We show that known criteria established in the literature for unique fixpoints of the Lindblad master equation can be better treated in a graph-theoretic framework via a focus on the connectivity of directed graphs associated to the Hamiltonian and jump operators.","authors_text":"Berislav Buca, Martin Seltmann","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-04-16T21:59:05Z","title":"UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.12507","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:ee37995b8821c674309f954d7149e79b35c12feeada19d82d06b39959658f0f1","target":"record","created_at":"2026-07-05T10:50:17Z","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":"bcf95fedcdf0c597ddf5dad9daf28fa4321392c16c3c2ac40ac7b16c1fc86af8","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-04-16T21:59:05Z","title_canon_sha256":"3a38df2c2a3fdbc51a19f98995f3f19d816b5deef5199c5efdd42722d55e5938"},"schema_version":"1.0","source":{"id":"2504.12507","kind":"arxiv","version":1}},"canonical_sha256":"e6fb4d2e2348093c677f9bee1deffdecacc593a0a4309d58438b1be3277ca510","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6fb4d2e2348093c677f9bee1deffdecacc593a0a4309d58438b1be3277ca510","first_computed_at":"2026-07-05T10:50:17.604814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:50:17.604814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhH/EHZfUyCTd7mR02oQDINkpy9Dw8hWst3nvH7W2CeBDFhJm9bQtzYZ7SRjlKOoueJsyt8Fa846VkHUPkEmBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:50:17.605360Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.12507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee37995b8821c674309f954d7149e79b35c12feeada19d82d06b39959658f0f1","sha256:752b9ff83bd4310a9e349865dc20a25521fc1ed676ed3c827022bde0dbfa56c5"],"state_sha256":"70f069ba464239b9eaf5ca20ef8a4a54a2c864e6d22adfe1384d47a473e9dd02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/xyIGo7Owkg5NkpaFE6QixrlZyH1kbn3xmgroZm7n+q6lltRhO98ZDlrW5Z7FlTEmbjdRS/R53ptu/92r/VDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T11:35:02.944181Z","bundle_sha256":"7d24a11e62e91e4f5a5b148d68322885e2270978ec6262b44a48dfc8ff7eb584"}}