{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WQIMPREFHCWZ63VKZX72HYJSCF","short_pith_number":"pith:WQIMPREF","canonical_record":{"source":{"id":"2408.00081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-31T18:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"52cd7557537261f120b1abe856b97492f70d10eeb5d75ed693a6d21f7b08e91f","abstract_canon_sha256":"4a15bc107b9cba99fb56c4dc73d86020be9a1f733412f6ae7af851c3158115bf"},"schema_version":"1.0"},"canonical_sha256":"b410c7c48538ad9f6eaacdffa3e1321143d0263433a08875443cdd34338e12c1","source":{"kind":"arxiv","id":"2408.00081","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.00081","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"arxiv_version","alias_value":"2408.00081v1","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.00081","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"pith_short_12","alias_value":"WQIMPREFHCWZ","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"pith_short_16","alias_value":"WQIMPREFHCWZ63VK","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"pith_short_8","alias_value":"WQIMPREF","created_at":"2026-07-05T08:50:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WQIMPREFHCWZ63VKZX72HYJSCF","target":"record","payload":{"canonical_record":{"source":{"id":"2408.00081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-31T18:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"52cd7557537261f120b1abe856b97492f70d10eeb5d75ed693a6d21f7b08e91f","abstract_canon_sha256":"4a15bc107b9cba99fb56c4dc73d86020be9a1f733412f6ae7af851c3158115bf"},"schema_version":"1.0"},"canonical_sha256":"b410c7c48538ad9f6eaacdffa3e1321143d0263433a08875443cdd34338e12c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:50:44.909760Z","signature_b64":"SE/R3kOb45kQJnkBCSjdCEL5BRA5YAEVXeURXX2yL4+lBsY5MrOMd9JqabQKhL3GlPk/TDJG/fqgRhisgUu5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b410c7c48538ad9f6eaacdffa3e1321143d0263433a08875443cdd34338e12c1","last_reissued_at":"2026-07-05T08:50:44.909285Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:50:44.909285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.00081","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":"2026-07-05T08:50:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZM2BhVQ138YJx4sSnszyHtQolm6mwvRljbogk90prKiI48JTpf958WU+ARuZGuOxUQDKtv+0qfLyFe11K/Z3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T17:39:25.020780Z"},"content_sha256":"110f77186deaf5a51aaae6dd4fcee086d816a875bcb3d16397704be6b0fe73c6","schema_version":"1.0","event_id":"sha256:110f77186deaf5a51aaae6dd4fcee086d816a875bcb3d16397704be6b0fe73c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WQIMPREFHCWZ63VKZX72HYJSCF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full classification of Pauli Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Gerard Aguilar, Jens Eisert, Lennart Bittel, Simon Cichy","submitted_at":"2024-07-31T18:00:11Z","abstract_excerpt":"Lie groups, and therefore Lie algebras, are fundamental structures in quantum physics that determine the space of possible trajectories of evolving systems. However, classification and characterization methods for these structures are often impractical for larger systems. In this work, we provide a comprehensive classification of Lie algebras generated by an arbitrary set of Pauli operators, from which an efficient method to characterize them follows. By mapping the problem to a graph setting, we identify a reduced set of equivalence classes: the free-fermionic Lie algebra, the set of all anti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.00081","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/2408.00081/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":"2026-07-05T08:50:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KenroFllvzdHt9vrITtQNvv4+fxM3oYhVXgq1EDT6cNH8SAHmBZQEuiyusVwR69VRt2Ymyi6PxO5Vj7ID/OuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T17:39:25.021780Z"},"content_sha256":"35321bcddf6bd29226d5f3b1a3c5b6023a612eb8d74976bbeaa075a8903b526f","schema_version":"1.0","event_id":"sha256:35321bcddf6bd29226d5f3b1a3c5b6023a612eb8d74976bbeaa075a8903b526f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQIMPREFHCWZ63VKZX72HYJSCF/bundle.json","state_url":"https://pith.science/pith/WQIMPREFHCWZ63VKZX72HYJSCF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQIMPREFHCWZ63VKZX72HYJSCF/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":"2026-08-06T17:39:25Z","links":{"resolver":"https://pith.science/pith/WQIMPREFHCWZ63VKZX72HYJSCF","bundle":"https://pith.science/pith/WQIMPREFHCWZ63VKZX72HYJSCF/bundle.json","state":"https://pith.science/pith/WQIMPREFHCWZ63VKZX72HYJSCF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQIMPREFHCWZ63VKZX72HYJSCF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WQIMPREFHCWZ63VKZX72HYJSCF","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":"4a15bc107b9cba99fb56c4dc73d86020be9a1f733412f6ae7af851c3158115bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-31T18:00:11Z","title_canon_sha256":"52cd7557537261f120b1abe856b97492f70d10eeb5d75ed693a6d21f7b08e91f"},"schema_version":"1.0","source":{"id":"2408.00081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.00081","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"arxiv_version","alias_value":"2408.00081v1","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.00081","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"pith_short_12","alias_value":"WQIMPREFHCWZ","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"pith_short_16","alias_value":"WQIMPREFHCWZ63VK","created_at":"2026-07-05T08:50:44Z"},{"alias_kind":"pith_short_8","alias_value":"WQIMPREF","created_at":"2026-07-05T08:50:44Z"}],"graph_snapshots":[{"event_id":"sha256:35321bcddf6bd29226d5f3b1a3c5b6023a612eb8d74976bbeaa075a8903b526f","target":"graph","created_at":"2026-07-05T08:50:44Z","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/2408.00081/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lie groups, and therefore Lie algebras, are fundamental structures in quantum physics that determine the space of possible trajectories of evolving systems. However, classification and characterization methods for these structures are often impractical for larger systems. In this work, we provide a comprehensive classification of Lie algebras generated by an arbitrary set of Pauli operators, from which an efficient method to characterize them follows. By mapping the problem to a graph setting, we identify a reduced set of equivalence classes: the free-fermionic Lie algebra, the set of all anti","authors_text":"Gerard Aguilar, Jens Eisert, Lennart Bittel, Simon Cichy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-31T18:00:11Z","title":"Full classification of Pauli Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.00081","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":"sha256:110f77186deaf5a51aaae6dd4fcee086d816a875bcb3d16397704be6b0fe73c6","target":"record","created_at":"2026-07-05T08:50:44Z","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":"4a15bc107b9cba99fb56c4dc73d86020be9a1f733412f6ae7af851c3158115bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-31T18:00:11Z","title_canon_sha256":"52cd7557537261f120b1abe856b97492f70d10eeb5d75ed693a6d21f7b08e91f"},"schema_version":"1.0","source":{"id":"2408.00081","kind":"arxiv","version":1}},"canonical_sha256":"b410c7c48538ad9f6eaacdffa3e1321143d0263433a08875443cdd34338e12c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b410c7c48538ad9f6eaacdffa3e1321143d0263433a08875443cdd34338e12c1","first_computed_at":"2026-07-05T08:50:44.909285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:50:44.909285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SE/R3kOb45kQJnkBCSjdCEL5BRA5YAEVXeURXX2yL4+lBsY5MrOMd9JqabQKhL3GlPk/TDJG/fqgRhisgUu5AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:50:44.909760Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.00081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:110f77186deaf5a51aaae6dd4fcee086d816a875bcb3d16397704be6b0fe73c6","sha256:35321bcddf6bd29226d5f3b1a3c5b6023a612eb8d74976bbeaa075a8903b526f"],"state_sha256":"ddb733ad696441d924ca8faf683d0216e0c20512fcca8484e493de67075370a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vyNWT6PNmmQryQM3MNmWc92BhdxBWfaJcLtFqHm+WrtHmlgBSIXNUvrhGJriFf/y5iRgMd71x0CQ93Nlrms1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T17:39:25.028093Z","bundle_sha256":"1a2c32a0ddea5b5a8f153f9e3bf679bcc3b0e3fe1749274be2bd8b8bc01f088e"}}