{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:K23QNLG2XFGPK43Z57WBCW7P2M","short_pith_number":"pith:K23QNLG2","canonical_record":{"source":{"id":"1910.07508","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-16T17:50:51Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"96e3c3927cb1ad05dd44ad5189950d5e92b009f18252fa626d9553a76b6a89b3","abstract_canon_sha256":"53704689252e482e480e8c8d04c1893f7480de7e0f976fd54e5f865b77f148ff"},"schema_version":"1.0"},"canonical_sha256":"56b706acdab94cf57379efec115befd3090d422cf55a6af9dbf3fe224be99904","source":{"kind":"arxiv","id":"1910.07508","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07508","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07508v2","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07508","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"K23QNLG2XFGP","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"pith_short_16","alias_value":"K23QNLG2XFGPK43Z","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"pith_short_8","alias_value":"K23QNLG2","created_at":"2026-07-05T02:18:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:K23QNLG2XFGPK43Z57WBCW7P2M","target":"record","payload":{"canonical_record":{"source":{"id":"1910.07508","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-16T17:50:51Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"96e3c3927cb1ad05dd44ad5189950d5e92b009f18252fa626d9553a76b6a89b3","abstract_canon_sha256":"53704689252e482e480e8c8d04c1893f7480de7e0f976fd54e5f865b77f148ff"},"schema_version":"1.0"},"canonical_sha256":"56b706acdab94cf57379efec115befd3090d422cf55a6af9dbf3fe224be99904","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:18:27.831835Z","signature_b64":"kvyIR8zUZmI4zel0rtBgpGqQaCiqgRYF7rULm+Nbw1z1WW9BH+3yx0GpL5E2K1pv8dB2YcRZQ2vEyEBFtP6/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56b706acdab94cf57379efec115befd3090d422cf55a6af9dbf3fe224be99904","last_reissued_at":"2026-07-05T02:18:27.831400Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:18:27.831400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.07508","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sc0oJOqOFDYuXZv7ndcdmK3LIQf5pML2lGeOz8F/FAoTYDDITlUKGiohHdqSugcTMrJ71FDhAQuqKraBiEg2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:14:52.803034Z"},"content_sha256":"90da9d8e2de8171170472dbffd9dcbaf506b3c317aefaf100d4438659830ce4a","schema_version":"1.0","event_id":"sha256:90da9d8e2de8171170472dbffd9dcbaf506b3c317aefaf100d4438659830ce4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:K23QNLG2XFGPK43Z57WBCW7P2M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Charged Complexity and the Thermofield Double State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Hong Zhe Chen, Shira Chapman","submitted_at":"2019-10-16T17:50:51Z","abstract_excerpt":"We establish a systematic framework for studying quantum computational complexity of Gaussian states of charged systems based on Nielsen's geometric approach. We use this framework to examine the effect of a chemical potential on the dynamics of complexity. As an example, we consider the complexity of a charged thermofield double state constructed from two free massive complex scalar fields in the presence of a chemical potential. We show that this state factorizes between positively and negatively charged modes and demonstrate that this fact can be used to relate it, for each momentum mode se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07508","kind":"arxiv","version":2},"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/1910.07508/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":"2026-07-05T02:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXVk9POu0INoW/tYZq7oabAcQZ5Ya7q6425C5cqPtBaDMNSfy1vobheTZ3Eucw0itAVGl7PmzFR7lNrKeWuQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:14:52.803574Z"},"content_sha256":"48810c9a4ff3df280fbd56cdbaf0a570e357a94df58f181ba4412bffc4bd8cfa","schema_version":"1.0","event_id":"sha256:48810c9a4ff3df280fbd56cdbaf0a570e357a94df58f181ba4412bffc4bd8cfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K23QNLG2XFGPK43Z57WBCW7P2M/bundle.json","state_url":"https://pith.science/pith/K23QNLG2XFGPK43Z57WBCW7P2M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K23QNLG2XFGPK43Z57WBCW7P2M/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":"2026-08-10T06:14:52Z","links":{"resolver":"https://pith.science/pith/K23QNLG2XFGPK43Z57WBCW7P2M","bundle":"https://pith.science/pith/K23QNLG2XFGPK43Z57WBCW7P2M/bundle.json","state":"https://pith.science/pith/K23QNLG2XFGPK43Z57WBCW7P2M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K23QNLG2XFGPK43Z57WBCW7P2M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K23QNLG2XFGPK43Z57WBCW7P2M","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":"53704689252e482e480e8c8d04c1893f7480de7e0f976fd54e5f865b77f148ff","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-16T17:50:51Z","title_canon_sha256":"96e3c3927cb1ad05dd44ad5189950d5e92b009f18252fa626d9553a76b6a89b3"},"schema_version":"1.0","source":{"id":"1910.07508","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07508","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07508v2","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07508","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"K23QNLG2XFGP","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"pith_short_16","alias_value":"K23QNLG2XFGPK43Z","created_at":"2026-07-05T02:18:27Z"},{"alias_kind":"pith_short_8","alias_value":"K23QNLG2","created_at":"2026-07-05T02:18:27Z"}],"graph_snapshots":[{"event_id":"sha256:48810c9a4ff3df280fbd56cdbaf0a570e357a94df58f181ba4412bffc4bd8cfa","target":"graph","created_at":"2026-07-05T02:18:27Z","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/1910.07508/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a systematic framework for studying quantum computational complexity of Gaussian states of charged systems based on Nielsen's geometric approach. We use this framework to examine the effect of a chemical potential on the dynamics of complexity. As an example, we consider the complexity of a charged thermofield double state constructed from two free massive complex scalar fields in the presence of a chemical potential. We show that this state factorizes between positively and negatively charged modes and demonstrate that this fact can be used to relate it, for each momentum mode se","authors_text":"Hong Zhe Chen, Shira Chapman","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-16T17:50:51Z","title":"Charged Complexity and the Thermofield Double State"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07508","kind":"arxiv","version":2},"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":"sha256:90da9d8e2de8171170472dbffd9dcbaf506b3c317aefaf100d4438659830ce4a","target":"record","created_at":"2026-07-05T02:18:27Z","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":"53704689252e482e480e8c8d04c1893f7480de7e0f976fd54e5f865b77f148ff","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-16T17:50:51Z","title_canon_sha256":"96e3c3927cb1ad05dd44ad5189950d5e92b009f18252fa626d9553a76b6a89b3"},"schema_version":"1.0","source":{"id":"1910.07508","kind":"arxiv","version":2}},"canonical_sha256":"56b706acdab94cf57379efec115befd3090d422cf55a6af9dbf3fe224be99904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56b706acdab94cf57379efec115befd3090d422cf55a6af9dbf3fe224be99904","first_computed_at":"2026-07-05T02:18:27.831400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:18:27.831400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kvyIR8zUZmI4zel0rtBgpGqQaCiqgRYF7rULm+Nbw1z1WW9BH+3yx0GpL5E2K1pv8dB2YcRZQ2vEyEBFtP6/BA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:18:27.831835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.07508","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90da9d8e2de8171170472dbffd9dcbaf506b3c317aefaf100d4438659830ce4a","sha256:48810c9a4ff3df280fbd56cdbaf0a570e357a94df58f181ba4412bffc4bd8cfa"],"state_sha256":"d406149fc135b9646c2e1354817e29547584a6757fbdfb98240c073d7e648b01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XkEGUt2gGub9zfuxB7gp+iO/Sjhex2KV5ZAMMp76a/dTqrxJit0j0kuwy1Umwnyozm6CQW8hhOi5bJYkJtsMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T06:14:52.809507Z","bundle_sha256":"06884dda0ab7622a60f5a9424b30baed87ce6dc2e0235dd584dfeea677e3ffa3"}}