{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KWFJVNVVYJ6YOULXBHW2LKP45I","short_pith_number":"pith:KWFJVNVV","canonical_record":{"source":{"id":"1810.02630","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-05T11:59:24Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"6be2cb81c21b9cdb1fb7994c88f8b3828071fa85f731d4e0191cfcedf3c04f72","abstract_canon_sha256":"6992dc78c646c68006a2b0f25a09c2f40e9218a952dea406e249de65db938f87"},"schema_version":"1.0"},"canonical_sha256":"558a9ab6b5c27d87517709eda5a9fcea234be64ae3fd9b64b086245d2abb3575","source":{"kind":"arxiv","id":"1810.02630","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02630","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02630v2","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02630","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_12","alias_value":"KWFJVNVVYJ6Y","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_16","alias_value":"KWFJVNVVYJ6YOULX","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_8","alias_value":"KWFJVNVV","created_at":"2026-07-05T00:18:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KWFJVNVVYJ6YOULXBHW2LKP45I","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02630","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-05T11:59:24Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"6be2cb81c21b9cdb1fb7994c88f8b3828071fa85f731d4e0191cfcedf3c04f72","abstract_canon_sha256":"6992dc78c646c68006a2b0f25a09c2f40e9218a952dea406e249de65db938f87"},"schema_version":"1.0"},"canonical_sha256":"558a9ab6b5c27d87517709eda5a9fcea234be64ae3fd9b64b086245d2abb3575","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:18:49.763983Z","signature_b64":"a5pbkg+ptPQn6sW76KYq0Zv53jfegUZgzPrwhpJZ7qEgwO94H5HGZk/MLNDmIlFjZNZEVpElce1DpIPTsCJJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"558a9ab6b5c27d87517709eda5a9fcea234be64ae3fd9b64b086245d2abb3575","last_reissued_at":"2026-07-05T00:18:49.763449Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:18:49.763449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02630","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":"2026-07-05T00:18:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BjQON0QP3jCd2+5x1ei+bZ2jKLlUw2qvKJcN1ne7TccY/M8iOhAZwcf1iR7UA+85QJUH/OuG2WmNjCNxkqpUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:31:29.625953Z"},"content_sha256":"c1e0dadbd059c9e0057f41732268ca4e852b3d41813450d58c37b5b1be86f546","schema_version":"1.0","event_id":"sha256:c1e0dadbd059c9e0057f41732268ca4e852b3d41813450d58c37b5b1be86f546"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KWFJVNVVYJ6YOULXBHW2LKP45I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duistermaat-Heckman measure and the mixture of quantum states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"quant-ph","authors_text":"Junde Wu, Lin Zhang, Yixin Jiang","submitted_at":"2018-10-05T11:59:24Z","abstract_excerpt":"In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum $\\bsA+\\bsB$ of two independent random Hermitian matrices $\\bsA$ and $\\bsB$. Some considerations about the mixture of quantum states are basically subsumed into the above mathematical problem. Instead, we focus on deriving the spectral density of the mixture of adjoint orbits of quantum states in terms of Duistermaat-Heckman measure, originated from the theory of symplectic geometry. Based on this method, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02630","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/1810.02630/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":"2026-07-05T00:18:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o6XeoPCRvzX9ZibYecQ9hk4sjq3Bkzfb6kgXrhy6l4WFVHho7ywUNq+LBwdgW0XA3JwZgYHzXWOzhe94MDQCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:31:29.626781Z"},"content_sha256":"7fc9bd56bd54339c701c1e8a4b10f80822481132b83a331cabd769e2aed7ce00","schema_version":"1.0","event_id":"sha256:7fc9bd56bd54339c701c1e8a4b10f80822481132b83a331cabd769e2aed7ce00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KWFJVNVVYJ6YOULXBHW2LKP45I/bundle.json","state_url":"https://pith.science/pith/KWFJVNVVYJ6YOULXBHW2LKP45I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KWFJVNVVYJ6YOULXBHW2LKP45I/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":"2026-08-11T11:31:29Z","links":{"resolver":"https://pith.science/pith/KWFJVNVVYJ6YOULXBHW2LKP45I","bundle":"https://pith.science/pith/KWFJVNVVYJ6YOULXBHW2LKP45I/bundle.json","state":"https://pith.science/pith/KWFJVNVVYJ6YOULXBHW2LKP45I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KWFJVNVVYJ6YOULXBHW2LKP45I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KWFJVNVVYJ6YOULXBHW2LKP45I","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":"6992dc78c646c68006a2b0f25a09c2f40e9218a952dea406e249de65db938f87","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-05T11:59:24Z","title_canon_sha256":"6be2cb81c21b9cdb1fb7994c88f8b3828071fa85f731d4e0191cfcedf3c04f72"},"schema_version":"1.0","source":{"id":"1810.02630","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02630","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02630v2","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02630","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_12","alias_value":"KWFJVNVVYJ6Y","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_16","alias_value":"KWFJVNVVYJ6YOULX","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_8","alias_value":"KWFJVNVV","created_at":"2026-07-05T00:18:49Z"}],"graph_snapshots":[{"event_id":"sha256:7fc9bd56bd54339c701c1e8a4b10f80822481132b83a331cabd769e2aed7ce00","target":"graph","created_at":"2026-07-05T00:18:49Z","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/1810.02630/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum $\\bsA+\\bsB$ of two independent random Hermitian matrices $\\bsA$ and $\\bsB$. Some considerations about the mixture of quantum states are basically subsumed into the above mathematical problem. Instead, we focus on deriving the spectral density of the mixture of adjoint orbits of quantum states in terms of Duistermaat-Heckman measure, originated from the theory of symplectic geometry. Based on this method, we ","authors_text":"Junde Wu, Lin Zhang, Yixin Jiang","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-05T11:59:24Z","title":"Duistermaat-Heckman measure and the mixture of quantum states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02630","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:c1e0dadbd059c9e0057f41732268ca4e852b3d41813450d58c37b5b1be86f546","target":"record","created_at":"2026-07-05T00:18:49Z","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":"6992dc78c646c68006a2b0f25a09c2f40e9218a952dea406e249de65db938f87","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-05T11:59:24Z","title_canon_sha256":"6be2cb81c21b9cdb1fb7994c88f8b3828071fa85f731d4e0191cfcedf3c04f72"},"schema_version":"1.0","source":{"id":"1810.02630","kind":"arxiv","version":2}},"canonical_sha256":"558a9ab6b5c27d87517709eda5a9fcea234be64ae3fd9b64b086245d2abb3575","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"558a9ab6b5c27d87517709eda5a9fcea234be64ae3fd9b64b086245d2abb3575","first_computed_at":"2026-07-05T00:18:49.763449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:18:49.763449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5pbkg+ptPQn6sW76KYq0Zv53jfegUZgzPrwhpJZ7qEgwO94H5HGZk/MLNDmIlFjZNZEVpElce1DpIPTsCJJDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:18:49.763983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02630","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e0dadbd059c9e0057f41732268ca4e852b3d41813450d58c37b5b1be86f546","sha256:7fc9bd56bd54339c701c1e8a4b10f80822481132b83a331cabd769e2aed7ce00"],"state_sha256":"6d0984574ff747d162a5b1384e2e40558565ce24ec9ff7fcfad0c411eed48a11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgltxbi5cw/+2Klp9TnnO6aPrG9/GNyqfRs75BqSJkIaxMMNlrvuFUORg/RtZoRCG42Nz7z498TYmGemFFe6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T11:31:29.631190Z","bundle_sha256":"a9fa2e79ba67e26628f7da571ede95c1a235d284b45af0b0013a7c840b184240"}}