{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:4D5TZJFBCI3PTSLIMLYW3XKOOF","short_pith_number":"pith:4D5TZJFB","canonical_record":{"source":{"id":"quant-ph/0412046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-06T17:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"2d3974f04e6623e4e2e4a3edbdb01800a8e0d78fb7f4d6725aad5f920d809d2a","abstract_canon_sha256":"98571fb346f0fcccf0206cbde55c1ad37fd20223c10b312154a5755e1168cdd0"},"schema_version":"1.0"},"canonical_sha256":"e0fb3ca4a11236f9c96862f16ddd4e7165abafafb64271358297916bfeee474d","source":{"kind":"arxiv","id":"quant-ph/0412046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0412046","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0412046v1","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0412046","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"pith_short_12","alias_value":"4D5TZJFBCI3P","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"pith_short_16","alias_value":"4D5TZJFBCI3PTSLI","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"pith_short_8","alias_value":"4D5TZJFB","created_at":"2026-07-04T14:46:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:4D5TZJFBCI3PTSLIMLYW3XKOOF","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0412046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-06T17:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"2d3974f04e6623e4e2e4a3edbdb01800a8e0d78fb7f4d6725aad5f920d809d2a","abstract_canon_sha256":"98571fb346f0fcccf0206cbde55c1ad37fd20223c10b312154a5755e1168cdd0"},"schema_version":"1.0"},"canonical_sha256":"e0fb3ca4a11236f9c96862f16ddd4e7165abafafb64271358297916bfeee474d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:46:52.007093Z","signature_b64":"jdJ0OfpYQVpECx7YEBsrxq5BkGurmuvMi4RuWtFSzINWuLOHYGLh1AFUGlAOMouyUXLFmTAhc12uRirfftycAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0fb3ca4a11236f9c96862f16ddd4e7165abafafb64271358297916bfeee474d","last_reissued_at":"2026-07-04T14:46:52.006668Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:46:52.006668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0412046","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":"2026-07-04T14:46:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8iQSUzOqxnyrxpdRE8bEI4UoJ3KfhfS9bP3lDWUf209RX2WNlQ0yjkD13SuJ9ZeGkjNUfH6nO7v40pAOMyzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:30:18.660819Z"},"content_sha256":"07e937572024a81eca164c1e5ea47662d33ae17a469d07fca39ec4179be877b0","schema_version":"1.0","event_id":"sha256:07e937572024a81eca164c1e5ea47662d33ae17a469d07fca39ec4179be877b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:4D5TZJFBCI3PTSLIMLYW3XKOOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An application of a matrix inequality in quantum information theory","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C. King","submitted_at":"2004-12-06T17:27:38Z","abstract_excerpt":"Quantum information theory has generated several interesting conjectures involving products of completely positive maps on matrix algebras, also known as quantum channels. In particular it is conjectured that the output state with maximal p-norm from a product channel is always a product state. It is shown here that the Lieb-Thirring inequality can be used to prove this conjecture for one special case, namely when one of the components of the product channel is of the type known as a diagonal channel, which acts on a state by taking the Hadamard product with a positive matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0412046","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/quant-ph/0412046/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":"2026-07-04T14:46:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zaebu1rNRjAxnZpdpFCTduocBlhRmzLWJKSjc+K+HX9Wb1hT/1KQQYVs5ztU3l1QzjD7Gy2KBteYqt83viV1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:30:18.661361Z"},"content_sha256":"fe4a527a391ff67b21eb782d325c5a33d023125f2445ae7f446f6a8abc20044a","schema_version":"1.0","event_id":"sha256:fe4a527a391ff67b21eb782d325c5a33d023125f2445ae7f446f6a8abc20044a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4D5TZJFBCI3PTSLIMLYW3XKOOF/bundle.json","state_url":"https://pith.science/pith/4D5TZJFBCI3PTSLIMLYW3XKOOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4D5TZJFBCI3PTSLIMLYW3XKOOF/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":"2026-08-11T14:30:18Z","links":{"resolver":"https://pith.science/pith/4D5TZJFBCI3PTSLIMLYW3XKOOF","bundle":"https://pith.science/pith/4D5TZJFBCI3PTSLIMLYW3XKOOF/bundle.json","state":"https://pith.science/pith/4D5TZJFBCI3PTSLIMLYW3XKOOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4D5TZJFBCI3PTSLIMLYW3XKOOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:4D5TZJFBCI3PTSLIMLYW3XKOOF","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":"98571fb346f0fcccf0206cbde55c1ad37fd20223c10b312154a5755e1168cdd0","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-06T17:27:38Z","title_canon_sha256":"2d3974f04e6623e4e2e4a3edbdb01800a8e0d78fb7f4d6725aad5f920d809d2a"},"schema_version":"1.0","source":{"id":"quant-ph/0412046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0412046","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0412046v1","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0412046","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"pith_short_12","alias_value":"4D5TZJFBCI3P","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"pith_short_16","alias_value":"4D5TZJFBCI3PTSLI","created_at":"2026-07-04T14:46:52Z"},{"alias_kind":"pith_short_8","alias_value":"4D5TZJFB","created_at":"2026-07-04T14:46:52Z"}],"graph_snapshots":[{"event_id":"sha256:fe4a527a391ff67b21eb782d325c5a33d023125f2445ae7f446f6a8abc20044a","target":"graph","created_at":"2026-07-04T14:46:52Z","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/quant-ph/0412046/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Quantum information theory has generated several interesting conjectures involving products of completely positive maps on matrix algebras, also known as quantum channels. In particular it is conjectured that the output state with maximal p-norm from a product channel is always a product state. It is shown here that the Lieb-Thirring inequality can be used to prove this conjecture for one special case, namely when one of the components of the product channel is of the type known as a diagonal channel, which acts on a state by taking the Hadamard product with a positive matrix.","authors_text":"C. King","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-12-06T17:27:38Z","title":"An application of a matrix inequality in quantum information theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0412046","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":"sha256:07e937572024a81eca164c1e5ea47662d33ae17a469d07fca39ec4179be877b0","target":"record","created_at":"2026-07-04T14:46:52Z","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":"98571fb346f0fcccf0206cbde55c1ad37fd20223c10b312154a5755e1168cdd0","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-06T17:27:38Z","title_canon_sha256":"2d3974f04e6623e4e2e4a3edbdb01800a8e0d78fb7f4d6725aad5f920d809d2a"},"schema_version":"1.0","source":{"id":"quant-ph/0412046","kind":"arxiv","version":1}},"canonical_sha256":"e0fb3ca4a11236f9c96862f16ddd4e7165abafafb64271358297916bfeee474d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0fb3ca4a11236f9c96862f16ddd4e7165abafafb64271358297916bfeee474d","first_computed_at":"2026-07-04T14:46:52.006668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:46:52.006668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jdJ0OfpYQVpECx7YEBsrxq5BkGurmuvMi4RuWtFSzINWuLOHYGLh1AFUGlAOMouyUXLFmTAhc12uRirfftycAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:46:52.007093Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0412046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07e937572024a81eca164c1e5ea47662d33ae17a469d07fca39ec4179be877b0","sha256:fe4a527a391ff67b21eb782d325c5a33d023125f2445ae7f446f6a8abc20044a"],"state_sha256":"32b446b02938c3626a57c0fc19b9fe3142430d41087572cf142deddf08ec42a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zd3A5GtNawGbMXiZwxdotRRIFvz2fwgiuKOFMr5/ntwLQj1SxK78NiQL0OBXILWr/pIUu9J1J9LGNFwoAECBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T14:30:18.665111Z","bundle_sha256":"9daefa800b1434ed71982cff20747a16ac0ebb51d4901d2e7ca7c5d2343e91b8"}}