{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:A3NNQKWV4NDUEV3DGEVRH2SDHC","short_pith_number":"pith:A3NNQKWV","canonical_record":{"source":{"id":"1707.07264","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-23T08:09:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"612601f1ffbdf528446cf7e18795ea898ddb61cdce3e2335dbc0151d9eb00923","abstract_canon_sha256":"03c15e595eb408badf7041f82a85ae3042e877e83d4cd7bfd6b2b6194666d166"},"schema_version":"1.0"},"canonical_sha256":"06dad82ad5e347425763312b13ea43389210dac22ec3e93756e16a46c2e63dfe","source":{"kind":"arxiv","id":"1707.07264","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07264","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07264v4","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07264","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"pith_short_12","alias_value":"A3NNQKWV4NDU","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"pith_short_16","alias_value":"A3NNQKWV4NDUEV3D","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"pith_short_8","alias_value":"A3NNQKWV","created_at":"2026-07-05T00:05:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:A3NNQKWV4NDUEV3DGEVRH2SDHC","target":"record","payload":{"canonical_record":{"source":{"id":"1707.07264","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-23T08:09:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"612601f1ffbdf528446cf7e18795ea898ddb61cdce3e2335dbc0151d9eb00923","abstract_canon_sha256":"03c15e595eb408badf7041f82a85ae3042e877e83d4cd7bfd6b2b6194666d166"},"schema_version":"1.0"},"canonical_sha256":"06dad82ad5e347425763312b13ea43389210dac22ec3e93756e16a46c2e63dfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:05:43.883682Z","signature_b64":"AkHJzw/o+gxf43dmwK/drAVrnt9qn4+naO04ej2/92vvE4a4CFuD/W3LKCue1n6v+DEUQS2qE7Y4ga+W3HduDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06dad82ad5e347425763312b13ea43389210dac22ec3e93756e16a46c2e63dfe","last_reissued_at":"2026-07-05T00:05:43.883337Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:05:43.883337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.07264","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:05:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"41/waJ3amvvC8UE4dahmYXJ5WtllcWSExvMXUQjtQyOMHlGuySS93IATU5VWej07vwF6lMDx6UtZ22vtgA52Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:17:25.793570Z"},"content_sha256":"89618b9b72493cbe259478c87e974383031eb78beb6d7d07d496f18563806a76","schema_version":"1.0","event_id":"sha256:89618b9b72493cbe259478c87e974383031eb78beb6d7d07d496f18563806a76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:A3NNQKWV4NDUEV3DGEVRH2SDHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variant of Horn's problem and derivative principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Hua Xiang, Lin Zhang","submitted_at":"2017-07-23T08:09:05Z","abstract_excerpt":"Identifying the spectrum of the sum of two given Hermitian matrices with fixed eigenvalues is the famous Horn's problem.In this note, we investigate a variant of Horn's problem, i.e., we identify the probability density function (abbr. pdf) of the diagonals of the sum of two random Hermitian matrices with given spectra. We then use it to re-derive the pdf of the eigenvalues of the sum of two random Hermitian matrices with given eigenvalues via \\emph{derivative principle}, a powerful tool used to get the exact probability distribution by reducing to the corresponding distribution of diagonal en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07264","kind":"arxiv","version":4},"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/1707.07264/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":"2026-07-05T00:05:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZG42NvArMkmlL/OlyREZ0mHqImDZr0Z+o0MvyFoDFIGqpQj5sA0/kPNNKc0so7S9b7M/g3hwBDOqL6BrAP6IAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:17:25.794288Z"},"content_sha256":"7cae520f297eaa69be96f3746d3ec12964d869dfd7336b8fa169343f6f320905","schema_version":"1.0","event_id":"sha256:7cae520f297eaa69be96f3746d3ec12964d869dfd7336b8fa169343f6f320905"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3NNQKWV4NDUEV3DGEVRH2SDHC/bundle.json","state_url":"https://pith.science/pith/A3NNQKWV4NDUEV3DGEVRH2SDHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3NNQKWV4NDUEV3DGEVRH2SDHC/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":"2026-08-11T08:17:25Z","links":{"resolver":"https://pith.science/pith/A3NNQKWV4NDUEV3DGEVRH2SDHC","bundle":"https://pith.science/pith/A3NNQKWV4NDUEV3DGEVRH2SDHC/bundle.json","state":"https://pith.science/pith/A3NNQKWV4NDUEV3DGEVRH2SDHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3NNQKWV4NDUEV3DGEVRH2SDHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A3NNQKWV4NDUEV3DGEVRH2SDHC","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":"03c15e595eb408badf7041f82a85ae3042e877e83d4cd7bfd6b2b6194666d166","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-23T08:09:05Z","title_canon_sha256":"612601f1ffbdf528446cf7e18795ea898ddb61cdce3e2335dbc0151d9eb00923"},"schema_version":"1.0","source":{"id":"1707.07264","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07264","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07264v4","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07264","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"pith_short_12","alias_value":"A3NNQKWV4NDU","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"pith_short_16","alias_value":"A3NNQKWV4NDUEV3D","created_at":"2026-07-05T00:05:43Z"},{"alias_kind":"pith_short_8","alias_value":"A3NNQKWV","created_at":"2026-07-05T00:05:43Z"}],"graph_snapshots":[{"event_id":"sha256:7cae520f297eaa69be96f3746d3ec12964d869dfd7336b8fa169343f6f320905","target":"graph","created_at":"2026-07-05T00:05:43Z","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/1707.07264/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Identifying the spectrum of the sum of two given Hermitian matrices with fixed eigenvalues is the famous Horn's problem.In this note, we investigate a variant of Horn's problem, i.e., we identify the probability density function (abbr. pdf) of the diagonals of the sum of two random Hermitian matrices with given spectra. We then use it to re-derive the pdf of the eigenvalues of the sum of two random Hermitian matrices with given eigenvalues via \\emph{derivative principle}, a powerful tool used to get the exact probability distribution by reducing to the corresponding distribution of diagonal en","authors_text":"Hua Xiang, Lin Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-23T08:09:05Z","title":"A variant of Horn's problem and derivative principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07264","kind":"arxiv","version":4},"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":"sha256:89618b9b72493cbe259478c87e974383031eb78beb6d7d07d496f18563806a76","target":"record","created_at":"2026-07-05T00:05:43Z","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":"03c15e595eb408badf7041f82a85ae3042e877e83d4cd7bfd6b2b6194666d166","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-23T08:09:05Z","title_canon_sha256":"612601f1ffbdf528446cf7e18795ea898ddb61cdce3e2335dbc0151d9eb00923"},"schema_version":"1.0","source":{"id":"1707.07264","kind":"arxiv","version":4}},"canonical_sha256":"06dad82ad5e347425763312b13ea43389210dac22ec3e93756e16a46c2e63dfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06dad82ad5e347425763312b13ea43389210dac22ec3e93756e16a46c2e63dfe","first_computed_at":"2026-07-05T00:05:43.883337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:05:43.883337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AkHJzw/o+gxf43dmwK/drAVrnt9qn4+naO04ej2/92vvE4a4CFuD/W3LKCue1n6v+DEUQS2qE7Y4ga+W3HduDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:05:43.883682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07264","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89618b9b72493cbe259478c87e974383031eb78beb6d7d07d496f18563806a76","sha256:7cae520f297eaa69be96f3746d3ec12964d869dfd7336b8fa169343f6f320905"],"state_sha256":"25a75e63933adcc06d1f59c7ca8b979c333610d35d5074faeff3c1ea3cdda5a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOeTZNjH0gIUCITaxxfpm5yjk1ntDiUbrfgWs8T8v+8onRolAaAq+tOdLBEIt49x9yf8Kklj12vvWAqyEJzsAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T08:17:25.800499Z","bundle_sha256":"eb1312be9e1b5471420d6992b3ed6bb89da8510208969254cc1a0efb3f1c3236"}}