{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WVMYTYINHW2QRCCHZTEJGSZFSL","short_pith_number":"pith:WVMYTYIN","canonical_record":{"source":{"id":"1501.05506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T14:23:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"228e10028714204925bc9610b4bb946ff2a31b7a0fd25aa91c4dbae0488af271","abstract_canon_sha256":"906eb0664177d5dea0b50bc875d7b5b6daa03c5d28b54b3396f39fc6dc1cda0c"},"schema_version":"1.0"},"canonical_sha256":"b55989e10d3db5088847ccc8934b2592cdde181b1592f9b5c2648138f98ccc3e","source":{"kind":"arxiv","id":"1501.05506","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05506","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05506v2","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05506","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"WVMYTYINHW2Q","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WVMYTYINHW2QRCCH","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WVMYTYIN","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WVMYTYINHW2QRCCHZTEJGSZFSL","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T14:23:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"228e10028714204925bc9610b4bb946ff2a31b7a0fd25aa91c4dbae0488af271","abstract_canon_sha256":"906eb0664177d5dea0b50bc875d7b5b6daa03c5d28b54b3396f39fc6dc1cda0c"},"schema_version":"1.0"},"canonical_sha256":"b55989e10d3db5088847ccc8934b2592cdde181b1592f9b5c2648138f98ccc3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:47.434859Z","signature_b64":"tkca2ROgFV2zNE1NUDq1uRH60FTS38y0w88lXahsHpOjB5ysZ2FFlWMO1/kP3Q9Koo2B7U2yoJQzcgqRvrp5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b55989e10d3db5088847ccc8934b2592cdde181b1592f9b5c2648138f98ccc3e","last_reissued_at":"2026-05-17T23:50:47.434196Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:47.434196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05506","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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sD/BZbDEmI0cPbNheCKAK5P5dbS1NkwMipa1+afHTISCt7wbw9ARo+O7MZaMqqQC/Ipa8haHA06/h9Q3C9jJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:42:44.761573Z"},"content_sha256":"c341156ce6e6eeb384b26c707da5b27448de42eb8b11b93e762b30275fe5949a","schema_version":"1.0","event_id":"sha256:c341156ce6e6eeb384b26c707da5b27448de42eb8b11b93e762b30275fe5949a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WVMYTYINHW2QRCCHZTEJGSZFSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transformations of polynomial ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Arno B.J. Kuijlaars","submitted_at":"2015-01-22T14:23:51Z","abstract_excerpt":"A polynomial ensemble is a probability density function for the position of $n$ real particles of the form $\\frac{1}{Z_n} \\, \\prod_{j<k} (x_k-x_j) \\, \\det \\left[ f_k (x_j) \\right]_{j,k=1}^n$, for certain functions $f_1, \\ldots, f_n$. Such ensembles appear frequently as the joint eigenvalue density of random matrices. We present a number of transformations that preserve the structure of a polynomial ensemble. These transformations include the restriction of a Hermitian matrix by removing one row and one column, a rank-one modification of a Hermitian matrix, and the extension of a Hermitian matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05506","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":""},"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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ipaua+yD7bfeoqChpBpxnJABBY2/lwGeBKwPO+xj78FYkATGD051de4OMIKHdw1B704lRDWofIVTiPEHqKNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:42:44.762030Z"},"content_sha256":"6dfa610fbe95907da382f5eafbbf9f2d9982b194fed96942c2d42441c8509cc7","schema_version":"1.0","event_id":"sha256:6dfa610fbe95907da382f5eafbbf9f2d9982b194fed96942c2d42441c8509cc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVMYTYINHW2QRCCHZTEJGSZFSL/bundle.json","state_url":"https://pith.science/pith/WVMYTYINHW2QRCCHZTEJGSZFSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVMYTYINHW2QRCCHZTEJGSZFSL/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":"2026-08-11T16:42:44Z","links":{"resolver":"https://pith.science/pith/WVMYTYINHW2QRCCHZTEJGSZFSL","bundle":"https://pith.science/pith/WVMYTYINHW2QRCCHZTEJGSZFSL/bundle.json","state":"https://pith.science/pith/WVMYTYINHW2QRCCHZTEJGSZFSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVMYTYINHW2QRCCHZTEJGSZFSL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WVMYTYINHW2QRCCHZTEJGSZFSL","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":"906eb0664177d5dea0b50bc875d7b5b6daa03c5d28b54b3396f39fc6dc1cda0c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T14:23:51Z","title_canon_sha256":"228e10028714204925bc9610b4bb946ff2a31b7a0fd25aa91c4dbae0488af271"},"schema_version":"1.0","source":{"id":"1501.05506","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05506","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05506v2","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05506","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"WVMYTYINHW2Q","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WVMYTYINHW2QRCCH","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WVMYTYIN","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:6dfa610fbe95907da382f5eafbbf9f2d9982b194fed96942c2d42441c8509cc7","target":"graph","created_at":"2026-05-17T23:50:47Z","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"},"paper":{"abstract_excerpt":"A polynomial ensemble is a probability density function for the position of $n$ real particles of the form $\\frac{1}{Z_n} \\, \\prod_{j<k} (x_k-x_j) \\, \\det \\left[ f_k (x_j) \\right]_{j,k=1}^n$, for certain functions $f_1, \\ldots, f_n$. Such ensembles appear frequently as the joint eigenvalue density of random matrices. We present a number of transformations that preserve the structure of a polynomial ensemble. These transformations include the restriction of a Hermitian matrix by removing one row and one column, a rank-one modification of a Hermitian matrix, and the extension of a Hermitian matr","authors_text":"Arno B.J. Kuijlaars","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T14:23:51Z","title":"Transformations of polynomial ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05506","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:c341156ce6e6eeb384b26c707da5b27448de42eb8b11b93e762b30275fe5949a","target":"record","created_at":"2026-05-17T23:50:47Z","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":"906eb0664177d5dea0b50bc875d7b5b6daa03c5d28b54b3396f39fc6dc1cda0c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T14:23:51Z","title_canon_sha256":"228e10028714204925bc9610b4bb946ff2a31b7a0fd25aa91c4dbae0488af271"},"schema_version":"1.0","source":{"id":"1501.05506","kind":"arxiv","version":2}},"canonical_sha256":"b55989e10d3db5088847ccc8934b2592cdde181b1592f9b5c2648138f98ccc3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b55989e10d3db5088847ccc8934b2592cdde181b1592f9b5c2648138f98ccc3e","first_computed_at":"2026-05-17T23:50:47.434196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:47.434196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkca2ROgFV2zNE1NUDq1uRH60FTS38y0w88lXahsHpOjB5ysZ2FFlWMO1/kP3Q9Koo2B7U2yoJQzcgqRvrp5CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:47.434859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05506","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c341156ce6e6eeb384b26c707da5b27448de42eb8b11b93e762b30275fe5949a","sha256:6dfa610fbe95907da382f5eafbbf9f2d9982b194fed96942c2d42441c8509cc7"],"state_sha256":"6223d88803b164560bb6d314c35cb7dea40350bed74aa8dfdecd1a23cdae9e99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uXke+z2qAdHYHfDPTE69cXgd8FAL2wSkdHRYbE1NGEzqXKe8t54RE4TsqlYR+2WYj7Oc+HhHa0xRwn+cn3BtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T16:42:44.766637Z","bundle_sha256":"aa7564ceb5fdb279fb5e5af05194a30ebd6daa4d75553d14bb4b2daa9fb2bce9"}}