{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GPM6QEYEBD6J6GKBEKWFX5KNOL","short_pith_number":"pith:GPM6QEYE","schema_version":"1.0","canonical_sha256":"33d9e8130408fc9f194122ac5bf54d72c397217e734ea47da95fcfea57458e4d","source":{"kind":"arxiv","id":"2606.00527","version":1},"attestation_state":"computed","paper":{"title":"Finite-Sample Selected Covariance Spectra in Classical Shadows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Masahito Hayashi","submitted_at":"2026-05-30T04:46:49Z","abstract_excerpt":"We study finite-sample estimation of selected covariance matrices of classical-shadow outputs. For a general shadow-output vector, we consider its covariance matrix and a fixed selected compression. Our main theorem applies to arbitrary shadow protocols and gives an operator-norm error bound for the selected sample-centered empirical covariance. When the protocol-dependent constants appearing in this bound remain independent of the ambient system size, the required sample size is also independent of the ambient dimension. The proof combines matrix Bernstein concentration, an exact rank-one cen"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.00527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-30T04:46:49Z","cross_cats_sorted":[],"title_canon_sha256":"96696c0cc81636a2635e6ae2dea54947d5d799437ef26096c714e70b8d6951c8","abstract_canon_sha256":"fc9c9bf53bda15e8a6dbeeb1d857ca7a0e4283db926cc7dd8ea879ecf22d03b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:57.254466Z","signature_b64":"FBSB7fAC4LJYPOHT5fJA3NNgCeTE0+LaQDJ1uGUYTcNaNpsAnwklUbLB58Hvkf08/tBHIRr7QY5lv5uVrretDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33d9e8130408fc9f194122ac5bf54d72c397217e734ea47da95fcfea57458e4d","last_reissued_at":"2026-06-02T01:03:57.254037Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:57.254037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite-Sample Selected Covariance Spectra in Classical Shadows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Masahito Hayashi","submitted_at":"2026-05-30T04:46:49Z","abstract_excerpt":"We study finite-sample estimation of selected covariance matrices of classical-shadow outputs. For a general shadow-output vector, we consider its covariance matrix and a fixed selected compression. Our main theorem applies to arbitrary shadow protocols and gives an operator-norm error bound for the selected sample-centered empirical covariance. When the protocol-dependent constants appearing in this bound remain independent of the ambient system size, the required sample size is also independent of the ambient dimension. The proof combines matrix Bernstein concentration, an exact rank-one cen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00527","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/2606.00527/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.00527","created_at":"2026-06-02T01:03:57.254099+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.00527v1","created_at":"2026-06-02T01:03:57.254099+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00527","created_at":"2026-06-02T01:03:57.254099+00:00"},{"alias_kind":"pith_short_12","alias_value":"GPM6QEYEBD6J","created_at":"2026-06-02T01:03:57.254099+00:00"},{"alias_kind":"pith_short_16","alias_value":"GPM6QEYEBD6J6GKB","created_at":"2026-06-02T01:03:57.254099+00:00"},{"alias_kind":"pith_short_8","alias_value":"GPM6QEYE","created_at":"2026-06-02T01:03:57.254099+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL","json":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL.json","graph_json":"https://pith.science/api/pith-number/GPM6QEYEBD6J6GKBEKWFX5KNOL/graph.json","events_json":"https://pith.science/api/pith-number/GPM6QEYEBD6J6GKBEKWFX5KNOL/events.json","paper":"https://pith.science/paper/GPM6QEYE"},"agent_actions":{"view_html":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL","download_json":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL.json","view_paper":"https://pith.science/paper/GPM6QEYE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.00527&json=true","fetch_graph":"https://pith.science/api/pith-number/GPM6QEYEBD6J6GKBEKWFX5KNOL/graph.json","fetch_events":"https://pith.science/api/pith-number/GPM6QEYEBD6J6GKBEKWFX5KNOL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL/action/storage_attestation","attest_author":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL/action/author_attestation","sign_citation":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL/action/citation_signature","submit_replication":"https://pith.science/pith/GPM6QEYEBD6J6GKBEKWFX5KNOL/action/replication_record"}},"created_at":"2026-06-02T01:03:57.254099+00:00","updated_at":"2026-06-02T01:03:57.254099+00:00"}