{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GUW4OBEAUT3WTF5VHC3ASH3NY5","short_pith_number":"pith:GUW4OBEA","schema_version":"1.0","canonical_sha256":"352dc70480a4f76997b538b6091f6dc77da5ae7e73a641b1bafe6668ca36b45b","source":{"kind":"arxiv","id":"2502.08029","version":2},"attestation_state":"computed","paper":{"title":"Understanding the Kronecker Matrix-Vector Complexity of Linear Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Raphael A. Meyer, William Swartworth","submitted_at":"2025-02-12T00:09:18Z","abstract_excerpt":"We study the computational model where we can access a matrix $\\mathbf{A}$ only by computing matrix-vector products $\\mathbf{A}\\mathrm{x}$ for vectors of the form $\\mathrm{x} = \\mathrm{x}_1 \\otimes \\cdots \\otimes \\mathrm{x}_q$. We prove exponential lower bounds on the number of queries needed to estimate various properties, including the trace and the top eigenvalue of $\\mathbf{A}$. Our proofs hold for all adaptive algorithms, modulo a mild conditioning assumption on the algorithm's queries. We further prove that algorithms whose queries come from a small alphabet (e.g., $\\mathrm{x}_i \\in \\{\\p"},"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":"2502.08029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-02-12T00:09:18Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"35a79a0d234947a189da44a5f1e738282836f33f4e303826107cb7be2afbe2c2","abstract_canon_sha256":"fba7c950d395f09784217c0ee547baf83815eff189bd787e37a040ada18d9d90"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:48.359354Z","signature_b64":"yTnMj/oY5+Btg5DZ63YG8PaIK/F5l3bPuMheriX0oSkfVxQk5t5X16LHyxSKV2YkbTnla9Z11MigMx25BM6xDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"352dc70480a4f76997b538b6091f6dc77da5ae7e73a641b1bafe6668ca36b45b","last_reissued_at":"2026-07-05T10:13:48.358877Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:48.358877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Understanding the Kronecker Matrix-Vector Complexity of Linear Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Raphael A. Meyer, William Swartworth","submitted_at":"2025-02-12T00:09:18Z","abstract_excerpt":"We study the computational model where we can access a matrix $\\mathbf{A}$ only by computing matrix-vector products $\\mathbf{A}\\mathrm{x}$ for vectors of the form $\\mathrm{x} = \\mathrm{x}_1 \\otimes \\cdots \\otimes \\mathrm{x}_q$. We prove exponential lower bounds on the number of queries needed to estimate various properties, including the trace and the top eigenvalue of $\\mathbf{A}$. Our proofs hold for all adaptive algorithms, modulo a mild conditioning assumption on the algorithm's queries. We further prove that algorithms whose queries come from a small alphabet (e.g., $\\mathrm{x}_i \\in \\{\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08029","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/2502.08029/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":"2502.08029","created_at":"2026-07-05T10:13:48.358931+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.08029v2","created_at":"2026-07-05T10:13:48.358931+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08029","created_at":"2026-07-05T10:13:48.358931+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUW4OBEAUT3W","created_at":"2026-07-05T10:13:48.358931+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUW4OBEAUT3WTF5V","created_at":"2026-07-05T10:13:48.358931+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUW4OBEA","created_at":"2026-07-05T10:13:48.358931+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.21189","citing_title":"Faster Linear Algebra Algorithms with Structured Random Matrices","ref_index":81,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5","json":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5.json","graph_json":"https://pith.science/api/pith-number/GUW4OBEAUT3WTF5VHC3ASH3NY5/graph.json","events_json":"https://pith.science/api/pith-number/GUW4OBEAUT3WTF5VHC3ASH3NY5/events.json","paper":"https://pith.science/paper/GUW4OBEA"},"agent_actions":{"view_html":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5","download_json":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5.json","view_paper":"https://pith.science/paper/GUW4OBEA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.08029&json=true","fetch_graph":"https://pith.science/api/pith-number/GUW4OBEAUT3WTF5VHC3ASH3NY5/graph.json","fetch_events":"https://pith.science/api/pith-number/GUW4OBEAUT3WTF5VHC3ASH3NY5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5/action/storage_attestation","attest_author":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5/action/author_attestation","sign_citation":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5/action/citation_signature","submit_replication":"https://pith.science/pith/GUW4OBEAUT3WTF5VHC3ASH3NY5/action/replication_record"}},"created_at":"2026-07-05T10:13:48.358931+00:00","updated_at":"2026-07-05T10:13:48.358931+00:00"}