{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XUGDASQLOX6HLEG3C54IIZ5FK4","short_pith_number":"pith:XUGDASQL","schema_version":"1.0","canonical_sha256":"bd0c304a0b75fc7590db17788467a5572d32d820787d4757691efd1fafe97128","source":{"kind":"arxiv","id":"2508.13108","version":1},"attestation_state":"computed","paper":{"title":"A simple analysis of a quantum-inspired algorithm for solving low-rank linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.DS","authors_text":"Archan Ray, Dylan Herman, Junhyung Lyle Kim, Niraj Kumar, Shouvanik Chakrabarti, Tyler Chen","submitted_at":"2025-08-18T17:14:35Z","abstract_excerpt":"We describe and analyze a simple algorithm for sampling from the solution $\\mathbf{x}^* := \\mathbf{A}^+\\mathbf{b}$ to a linear system $\\mathbf{A}\\mathbf{x} = \\mathbf{b}$. We assume access to a sampler which allows us to draw indices proportional to the squared row/column-norms of $\\mathbf{A}$. Our algorithm produces a compressed representation of some vector $\\mathbf{x}$ for which $\\|\\mathbf{x}^* - \\mathbf{x}\\| < \\varepsilon \\|\\mathbf{x}^* \\|$ in $\\widetilde{O}(\\kappa_{\\mathsf{F}}^4 \\kappa^2 / \\varepsilon^2)$ time, where $\\kappa_{\\mathsf{F}} := \\|\\mathbf{A}\\|_{\\mathsf{F}}\\|\\mathbf{A}^{+}\\|$ an"},"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":"2508.13108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-08-18T17:14:35Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"aa0244f719cb1ff2d18c2517d8e397e23b1daac40f77fb89265c2e691a408abe","abstract_canon_sha256":"e4ad8d2067b71fdfebd6fbb56a083b27863dbb5a153583c6a0a3bc607621a257"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:32.564936Z","signature_b64":"4xbqf3z7MKKLq4j0fBYLoPOZ/srqI3CyhGUMc3G8Jp1q9ZCHCiHxVFfss6wLGnaxep9tDgzydN/3r5BfeynhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd0c304a0b75fc7590db17788467a5572d32d820787d4757691efd1fafe97128","last_reissued_at":"2026-07-05T11:55:32.564376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:32.564376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A simple analysis of a quantum-inspired algorithm for solving low-rank linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.DS","authors_text":"Archan Ray, Dylan Herman, Junhyung Lyle Kim, Niraj Kumar, Shouvanik Chakrabarti, Tyler Chen","submitted_at":"2025-08-18T17:14:35Z","abstract_excerpt":"We describe and analyze a simple algorithm for sampling from the solution $\\mathbf{x}^* := \\mathbf{A}^+\\mathbf{b}$ to a linear system $\\mathbf{A}\\mathbf{x} = \\mathbf{b}$. We assume access to a sampler which allows us to draw indices proportional to the squared row/column-norms of $\\mathbf{A}$. Our algorithm produces a compressed representation of some vector $\\mathbf{x}$ for which $\\|\\mathbf{x}^* - \\mathbf{x}\\| < \\varepsilon \\|\\mathbf{x}^* \\|$ in $\\widetilde{O}(\\kappa_{\\mathsf{F}}^4 \\kappa^2 / \\varepsilon^2)$ time, where $\\kappa_{\\mathsf{F}} := \\|\\mathbf{A}\\|_{\\mathsf{F}}\\|\\mathbf{A}^{+}\\|$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.13108","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/2508.13108/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":"2508.13108","created_at":"2026-07-05T11:55:32.564461+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.13108v1","created_at":"2026-07-05T11:55:32.564461+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.13108","created_at":"2026-07-05T11:55:32.564461+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUGDASQLOX6H","created_at":"2026-07-05T11:55:32.564461+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUGDASQLOX6HLEG3","created_at":"2026-07-05T11:55:32.564461+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUGDASQL","created_at":"2026-07-05T11:55:32.564461+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/XUGDASQLOX6HLEG3C54IIZ5FK4","json":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4.json","graph_json":"https://pith.science/api/pith-number/XUGDASQLOX6HLEG3C54IIZ5FK4/graph.json","events_json":"https://pith.science/api/pith-number/XUGDASQLOX6HLEG3C54IIZ5FK4/events.json","paper":"https://pith.science/paper/XUGDASQL"},"agent_actions":{"view_html":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4","download_json":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4.json","view_paper":"https://pith.science/paper/XUGDASQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.13108&json=true","fetch_graph":"https://pith.science/api/pith-number/XUGDASQLOX6HLEG3C54IIZ5FK4/graph.json","fetch_events":"https://pith.science/api/pith-number/XUGDASQLOX6HLEG3C54IIZ5FK4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4/action/storage_attestation","attest_author":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4/action/author_attestation","sign_citation":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4/action/citation_signature","submit_replication":"https://pith.science/pith/XUGDASQLOX6HLEG3C54IIZ5FK4/action/replication_record"}},"created_at":"2026-07-05T11:55:32.564461+00:00","updated_at":"2026-07-05T11:55:32.564461+00:00"}