{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FEUSRGRSZFVLIFG4IFRPMUONCA","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":"4717f0914d211f148f9768b783753639e3a6a45c313c0a9485078897cf11b620","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2026-07-07T09:02:06Z","title_canon_sha256":"74760c887a795fc5f6ae33f753aa6ef02f0891856e2c8f76d828857a956e2d94"},"schema_version":"1.0","source":{"id":"2607.06021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06021","created_at":"2026-07-08T01:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06021v1","created_at":"2026-07-08T01:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06021","created_at":"2026-07-08T01:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"FEUSRGRSZFVL","created_at":"2026-07-08T01:18:54Z"},{"alias_kind":"pith_short_16","alias_value":"FEUSRGRSZFVLIFG4","created_at":"2026-07-08T01:18:54Z"},{"alias_kind":"pith_short_8","alias_value":"FEUSRGRS","created_at":"2026-07-08T01:18:54Z"}],"graph_snapshots":[{"event_id":"sha256:fcf62bd03adeee9221e976372f0b9a1f61db46660414092a4de51104918e4a3a","target":"graph","created_at":"2026-07-08T01:18:54Z","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/2607.06021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we explore a fast Poisson solver for problems with a solution that is known to be low-rank. We use an adaptive and warm started cross approximation called Cross-DEIM that iterates between index selection and and cross approximation to generate a low-rank solution. This paper focuses on leveraging a modern machine learning framework, PyTorch, as a general purpose array language to implement low-rank solvers based on Cross-DEIM. PyTorch enables native access to GPUs and accelerators but with a user-friendly high-level interface. We investigate statistical leverage scores for the in","authors_text":"Daniel Appel\\\"o, M{\\aa}ns I. Andersson","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2026-07-07T09:02:06Z","title":"A Sub-linear Low-Rank Solver for Poisson's Equation using Machine Learning Frameworks for GPU Acceleration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06021","kind":"arxiv","version":1},"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":"sha256:5a2d67186c8eccccbbcffbf36778279ecc7006634d55d23cf2263faadc8e63c9","target":"record","created_at":"2026-07-08T01:18:54Z","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":"4717f0914d211f148f9768b783753639e3a6a45c313c0a9485078897cf11b620","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2026-07-07T09:02:06Z","title_canon_sha256":"74760c887a795fc5f6ae33f753aa6ef02f0891856e2c8f76d828857a956e2d94"},"schema_version":"1.0","source":{"id":"2607.06021","kind":"arxiv","version":1}},"canonical_sha256":"2929289a32c96ab414dc4162f651cd101352f4b074a0d081d1e46347a87bea32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2929289a32c96ab414dc4162f651cd101352f4b074a0d081d1e46347a87bea32","first_computed_at":"2026-07-08T01:18:54.205396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:54.205396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCXZ5rbnLaDOWy/gFGeuV8R44N33hJ2Cfkzh/yhs1//e8EiMh9L72Qrd9Ymc+Flkd7EYg7bLV6FBnCgbzdQxCQ==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:54.205850Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a2d67186c8eccccbbcffbf36778279ecc7006634d55d23cf2263faadc8e63c9","sha256:fcf62bd03adeee9221e976372f0b9a1f61db46660414092a4de51104918e4a3a"],"state_sha256":"d718a5b5e5d520fac4985111e5d4bf1c4c13f516952f5ed044e694f89f837b74"}