{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3LJ3ST4MT72YKCFPHHOOUW5NK4","short_pith_number":"pith:3LJ3ST4M","schema_version":"1.0","canonical_sha256":"dad3b94f8c9ff58508af39dcea5bad5702b07cc2b20a6d96012de8bbbe38c9a5","source":{"kind":"arxiv","id":"2606.25148","version":1},"attestation_state":"computed","paper":{"title":"No 3D Matrices: A Unified Tensor-Product View of Matrix-Free Cartesian PDE Solvers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CE","cs.NA","physics.comp-ph","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Kathleen A. Yearick, Yong Yi Bay","submitted_at":"2026-06-23T20:30:10Z","abstract_excerpt":"Every Cartesian three-dimensional PDE solver hides a structural secret that production CFD codes have used for half a century and that graduate-level textbooks rarely state plainly. The derivative matrices, the compact Pad\\'e line solves, the Galerkin mass inversions, the alternating-direction-implicit substeps, and even the fast Poisson and Helmholtz diagonalization transforms all factor along the coordinate axes and collapse into repeated one-dimensional banded kernels executed along the grid lines. The three-dimensional operator exists only on paper; it is never assembled, factored, or stor"},"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":"2606.25148","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-23T20:30:10Z","cross_cats_sorted":["cs.CE","cs.NA","physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"8f703e5b04d56a4d1f5c5952bd7e2cd0fa01d19d5c26d4718998e2f9b3c97962","abstract_canon_sha256":"073ec2d6aecccbd84f9e3de1285802ea8c1d5ccbe20c6da647d507fa9f731c9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T00:18:19.359599Z","signature_b64":"Ss/NJw0r6IjAHWOzzK9kSDPKHCW6XfiGYmXPnPVBcFaR1XYuCFgBLjgIehv//DB/CHAiYyFam3Z9d5+qKXLBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dad3b94f8c9ff58508af39dcea5bad5702b07cc2b20a6d96012de8bbbe38c9a5","last_reissued_at":"2026-06-25T00:18:19.359185Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T00:18:19.359185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"No 3D Matrices: A Unified Tensor-Product View of Matrix-Free Cartesian PDE Solvers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CE","cs.NA","physics.comp-ph","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Kathleen A. Yearick, Yong Yi Bay","submitted_at":"2026-06-23T20:30:10Z","abstract_excerpt":"Every Cartesian three-dimensional PDE solver hides a structural secret that production CFD codes have used for half a century and that graduate-level textbooks rarely state plainly. The derivative matrices, the compact Pad\\'e line solves, the Galerkin mass inversions, the alternating-direction-implicit substeps, and even the fast Poisson and Helmholtz diagonalization transforms all factor along the coordinate axes and collapse into repeated one-dimensional banded kernels executed along the grid lines. The three-dimensional operator exists only on paper; it is never assembled, factored, or stor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25148","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/2606.25148/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":"2606.25148","created_at":"2026-06-25T00:18:19.359248+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25148v1","created_at":"2026-06-25T00:18:19.359248+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25148","created_at":"2026-06-25T00:18:19.359248+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LJ3ST4MT72Y","created_at":"2026-06-25T00:18:19.359248+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LJ3ST4MT72YKCFP","created_at":"2026-06-25T00:18:19.359248+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LJ3ST4M","created_at":"2026-06-25T00:18:19.359248+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/3LJ3ST4MT72YKCFPHHOOUW5NK4","json":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4.json","graph_json":"https://pith.science/api/pith-number/3LJ3ST4MT72YKCFPHHOOUW5NK4/graph.json","events_json":"https://pith.science/api/pith-number/3LJ3ST4MT72YKCFPHHOOUW5NK4/events.json","paper":"https://pith.science/paper/3LJ3ST4M"},"agent_actions":{"view_html":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4","download_json":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4.json","view_paper":"https://pith.science/paper/3LJ3ST4M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25148&json=true","fetch_graph":"https://pith.science/api/pith-number/3LJ3ST4MT72YKCFPHHOOUW5NK4/graph.json","fetch_events":"https://pith.science/api/pith-number/3LJ3ST4MT72YKCFPHHOOUW5NK4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4/action/storage_attestation","attest_author":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4/action/author_attestation","sign_citation":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4/action/citation_signature","submit_replication":"https://pith.science/pith/3LJ3ST4MT72YKCFPHHOOUW5NK4/action/replication_record"}},"created_at":"2026-06-25T00:18:19.359248+00:00","updated_at":"2026-06-25T00:18:19.359248+00:00"}