{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QSG464CMGB2W2SDJA4BZ7SWC6A","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":"8bb89311c198a322e7b396737b3c3c3babfcdb48a22bebe9af97192b23857f0b","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-27T14:07:11Z","title_canon_sha256":"1c0b000f4c7622b9a2858f9fa807029e9f33814d1dc331f90edf86757384444b"},"schema_version":"1.0","source":{"id":"2411.18361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18361","created_at":"2026-07-05T09:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18361v1","created_at":"2026-07-05T09:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18361","created_at":"2026-07-05T09:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"QSG464CMGB2W","created_at":"2026-07-05T09:41:15Z"},{"alias_kind":"pith_short_16","alias_value":"QSG464CMGB2W2SDJ","created_at":"2026-07-05T09:41:15Z"},{"alias_kind":"pith_short_8","alias_value":"QSG464CM","created_at":"2026-07-05T09:41:15Z"}],"graph_snapshots":[{"event_id":"sha256:481cc5e26652c29349f2b857d738a104b4093b71e8a73aa757f856b5d36ad38c","target":"graph","created_at":"2026-07-05T09:41:15Z","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/2411.18361/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First, we introduce a validated Matrix Multiplication Transform (MMT) algorithm, analogous to the discrete Fourier transform, which offers a reliable framework for evaluating nonlinearities in spectral methods while effectively mitigating challenges associated with rounding errors. Second, we examine the Zernike polynomials, a spectral basis well-suited for problems on the disk, and highlight their essential properties. We ","authors_text":"Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette, Matthieu Cadiot","cross_cats":["cs.NA","math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-27T14:07:11Z","title":"Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18361","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":"sha256:2324f63bf309c997d75db47c9d5f02c656e5b0f6c36e35e0d437ff808a0ecda1","target":"record","created_at":"2026-07-05T09:41:15Z","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":"8bb89311c198a322e7b396737b3c3c3babfcdb48a22bebe9af97192b23857f0b","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-27T14:07:11Z","title_canon_sha256":"1c0b000f4c7622b9a2858f9fa807029e9f33814d1dc331f90edf86757384444b"},"schema_version":"1.0","source":{"id":"2411.18361","kind":"arxiv","version":1}},"canonical_sha256":"848dcf704c30756d486907039fcac2f00c31525e9c75ec68091d9ead86f8ac3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"848dcf704c30756d486907039fcac2f00c31525e9c75ec68091d9ead86f8ac3b","first_computed_at":"2026-07-05T09:41:15.643455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:15.643455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DWEYpMEkV75mKvmhMuvtR3VXSh1sO1HEn83Lui9GRzEQKdKM7WqtIapEQ0vcKXaLVNpc/7yQzGCRJzqYOeMpCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:15.643884Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2324f63bf309c997d75db47c9d5f02c656e5b0f6c36e35e0d437ff808a0ecda1","sha256:481cc5e26652c29349f2b857d738a104b4093b71e8a73aa757f856b5d36ad38c"],"state_sha256":"0f8a0223b211b8d98a9717ee1b9f76c3955291f0ed9ee45a49195a57106460d1"}