{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QHMB7HQF6L6RKU3PKJSBCKTNSE","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":"b53535c1b641b54f0009a9be71bed3b3db2a9953b31324273ff2ca33004144e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-08T13:11:57Z","title_canon_sha256":"98ce0d740b7f30a3f258446ca0910e43a819d1ae8d85a8a5870c0e20cb912796"},"schema_version":"1.0","source":{"id":"1802.02839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02839","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02839v1","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02839","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"pith_short_12","alias_value":"QHMB7HQF6L6R","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QHMB7HQF6L6RKU3P","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QHMB7HQF","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:c8cef2096d0c0768b031199e83e366febba8054438e2a39e934a454b3c0fb5de","target":"graph","created_at":"2026-05-18T00:24:02Z","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"},"paper":{"abstract_excerpt":"The goal of this paper is to develop a numerical algorithm that solves a two-dimensional elliptic partial differential equation in a polygonal domain using tensor methods and ideas from isogeometric analysis. The proposed algorithm is based on the Finite Element (FE) approximation with Quantized Tensor Train decomposition (QTT) used for matrix representation and solution approximation. In this paper we propose a special discretisation scheme that allows to construct the global stiffness matrix in the QTT-format. The algorithm has $O(\\log n)$ complexity, where $n=2^d$ is the number of nodes per","authors_text":"I. Oseledets, I. Tsybulin, L. Markeeva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-08T13:11:57Z","title":"QTT-isogeometric solver in two dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02839","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":"sha256:9d11c5dc0d9814982e3f0c0e3e88aa08895a3ceb3e7c5ad4e459a1cf2c7b8839","target":"record","created_at":"2026-05-18T00:24:02Z","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":"b53535c1b641b54f0009a9be71bed3b3db2a9953b31324273ff2ca33004144e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-08T13:11:57Z","title_canon_sha256":"98ce0d740b7f30a3f258446ca0910e43a819d1ae8d85a8a5870c0e20cb912796"},"schema_version":"1.0","source":{"id":"1802.02839","kind":"arxiv","version":1}},"canonical_sha256":"81d81f9e05f2fd15536f5264112a6d912512ab33c0873952961401b25ade3efa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81d81f9e05f2fd15536f5264112a6d912512ab33c0873952961401b25ade3efa","first_computed_at":"2026-05-18T00:24:02.941555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:02.941555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iTdjbSXVGhkwdNOUvDEd0zZXxML61zH41QLQt4pkLf3G/KtlvbnMROgRDvB8l9pmMeGn8/y71VH8Zuup5LBuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:02.942035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d11c5dc0d9814982e3f0c0e3e88aa08895a3ceb3e7c5ad4e459a1cf2c7b8839","sha256:c8cef2096d0c0768b031199e83e366febba8054438e2a39e934a454b3c0fb5de"],"state_sha256":"881017fa4eea9409a4a46de25c1a93bab9b85ab480a3c7f7e22464919364d7da"}