{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:F6PE5OJ2B7UJRB6EYESGJSHLPO","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":"7ed1895274043a60db34263fdce4ddd3b9366ff316a2cc5776d3832964e6bc78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-08T08:47:12Z","title_canon_sha256":"f68356df55116d34d0a653ea23a92cfc5468b1708a192cef88d5ac415d0f7b73"},"schema_version":"1.0","source":{"id":"1207.1854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1854","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1854v2","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1854","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"F6PE5OJ2B7UJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F6PE5OJ2B7UJRB6E","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F6PE5OJ2","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:21994489d1ba7bea87045ff2f4f57fffe35732bf7b09c27744f5f695427c4a6b","target":"graph","created_at":"2026-05-18T03:40:49Z","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":"In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or non-Abelian symmetries, and is friendly for grid-based discretizations such as finite difference, finite element or finite volume methods. With the formulation, we divide the original eigenvalue problem into a set of subproblems and require only a smaller number of eigenpairs for each subproblem. We implement the decomposition approach with finite elements and ","authors_text":"Aihui Zhou, Jun Fang, Xingyu Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-08T08:47:12Z","title":"A Symmetry-based Decomposition Approach to Eigenvalue Problems: Formulation, Discretization, and Implementation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1854","kind":"arxiv","version":2},"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":"sha256:14dbe4597e2dedaaebe03bec6d821123db8196e228db587332509b8be6e64747","target":"record","created_at":"2026-05-18T03:40:49Z","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":"7ed1895274043a60db34263fdce4ddd3b9366ff316a2cc5776d3832964e6bc78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-08T08:47:12Z","title_canon_sha256":"f68356df55116d34d0a653ea23a92cfc5468b1708a192cef88d5ac415d0f7b73"},"schema_version":"1.0","source":{"id":"1207.1854","kind":"arxiv","version":2}},"canonical_sha256":"2f9e4eb93a0fe89887c4c12464c8eb7ba2b67da848ab0d2367ef9e071d621781","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f9e4eb93a0fe89887c4c12464c8eb7ba2b67da848ab0d2367ef9e071d621781","first_computed_at":"2026-05-18T03:40:49.308749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:49.308749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PUUZDw6bo6sr7Urb8hmW33SeJdoSktvtA99gs8QVOdc0M0CH+KqrkhZL9rkGB7IK6TnAXBiSykgOlHf4B/1lDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:49.309571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14dbe4597e2dedaaebe03bec6d821123db8196e228db587332509b8be6e64747","sha256:21994489d1ba7bea87045ff2f4f57fffe35732bf7b09c27744f5f695427c4a6b"],"state_sha256":"a51f60761a15d565bc39804db2877d15b790c99489606f31afa752511a86717a"}