{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XIUOTYX22RDRC7ILRWAFJYMQVC","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":"b2ba6472114aa2c41ad68a3f04881fb18f3d46575b5c7d8292a9f9c378cedefc","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-27T01:57:29Z","title_canon_sha256":"e3bb48f65a2f7be970a861ba2a5e30a09da3323b9f03912838f47e0151532873"},"schema_version":"1.0","source":{"id":"2605.27842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27842","created_at":"2026-05-28T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27842v1","created_at":"2026-05-28T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27842","created_at":"2026-05-28T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"XIUOTYX22RDR","created_at":"2026-05-28T01:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"XIUOTYX22RDRC7IL","created_at":"2026-05-28T01:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"XIUOTYX2","created_at":"2026-05-28T01:04:50Z"}],"graph_snapshots":[{"event_id":"sha256:60b06d983fe8f37191906653f4b59ba649b1fab65ea491396109991900150f2f","target":"graph","created_at":"2026-05-28T01:04:50Z","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/2605.27842/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a spectral framework that embeds 1D and 2D quasiperiodic Helmholtz eigenvalue problems into higher-dimensional (2D and 4D) periodic spaces via the projection method \\cite{jiang2014numerical, jiang2024numerical}. To effectively map the elevated high-dimensional states back to the original physical space, we establish a novel validation framework based on the weighted expectation of pointwise Rayleigh quotients. Supported by comprehensive error and spectral analysis, we demonstrate that the eigenvalues derived from this expectation align more authentically with the orig","authors_text":"Teng-Chao Sun, Tiexiang Li, Wen-Wei Lin, Xing-Long Lyu","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-27T01:57:29Z","title":"A Novel Computational and Analytical Framework for 2D Quasiperiodic Helmholtz Eigenvalue Problems via the Projection Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27842","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:e7d42e5385503d34c8c6fc55e322ddfc480588e0930723793a36d14afbbe420b","target":"record","created_at":"2026-05-28T01:04:50Z","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":"b2ba6472114aa2c41ad68a3f04881fb18f3d46575b5c7d8292a9f9c378cedefc","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-27T01:57:29Z","title_canon_sha256":"e3bb48f65a2f7be970a861ba2a5e30a09da3323b9f03912838f47e0151532873"},"schema_version":"1.0","source":{"id":"2605.27842","kind":"arxiv","version":1}},"canonical_sha256":"ba28e9e2fad447117d0b8d8054e190a8a1964a41d49b1e5f86bbf13a60066909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba28e9e2fad447117d0b8d8054e190a8a1964a41d49b1e5f86bbf13a60066909","first_computed_at":"2026-05-28T01:04:50.190004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:50.190004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zgv0Mqmc6zGUsnYEIRz92eoSWi7A1JuXq1iYvJyCA9/sgNti/wgp6g+SHfaoOSiyLNtxLFa93X75khIPCF/VCw==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:50.190471Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7d42e5385503d34c8c6fc55e322ddfc480588e0930723793a36d14afbbe420b","sha256:60b06d983fe8f37191906653f4b59ba649b1fab65ea491396109991900150f2f"],"state_sha256":"bacc1488f38474ce3e37c92d2706c1ca13b70c6cfbaf7c998f651aa53b26967a"}