{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GABQZA5DF6A3BGMKXAMMYY54ZJ","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":"15864b2d82edc43f94ece570dbd97869b5db1f65c02fc692465bb647d21e5fd1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-06T18:39:42Z","title_canon_sha256":"0c93cdd83c92158787db6dab5340d4d49adc31570ef6134707a0e663d967dfb5"},"schema_version":"1.0","source":{"id":"1606.02329","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02329","created_at":"2026-05-18T00:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02329v2","created_at":"2026-05-18T00:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02329","created_at":"2026-05-18T00:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"GABQZA5DF6A3","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"GABQZA5DF6A3BGMK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"GABQZA5D","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:f1cb15ff951b7efa0eee94b12d269cb09f28519f15c8561c2c372ae50c4a8c23","target":"graph","created_at":"2026-05-18T00:37:18Z","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":"A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace-Beltrami operator on manifolds with boundary in any dimension is presented. The algorithm is based on the characterisation of a large class of self-adjoint extensions of Laplace-Beltrami operators in terms of their associated quadratic forms. The convergence of the scheme is proved. A two-dimensional version of the algorithm is implemented effectively and several numerical examples are computed showing that the algorithm treats in a unified way a wide variety of boundary conditions.","authors_text":"A. L\\'opez-Yela, J.M. P\\'erez-Pardo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-06T18:39:42Z","title":"Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02329","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":"sha256:53614ab0e34078c21624c1b6a490090daefcb95c46f3cbe4cb6a1acfea31b11c","target":"record","created_at":"2026-05-18T00:37:18Z","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":"15864b2d82edc43f94ece570dbd97869b5db1f65c02fc692465bb647d21e5fd1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-06T18:39:42Z","title_canon_sha256":"0c93cdd83c92158787db6dab5340d4d49adc31570ef6134707a0e663d967dfb5"},"schema_version":"1.0","source":{"id":"1606.02329","kind":"arxiv","version":2}},"canonical_sha256":"30030c83a32f81b0998ab818cc63bcca65a2668bb189c7b6ac3deb027338bfe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30030c83a32f81b0998ab818cc63bcca65a2668bb189c7b6ac3deb027338bfe0","first_computed_at":"2026-05-18T00:37:18.878700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:18.878700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GXnr+LP5A9YtWroWOGAKH2F2s4Vbll9lY0pAFnVTH9W4VUm64Ow/amXRefKrK4OCmQTMaFrJYvPWmMeHCUMxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:18.879286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02329","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53614ab0e34078c21624c1b6a490090daefcb95c46f3cbe4cb6a1acfea31b11c","sha256:f1cb15ff951b7efa0eee94b12d269cb09f28519f15c8561c2c372ae50c4a8c23"],"state_sha256":"97899fd57f222b5f26be26ce41c477ad932941c5b6364d3bea502af8e99f8cb7"}