{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R6FDVBRQVSPFOF5G2NXO6QCAHE","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":"5c5f09d902882942c9b4d668c2900c46e380e2a612e626b0d513eef821019600","cross_cats_sorted":["math.MP","math.NA","physics.atom-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-23T13:21:15Z","title_canon_sha256":"aa0d0bffaf0b0fea2aaedf6e3bcb1e4f33fb89dcd6cbf16e2976425a85a23016"},"schema_version":"1.0","source":{"id":"1306.5401","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5401","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5401v2","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5401","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"pith_short_12","alias_value":"R6FDVBRQVSPF","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R6FDVBRQVSPFOF5G","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R6FDVBRQ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:86148d8c035addca5f9f242bba64fdbd753fb84f6d686aca5301a3c0d3c56aed","target":"graph","created_at":"2026-05-18T00:30:09Z","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 consider the problem of the occurrence of spurious modes when computing the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an atom or a molecule. We present recent mathematical results which we illustrate by simple numerical experiments. We also discuss open problems.","authors_text":"Eric S\\'er\\'e, Mathieu Lewin","cross_cats":["math.MP","math.NA","physics.atom-ph","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-23T13:21:15Z","title":"Spurious Modes in Dirac Calculations and How to Avoid Them"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5401","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:c6d3bd1e1bd3f2291aa6ce163a70ba2dfccab0cb6a1f15e1224db6dcd46c716b","target":"record","created_at":"2026-05-18T00:30:09Z","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":"5c5f09d902882942c9b4d668c2900c46e380e2a612e626b0d513eef821019600","cross_cats_sorted":["math.MP","math.NA","physics.atom-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-23T13:21:15Z","title_canon_sha256":"aa0d0bffaf0b0fea2aaedf6e3bcb1e4f33fb89dcd6cbf16e2976425a85a23016"},"schema_version":"1.0","source":{"id":"1306.5401","kind":"arxiv","version":2}},"canonical_sha256":"8f8a3a8630ac9e5717a6d36eef404039344be616e27109687fbe01fe629cd931","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f8a3a8630ac9e5717a6d36eef404039344be616e27109687fbe01fe629cd931","first_computed_at":"2026-05-18T00:30:09.799495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:09.799495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SIgW+ke02T3JxHcMz7gyf9OtzLEZsaoQU7H26p71+vBfE776rTtfCmrgqQa5q/Ke0yxOxkAq0NxE8wh61QxhDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:09.800226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5401","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6d3bd1e1bd3f2291aa6ce163a70ba2dfccab0cb6a1f15e1224db6dcd46c716b","sha256:86148d8c035addca5f9f242bba64fdbd753fb84f6d686aca5301a3c0d3c56aed"],"state_sha256":"2317916fea72f1d54d51389ac62e82013776f4417ab8c713eb216d228385343a"}