{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:SE5CYNSAFL4AXRXCUMXXY3U4S3","short_pith_number":"pith:SE5CYNSA","schema_version":"1.0","canonical_sha256":"913a2c36402af80bc6e2a32f7c6e9c96c314a48ee75ba5ce3cb9e7b8211a41d6","source":{"kind":"arxiv","id":"0812.2153","version":1},"attestation_state":"computed","paper":{"title":"Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schr\\\"odinger Operators)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.SP","authors_text":"Eric s\\'er\\'e (CEREMADE), Mathieu Lewin (AGM)","submitted_at":"2008-12-11T14:12:15Z","abstract_excerpt":"This paper, devoted to the study of spectral pollution, contains both abstract results and applications to some self-adjoint operators with a gap in their essential spectrum occuring in Quantum Mechanics. First we consider Galerkin basis which respect the decomposition of the ambient Hilbert space into a direct sum $H=PH\\oplus(1-P)H$, given by a fixed orthogonal projector $P$, and we localize the polluted spectrum exactly. This is followed by applications to periodic Schr\\\"odinger operators (pollution is absent in a Wannier-type basis), and to Dirac operator (several natural decompositions are"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0812.2153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2008-12-11T14:12:15Z","cross_cats_sorted":["math-ph","math.MP","math.NA"],"title_canon_sha256":"f82e0f48b6ef49ca27143da1e4e4bf58737353fad7fb8c9c7d03130c6c65e00d","abstract_canon_sha256":"3c8b301102e7168b6725c0f7e3a57ab4f33468afe0f4738a41bee72cc4d58130"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.899124Z","signature_b64":"UgDrD8XV22fG9v9YsjM8t9NdOuUzsguPv18XKW/hvHcm4eNY7JuKsgsLGXszsE+DUb0eUt4lEmWnbfq+HW/jAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"913a2c36402af80bc6e2a32f7c6e9c96c314a48ee75ba5ce3cb9e7b8211a41d6","last_reissued_at":"2026-05-18T02:58:10.898654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.898654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schr\\\"odinger Operators)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.SP","authors_text":"Eric s\\'er\\'e (CEREMADE), Mathieu Lewin (AGM)","submitted_at":"2008-12-11T14:12:15Z","abstract_excerpt":"This paper, devoted to the study of spectral pollution, contains both abstract results and applications to some self-adjoint operators with a gap in their essential spectrum occuring in Quantum Mechanics. First we consider Galerkin basis which respect the decomposition of the ambient Hilbert space into a direct sum $H=PH\\oplus(1-P)H$, given by a fixed orthogonal projector $P$, and we localize the polluted spectrum exactly. This is followed by applications to periodic Schr\\\"odinger operators (pollution is absent in a Wannier-type basis), and to Dirac operator (several natural decompositions are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2153","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0812.2153","created_at":"2026-05-18T02:58:10.898725+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.2153v1","created_at":"2026-05-18T02:58:10.898725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2153","created_at":"2026-05-18T02:58:10.898725+00:00"},{"alias_kind":"pith_short_12","alias_value":"SE5CYNSAFL4A","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"SE5CYNSAFL4AXRXC","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"SE5CYNSA","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3","json":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3.json","graph_json":"https://pith.science/api/pith-number/SE5CYNSAFL4AXRXCUMXXY3U4S3/graph.json","events_json":"https://pith.science/api/pith-number/SE5CYNSAFL4AXRXCUMXXY3U4S3/events.json","paper":"https://pith.science/paper/SE5CYNSA"},"agent_actions":{"view_html":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3","download_json":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3.json","view_paper":"https://pith.science/paper/SE5CYNSA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.2153&json=true","fetch_graph":"https://pith.science/api/pith-number/SE5CYNSAFL4AXRXCUMXXY3U4S3/graph.json","fetch_events":"https://pith.science/api/pith-number/SE5CYNSAFL4AXRXCUMXXY3U4S3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3/action/storage_attestation","attest_author":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3/action/author_attestation","sign_citation":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3/action/citation_signature","submit_replication":"https://pith.science/pith/SE5CYNSAFL4AXRXCUMXXY3U4S3/action/replication_record"}},"created_at":"2026-05-18T02:58:10.898725+00:00","updated_at":"2026-05-18T02:58:10.898725+00:00"}