{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QSL5X5B252ZZZPG7ZH7OUVFDRE","short_pith_number":"pith:QSL5X5B2","canonical_record":{"source":{"id":"1205.0331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-02T06:23:49Z","cross_cats_sorted":[],"title_canon_sha256":"1d49fedea2295b47079d929d3f33f839d2c038446da6550a67798f420f5904a5","abstract_canon_sha256":"9ba5bb534ece997d812a7ab6001c70bcd16a936bac1642fa692418734f5e81b3"},"schema_version":"1.0"},"canonical_sha256":"8497dbf43aeeb39cbcdfc9feea54a3892b4ac937f870ab894f623f35e77591ae","source":{"kind":"arxiv","id":"1205.0331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0331","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0331v1","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0331","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"QSL5X5B252ZZ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QSL5X5B252ZZZPG7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QSL5X5B2","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QSL5X5B252ZZZPG7ZH7OUVFDRE","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-02T06:23:49Z","cross_cats_sorted":[],"title_canon_sha256":"1d49fedea2295b47079d929d3f33f839d2c038446da6550a67798f420f5904a5","abstract_canon_sha256":"9ba5bb534ece997d812a7ab6001c70bcd16a936bac1642fa692418734f5e81b3"},"schema_version":"1.0"},"canonical_sha256":"8497dbf43aeeb39cbcdfc9feea54a3892b4ac937f870ab894f623f35e77591ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:34.764848Z","signature_b64":"zGHMDPCiVsAWyZm6pU7B1oO4uTQdLWU1z8cFwE0tnlxCSjDQVNmr/V2ed4WyjXFLrRCRSmfe338D36px5U1jBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8497dbf43aeeb39cbcdfc9feea54a3892b4ac937f870ab894f623f35e77591ae","last_reissued_at":"2026-05-18T03:56:34.764384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:34.764384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0331","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBV9WpK8Jvv2rtUwEM6MPLz1Do3nzJ5TwWDiwb6rxqk0+fjxn4+SmUOOL7GV6EUcJRAJTXaG3CcVpKbpfSO1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:01:14.907600Z"},"content_sha256":"20090238005cde3dbfbb1d404c6cceb9940e72e3644d21690c226b08547331f5","schema_version":"1.0","event_id":"sha256:20090238005cde3dbfbb1d404c6cceb9940e72e3644d21690c226b08547331f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QSL5X5B252ZZZPG7ZH7OUVFDRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-consistent approximations of self-adjoint eigenproblems: Application to the supercell method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eric Canc\\`es, Virginie Ehrlacher, Yvon Maday","submitted_at":"2012-05-02T06:23:49Z","abstract_excerpt":"In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We first provide a priori error estimates on the eigenvalues and eigenvectors in the absence of spectral pollution. We then show that the supercell method for perturbed periodic Schr\\\"odinger operators falls into the scope of our study. We prove that this method is spectral pollution free, and we derive optimal convergence rates for the planewave discretization me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0331","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnxbNuLCgbAwU+vVrPtkedjenaUbj29dWu82TOKSYrZlxLCBP52n+L+oC4R4u3h1uminYUi4UAdGvZEBIi2lAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:01:14.907937Z"},"content_sha256":"7a9f22c9a98bb1b30cb37b7d937ad6f9a24c9a06dc91e150946d9cefa6fe4197","schema_version":"1.0","event_id":"sha256:7a9f22c9a98bb1b30cb37b7d937ad6f9a24c9a06dc91e150946d9cefa6fe4197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSL5X5B252ZZZPG7ZH7OUVFDRE/bundle.json","state_url":"https://pith.science/pith/QSL5X5B252ZZZPG7ZH7OUVFDRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSL5X5B252ZZZPG7ZH7OUVFDRE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T16:01:14Z","links":{"resolver":"https://pith.science/pith/QSL5X5B252ZZZPG7ZH7OUVFDRE","bundle":"https://pith.science/pith/QSL5X5B252ZZZPG7ZH7OUVFDRE/bundle.json","state":"https://pith.science/pith/QSL5X5B252ZZZPG7ZH7OUVFDRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSL5X5B252ZZZPG7ZH7OUVFDRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QSL5X5B252ZZZPG7ZH7OUVFDRE","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":"9ba5bb534ece997d812a7ab6001c70bcd16a936bac1642fa692418734f5e81b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-02T06:23:49Z","title_canon_sha256":"1d49fedea2295b47079d929d3f33f839d2c038446da6550a67798f420f5904a5"},"schema_version":"1.0","source":{"id":"1205.0331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0331","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0331v1","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0331","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"QSL5X5B252ZZ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QSL5X5B252ZZZPG7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QSL5X5B2","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:7a9f22c9a98bb1b30cb37b7d937ad6f9a24c9a06dc91e150946d9cefa6fe4197","target":"graph","created_at":"2026-05-18T03:56:34Z","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 article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We first provide a priori error estimates on the eigenvalues and eigenvectors in the absence of spectral pollution. We then show that the supercell method for perturbed periodic Schr\\\"odinger operators falls into the scope of our study. We prove that this method is spectral pollution free, and we derive optimal convergence rates for the planewave discretization me","authors_text":"Eric Canc\\`es, Virginie Ehrlacher, Yvon Maday","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-02T06:23:49Z","title":"Non-consistent approximations of self-adjoint eigenproblems: Application to the supercell method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0331","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":"sha256:20090238005cde3dbfbb1d404c6cceb9940e72e3644d21690c226b08547331f5","target":"record","created_at":"2026-05-18T03:56:34Z","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":"9ba5bb534ece997d812a7ab6001c70bcd16a936bac1642fa692418734f5e81b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-02T06:23:49Z","title_canon_sha256":"1d49fedea2295b47079d929d3f33f839d2c038446da6550a67798f420f5904a5"},"schema_version":"1.0","source":{"id":"1205.0331","kind":"arxiv","version":1}},"canonical_sha256":"8497dbf43aeeb39cbcdfc9feea54a3892b4ac937f870ab894f623f35e77591ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8497dbf43aeeb39cbcdfc9feea54a3892b4ac937f870ab894f623f35e77591ae","first_computed_at":"2026-05-18T03:56:34.764384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:34.764384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zGHMDPCiVsAWyZm6pU7B1oO4uTQdLWU1z8cFwE0tnlxCSjDQVNmr/V2ed4WyjXFLrRCRSmfe338D36px5U1jBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:34.764848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20090238005cde3dbfbb1d404c6cceb9940e72e3644d21690c226b08547331f5","sha256:7a9f22c9a98bb1b30cb37b7d937ad6f9a24c9a06dc91e150946d9cefa6fe4197"],"state_sha256":"9180500bb1adc4b30f8d8ae90c34319df69abf1ee1017b33d860b4bdc5e5050e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FpNIPdA8bF7AoSiDI40sOGlIqgFvOMWhTdj5osFjVv+EqzMonUUsag8bGZJauvVEQdVlOfEokvgAsihTJ+fsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:01:14.909840Z","bundle_sha256":"01d19e3670504ec8b1001496661a323577b36d70605d760bf01fd6a8e0387f06"}}