{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:BXVDBX6DWTWFPNA6XRD2NCONBZ","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":"e2ff2cf5c26679b29539638d6393e357f5351ffa4f218533097a23938e622dc3","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-08-05T20:02:53Z","title_canon_sha256":"d1b4a2e7ed8c4e43c6df53a04f1c8ff41b58bfe35fdc71fcedebaa2dc69fa572"},"schema_version":"1.0","source":{"id":"math/0508111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508111","created_at":"2026-06-03T22:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508111v1","created_at":"2026-06-03T22:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508111","created_at":"2026-06-03T22:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"BXVDBX6DWTWF","created_at":"2026-06-03T22:06:17Z"},{"alias_kind":"pith_short_16","alias_value":"BXVDBX6DWTWFPNA6","created_at":"2026-06-03T22:06:17Z"},{"alias_kind":"pith_short_8","alias_value":"BXVDBX6D","created_at":"2026-06-03T22:06:17Z"}],"graph_snapshots":[{"event_id":"sha256:b5431c5014f71eaace0491c043f6450d02043e73c81c8866fe08baf78fd32be0","target":"graph","created_at":"2026-06-03T22:06:17Z","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/math/0508111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for the largest sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted Lanczos method and in the Jacobi-Davidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximu","authors_text":"Matthias Bollhoefer, Olaf Schenk, Rudolf A. Roemer","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2005-08-05T20:02:53Z","title":"On Large Scale Diagonalization Techniques for the Anderson Model of Localization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508111","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":"sha256:6860a360cd699c7a16e382c7fcf76ccf7aec08fbe277aa7da32d9a0507a5f68e","target":"record","created_at":"2026-06-03T22:06:17Z","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":"e2ff2cf5c26679b29539638d6393e357f5351ffa4f218533097a23938e622dc3","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-08-05T20:02:53Z","title_canon_sha256":"d1b4a2e7ed8c4e43c6df53a04f1c8ff41b58bfe35fdc71fcedebaa2dc69fa572"},"schema_version":"1.0","source":{"id":"math/0508111","kind":"arxiv","version":1}},"canonical_sha256":"0dea30dfc3b4ec57b41ebc47a689cd0e4b36be5b42940c07d6bd5986424b3b92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dea30dfc3b4ec57b41ebc47a689cd0e4b36be5b42940c07d6bd5986424b3b92","first_computed_at":"2026-06-03T22:06:17.360832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:17.360832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bfxBPERwjkQASF6kVTXJ7EywqR7d05ZM50f4jTunod65OY3eJpM+eMhrutNHqiXfbtWMbnE55/fYbcDHubAyDw==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:17.361236Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6860a360cd699c7a16e382c7fcf76ccf7aec08fbe277aa7da32d9a0507a5f68e","sha256:b5431c5014f71eaace0491c043f6450d02043e73c81c8866fe08baf78fd32be0"],"state_sha256":"8e90d726361e06f5f9af7d0482fe12d48a3d8eb23494278d11b10be7304e086a"}