{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HCKHZRNL2BY4I5XPW6PPDM3G25","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":"848bc97377819349783939e0d85f6de657a96d08dc387bd06f85b5760d2b3882","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2022-06-07T18:30:52Z","title_canon_sha256":"f7fc74eb8c6a14ee8b83a95d68d1bfb8becd4de5aa5e69a4c01e732336734ca8"},"schema_version":"1.0","source":{"id":"2206.05122","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.05122","created_at":"2026-07-05T07:08:52Z"},{"alias_kind":"arxiv_version","alias_value":"2206.05122v4","created_at":"2026-07-05T07:08:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.05122","created_at":"2026-07-05T07:08:52Z"},{"alias_kind":"pith_short_12","alias_value":"HCKHZRNL2BY4","created_at":"2026-07-05T07:08:52Z"},{"alias_kind":"pith_short_16","alias_value":"HCKHZRNL2BY4I5XP","created_at":"2026-07-05T07:08:52Z"},{"alias_kind":"pith_short_8","alias_value":"HCKHZRNL","created_at":"2026-07-05T07:08:52Z"}],"graph_snapshots":[{"event_id":"sha256:f16796744c3f6ea93e4d52baf07aca79a846fbf057c35de6cb61cc1326543a61","target":"graph","created_at":"2026-07-05T07:08:52Z","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/2206.05122/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz variational method are increasingly accurate upper bounds to the exact ones. To this end, we resort to the variational principle, mentioned in most textbooks on quantum chemistry, and to a well known set of projection operators. We think that present approach may be suitable for an advanced course on quantum mechanics or quantum chemistry.","authors_text":"Francisco M. Fern\\'andez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2022-06-07T18:30:52Z","title":"On the Rayleigh-Ritz variational method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.05122","kind":"arxiv","version":4},"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":"sha256:2e3aca007fab891a8bb7e4ed9871e5a6c22452dd8734650c686752e784369594","target":"record","created_at":"2026-07-05T07:08:52Z","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":"848bc97377819349783939e0d85f6de657a96d08dc387bd06f85b5760d2b3882","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2022-06-07T18:30:52Z","title_canon_sha256":"f7fc74eb8c6a14ee8b83a95d68d1bfb8becd4de5aa5e69a4c01e732336734ca8"},"schema_version":"1.0","source":{"id":"2206.05122","kind":"arxiv","version":4}},"canonical_sha256":"38947cc5abd071c476efb79ef1b366d764ab8468126c73b3480748955892c10f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38947cc5abd071c476efb79ef1b366d764ab8468126c73b3480748955892c10f","first_computed_at":"2026-07-05T07:08:52.420813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:08:52.420813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z8SonCG5FltWbIB1X+kBbc0nQk7qtKXK97wCLZ66PAoTlifgbSzczKjDCLMYtCI7V53KJri3s1qFRq5/Dkl+DA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:08:52.421297Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.05122","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e3aca007fab891a8bb7e4ed9871e5a6c22452dd8734650c686752e784369594","sha256:f16796744c3f6ea93e4d52baf07aca79a846fbf057c35de6cb61cc1326543a61"],"state_sha256":"be886f2e6418f848f8dda720418a58d512eacca65f1330270fb20fec6600bc6a"}