{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VAZ2JBCMXAPYYYU77HXMY43JUV","short_pith_number":"pith:VAZ2JBCM","canonical_record":{"source":{"id":"2512.05520","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-05T08:24:32Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"9b9cba0cb25ce064aef8bf87d91cad1cf2c11fd0cfcbc916afd33e0fdbff3e9f","abstract_canon_sha256":"91fd970b2457bf3f282c2477bcd86861f2ba14b4034766f5ab9123d82da3bc5a"},"schema_version":"1.0"},"canonical_sha256":"a833a4844cb81f8c629ff9eecc7369a5782456ff1ed3a2fff5785e9bb52a3d9b","source":{"kind":"arxiv","id":"2512.05520","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.05520","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"2512.05520v2","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.05520","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"VAZ2JBCMXAPY","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"VAZ2JBCMXAPYYYU7","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"VAZ2JBCM","created_at":"2026-07-14T01:20:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VAZ2JBCMXAPYYYU77HXMY43JUV","target":"record","payload":{"canonical_record":{"source":{"id":"2512.05520","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-05T08:24:32Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"9b9cba0cb25ce064aef8bf87d91cad1cf2c11fd0cfcbc916afd33e0fdbff3e9f","abstract_canon_sha256":"91fd970b2457bf3f282c2477bcd86861f2ba14b4034766f5ab9123d82da3bc5a"},"schema_version":"1.0"},"canonical_sha256":"a833a4844cb81f8c629ff9eecc7369a5782456ff1ed3a2fff5785e9bb52a3d9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:20:49.414302Z","signature_b64":"KFKW3P1jt+plX1DGy8dJiQXs/lu3HFggqrsF2QKybsOew9qSkIOQ+AtimoNbOynzaizAGUQxPHCgvagG8YkaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a833a4844cb81f8c629ff9eecc7369a5782456ff1ed3a2fff5785e9bb52a3d9b","last_reissued_at":"2026-07-14T01:20:49.413331Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:20:49.413331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.05520","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T01:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PcnajsqngDAc8f45cWoofaHwltdvyHjpe7f/nAmmR9+LJuSPBvnx5cdBuOzGUhdaq9sZGtHh5FssMOZUzdX+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T16:39:03.383766Z"},"content_sha256":"8917d0109fd17904a81a5d97930fb8c68127f22f08f35eaff2f1732505648819","schema_version":"1.0","event_id":"sha256:8917d0109fd17904a81a5d97930fb8c68127f22f08f35eaff2f1732505648819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VAZ2JBCMXAPYYYU77HXMY43JUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Zeroth-Order Method for Computing Generalized Rayleigh Quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Gabriele Steidl, Jonas Bresch, Martin Schoen, Oleh Melnyk","submitted_at":"2025-12-05T08:24:32Z","abstract_excerpt":"The maximization of the (generalized) Rayleigh quotient is a central problem in numerical linear algebra. Conventional algorithms for its computation typically rely on matrix-adjoint products, making them sensitive to errors arrissing from adjoint mismatches. To address this issue, we introduce a stochastic zeroth-order Riemannian algorithm that maximizes the generalized Rayleigh quotient without requiring adjoint or matrix inverse computations. We provide theoretical convergence guarantees showing that the iterates converge to the set of global maximizers of the (generalized) Rayleigh quotien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.05520","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.05520/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-14T01:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UNtq5mc0692amE9JkX3LR0Gmi6h+E2dzdPNeYiZK0dkyE/7A304LDTvQ1uCfzMFeiqR7KKdBIhP3qEx+dZlCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T16:39:03.384340Z"},"content_sha256":"5bfda4361b48bcdb6e518727720ecd0806990171a284709203ed72e3e8432b13","schema_version":"1.0","event_id":"sha256:5bfda4361b48bcdb6e518727720ecd0806990171a284709203ed72e3e8432b13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VAZ2JBCMXAPYYYU77HXMY43JUV/bundle.json","state_url":"https://pith.science/pith/VAZ2JBCMXAPYYYU77HXMY43JUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VAZ2JBCMXAPYYYU77HXMY43JUV/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":"2026-08-10T16:39:03Z","links":{"resolver":"https://pith.science/pith/VAZ2JBCMXAPYYYU77HXMY43JUV","bundle":"https://pith.science/pith/VAZ2JBCMXAPYYYU77HXMY43JUV/bundle.json","state":"https://pith.science/pith/VAZ2JBCMXAPYYYU77HXMY43JUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VAZ2JBCMXAPYYYU77HXMY43JUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VAZ2JBCMXAPYYYU77HXMY43JUV","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":"91fd970b2457bf3f282c2477bcd86861f2ba14b4034766f5ab9123d82da3bc5a","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-05T08:24:32Z","title_canon_sha256":"9b9cba0cb25ce064aef8bf87d91cad1cf2c11fd0cfcbc916afd33e0fdbff3e9f"},"schema_version":"1.0","source":{"id":"2512.05520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.05520","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"2512.05520v2","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.05520","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"VAZ2JBCMXAPY","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"VAZ2JBCMXAPYYYU7","created_at":"2026-07-14T01:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"VAZ2JBCM","created_at":"2026-07-14T01:20:49Z"}],"graph_snapshots":[{"event_id":"sha256:5bfda4361b48bcdb6e518727720ecd0806990171a284709203ed72e3e8432b13","target":"graph","created_at":"2026-07-14T01:20:49Z","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/2512.05520/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The maximization of the (generalized) Rayleigh quotient is a central problem in numerical linear algebra. Conventional algorithms for its computation typically rely on matrix-adjoint products, making them sensitive to errors arrissing from adjoint mismatches. To address this issue, we introduce a stochastic zeroth-order Riemannian algorithm that maximizes the generalized Rayleigh quotient without requiring adjoint or matrix inverse computations. We provide theoretical convergence guarantees showing that the iterates converge to the set of global maximizers of the (generalized) Rayleigh quotien","authors_text":"Gabriele Steidl, Jonas Bresch, Martin Schoen, Oleh Melnyk","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-05T08:24:32Z","title":"Stochastic Zeroth-Order Method for Computing Generalized Rayleigh Quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.05520","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":"sha256:8917d0109fd17904a81a5d97930fb8c68127f22f08f35eaff2f1732505648819","target":"record","created_at":"2026-07-14T01:20:49Z","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":"91fd970b2457bf3f282c2477bcd86861f2ba14b4034766f5ab9123d82da3bc5a","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-05T08:24:32Z","title_canon_sha256":"9b9cba0cb25ce064aef8bf87d91cad1cf2c11fd0cfcbc916afd33e0fdbff3e9f"},"schema_version":"1.0","source":{"id":"2512.05520","kind":"arxiv","version":2}},"canonical_sha256":"a833a4844cb81f8c629ff9eecc7369a5782456ff1ed3a2fff5785e9bb52a3d9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a833a4844cb81f8c629ff9eecc7369a5782456ff1ed3a2fff5785e9bb52a3d9b","first_computed_at":"2026-07-14T01:20:49.413331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:20:49.413331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KFKW3P1jt+plX1DGy8dJiQXs/lu3HFggqrsF2QKybsOew9qSkIOQ+AtimoNbOynzaizAGUQxPHCgvagG8YkaCA==","signature_status":"signed_v1","signed_at":"2026-07-14T01:20:49.414302Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.05520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8917d0109fd17904a81a5d97930fb8c68127f22f08f35eaff2f1732505648819","sha256:5bfda4361b48bcdb6e518727720ecd0806990171a284709203ed72e3e8432b13"],"state_sha256":"fb5d4bae72dee0e9e9bffcb1909fdb989bf6b5e44138100e27a129d28d742be5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tW9ROcjYVlM+F1IuGyBnZruYx7knOjwhoTObSGkgYHsWlAzmmz62rYPDH86lFiuZiQHWw08NDM6FwA/rGv5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T16:39:03.390141Z","bundle_sha256":"fe2a67c10b01157c72f885c1e09c9bcda7d0de85d2ad587f921c7df9cdb7604d"}}