{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:Y6FP4NL6REQXJD2EVJLQFXETMS","short_pith_number":"pith:Y6FP4NL6","canonical_record":{"source":{"id":"2505.22498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-28T15:49:35Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0f14563119db497603a70ee5ed481f71ca46f01673b50f18452dbe8c5fd197ba","abstract_canon_sha256":"0d19e2f65210922c052dfa88b1fde6efa8d137eb50b65b5b91b50c3a0a9dd737"},"schema_version":"1.0"},"canonical_sha256":"c78afe357e8921748f44aa5702dc936482bc15ed98e40dd6aff01d8662e80b8c","source":{"kind":"arxiv","id":"2505.22498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22498","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22498v1","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22498","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y6FP4NL6REQX","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_16","alias_value":"Y6FP4NL6REQXJD2E","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_8","alias_value":"Y6FP4NL6","created_at":"2026-07-05T11:11:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:Y6FP4NL6REQXJD2EVJLQFXETMS","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-28T15:49:35Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0f14563119db497603a70ee5ed481f71ca46f01673b50f18452dbe8c5fd197ba","abstract_canon_sha256":"0d19e2f65210922c052dfa88b1fde6efa8d137eb50b65b5b91b50c3a0a9dd737"},"schema_version":"1.0"},"canonical_sha256":"c78afe357e8921748f44aa5702dc936482bc15ed98e40dd6aff01d8662e80b8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:25.291099Z","signature_b64":"UfppX7FhudbSpQ/JntBFHzbbWpPiBjqTsYKorMrqXmgRc+gwqXgyQlsNkVRM/klaf6vTr8Qk0GQ3U0AhOdTpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c78afe357e8921748f44aa5702dc936482bc15ed98e40dd6aff01d8662e80b8c","last_reissued_at":"2026-07-05T11:11:25.290509Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:25.290509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22498","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":"2026-07-05T11:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zvytLS6BHuwTXTtRM/CN+lj91dKRDArmFQyOM5QkSx9wdmuqQxmEdezjGuSwEXMqcaoZd3uRniiOSoPxv87yBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:10:36.006868Z"},"content_sha256":"1eae252c77a7eea3b17e973dd134a92e0f9414aaaab635561e6fa2af325e2088","schema_version":"1.0","event_id":"sha256:1eae252c77a7eea3b17e973dd134a92e0f9414aaaab635561e6fa2af325e2088"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:Y6FP4NL6REQXJD2EVJLQFXETMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lanczos with compression for symmetric matrix Lyapunov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Angelo A. Casulli, Daniel Kressner, Francesco Hrobat","submitted_at":"2025-05-28T15:49:35Z","abstract_excerpt":"This work considers large-scale Lyapunov matrix equations of the form $AX + XA = \\boldsymbol{c}\\boldsymbol{c}^T$, where $A$ is a symmetric positive definite matrix and $\\boldsymbol{c}$ is a vector. Motivated by the need to solve such equations in a wide range of applications, various numerical methods have been developed to compute low-rank approximations of the solution matrix $X$. In this work, we focus on the Lanczos method, which has the distinct advantage of requiring only matrix-vector products with $A$, making it broadly applicable. However, the Lanczos method may suffer from slow conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22498","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.22498/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":"2026-07-05T11:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9i75VNcpRseH3ho9tg+QoauL9EpNooDYS4dhonCeJkG6i/M+ExgNNIkW1g3CeDl/vxW5vh9c2lvVPf/fqDYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:10:36.007368Z"},"content_sha256":"3529b08c478a6fbcc18fa2eb1a50dd6a45f92a30fac87246382d3c7cafedd92e","schema_version":"1.0","event_id":"sha256:3529b08c478a6fbcc18fa2eb1a50dd6a45f92a30fac87246382d3c7cafedd92e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y6FP4NL6REQXJD2EVJLQFXETMS/bundle.json","state_url":"https://pith.science/pith/Y6FP4NL6REQXJD2EVJLQFXETMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y6FP4NL6REQXJD2EVJLQFXETMS/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":"2026-08-08T04:10:36Z","links":{"resolver":"https://pith.science/pith/Y6FP4NL6REQXJD2EVJLQFXETMS","bundle":"https://pith.science/pith/Y6FP4NL6REQXJD2EVJLQFXETMS/bundle.json","state":"https://pith.science/pith/Y6FP4NL6REQXJD2EVJLQFXETMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y6FP4NL6REQXJD2EVJLQFXETMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Y6FP4NL6REQXJD2EVJLQFXETMS","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":"0d19e2f65210922c052dfa88b1fde6efa8d137eb50b65b5b91b50c3a0a9dd737","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-28T15:49:35Z","title_canon_sha256":"0f14563119db497603a70ee5ed481f71ca46f01673b50f18452dbe8c5fd197ba"},"schema_version":"1.0","source":{"id":"2505.22498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22498","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22498v1","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22498","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y6FP4NL6REQX","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_16","alias_value":"Y6FP4NL6REQXJD2E","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_8","alias_value":"Y6FP4NL6","created_at":"2026-07-05T11:11:25Z"}],"graph_snapshots":[{"event_id":"sha256:3529b08c478a6fbcc18fa2eb1a50dd6a45f92a30fac87246382d3c7cafedd92e","target":"graph","created_at":"2026-07-05T11:11:25Z","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/2505.22498/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work considers large-scale Lyapunov matrix equations of the form $AX + XA = \\boldsymbol{c}\\boldsymbol{c}^T$, where $A$ is a symmetric positive definite matrix and $\\boldsymbol{c}$ is a vector. Motivated by the need to solve such equations in a wide range of applications, various numerical methods have been developed to compute low-rank approximations of the solution matrix $X$. In this work, we focus on the Lanczos method, which has the distinct advantage of requiring only matrix-vector products with $A$, making it broadly applicable. However, the Lanczos method may suffer from slow conve","authors_text":"Angelo A. Casulli, Daniel Kressner, Francesco Hrobat","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-28T15:49:35Z","title":"Lanczos with compression for symmetric matrix Lyapunov equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22498","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":"sha256:1eae252c77a7eea3b17e973dd134a92e0f9414aaaab635561e6fa2af325e2088","target":"record","created_at":"2026-07-05T11:11:25Z","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":"0d19e2f65210922c052dfa88b1fde6efa8d137eb50b65b5b91b50c3a0a9dd737","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-28T15:49:35Z","title_canon_sha256":"0f14563119db497603a70ee5ed481f71ca46f01673b50f18452dbe8c5fd197ba"},"schema_version":"1.0","source":{"id":"2505.22498","kind":"arxiv","version":1}},"canonical_sha256":"c78afe357e8921748f44aa5702dc936482bc15ed98e40dd6aff01d8662e80b8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c78afe357e8921748f44aa5702dc936482bc15ed98e40dd6aff01d8662e80b8c","first_computed_at":"2026-07-05T11:11:25.290509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:25.290509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UfppX7FhudbSpQ/JntBFHzbbWpPiBjqTsYKorMrqXmgRc+gwqXgyQlsNkVRM/klaf6vTr8Qk0GQ3U0AhOdTpAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:25.291099Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eae252c77a7eea3b17e973dd134a92e0f9414aaaab635561e6fa2af325e2088","sha256:3529b08c478a6fbcc18fa2eb1a50dd6a45f92a30fac87246382d3c7cafedd92e"],"state_sha256":"a1d468f63c9dcc6c82bbc6c2034154e7db7a51162f9f99aaaa70fbdbbf72294e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GlbnEhyLYZJ3VIGHR6A8lc8l3ctFEMJg9DE28vzYkFFf6rP1YN4wp5eOl2J6h6Y2KCb0wmseQliIb3SZZanCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:10:36.012371Z","bundle_sha256":"a45ee53f65c7225366fc99ca0f4f8be18472e7ea9c9f03ca472850e31d2c87a2"}}