{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QC76ZEYUHVHDEQWE26TDLD5CHJ","short_pith_number":"pith:QC76ZEYU","canonical_record":{"source":{"id":"1602.05033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-16T14:36:43Z","cross_cats_sorted":[],"title_canon_sha256":"9af1fc5429d653c1d988c63909f09c9f4cb0b092590e5813b16cab080aebdbf1","abstract_canon_sha256":"e6d6cea2ce36525047204477d68dcc4da87ad5c4f49de2f2862ec70df7176099"},"schema_version":"1.0"},"canonical_sha256":"80bfec93143d4e3242c4d7a6358fa23a5af78ed86f80d0f6b9d5a4b3d4e448b5","source":{"kind":"arxiv","id":"1602.05033","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05033","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05033v2","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05033","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"QC76ZEYUHVHD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QC76ZEYUHVHDEQWE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QC76ZEYU","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QC76ZEYUHVHDEQWE26TDLD5CHJ","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-16T14:36:43Z","cross_cats_sorted":[],"title_canon_sha256":"9af1fc5429d653c1d988c63909f09c9f4cb0b092590e5813b16cab080aebdbf1","abstract_canon_sha256":"e6d6cea2ce36525047204477d68dcc4da87ad5c4f49de2f2862ec70df7176099"},"schema_version":"1.0"},"canonical_sha256":"80bfec93143d4e3242c4d7a6358fa23a5af78ed86f80d0f6b9d5a4b3d4e448b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:34.176340Z","signature_b64":"TjgDkRl7Q+DYjhCidhi8JCodoAeZY3RjXZZ2tcpbFK1BL5NJ+UTDLN0u7PFV0rff0Kv1JaBwUSxydm3rJDucBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80bfec93143d4e3242c4d7a6358fa23a5af78ed86f80d0f6b9d5a4b3d4e448b5","last_reissued_at":"2026-05-18T00:51:34.175855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:34.175855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05033","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":"2026-05-18T00:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vX5hJdPLGTj5wrYHL1LUVQa0ze86eNXCBisX36i59KVzgXY+tVWXu81kszG+STVr1TFPJ+JeTGbUp7TeQwrcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:53:46.981157Z"},"content_sha256":"5072e235f5394c3d14f8179475fee71c54ab60584cbfd0158b168c50fd4b537e","schema_version":"1.0","event_id":"sha256:5072e235f5394c3d14f8179475fee71c54ab60584cbfd0158b168c50fd4b537e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QC76ZEYUHVHDEQWE26TDLD5CHJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Davide Palitta, Valeria Simoncini","submitted_at":"2016-02-16T14:36:43Z","abstract_excerpt":"In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the overall computational effort. When data are symmetric, we show that the Frobenius norm of the residual matrix can be computed at significantly lower cost than with available methods, without explicitly solving the reduced problem. For certain classes of problems, the new residual norm expression combined with a memory-reducing device make classical Krylov strate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05033","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":""},"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":"2026-05-18T00:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8vLnYHNQDZNjC7Cnd3bjIV0ghAUW3BnuIfhtmyLe5D6GbM/dezzeNFJJhmE7mRYpBsaJujAc0mXVdxz6F8yAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:53:46.981865Z"},"content_sha256":"82e97f64de103502483d84a78de3e4ec57ddafe3028e92c08469a68012b90d85","schema_version":"1.0","event_id":"sha256:82e97f64de103502483d84a78de3e4ec57ddafe3028e92c08469a68012b90d85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QC76ZEYUHVHDEQWE26TDLD5CHJ/bundle.json","state_url":"https://pith.science/pith/QC76ZEYUHVHDEQWE26TDLD5CHJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QC76ZEYUHVHDEQWE26TDLD5CHJ/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":"2026-06-06T06:53:46Z","links":{"resolver":"https://pith.science/pith/QC76ZEYUHVHDEQWE26TDLD5CHJ","bundle":"https://pith.science/pith/QC76ZEYUHVHDEQWE26TDLD5CHJ/bundle.json","state":"https://pith.science/pith/QC76ZEYUHVHDEQWE26TDLD5CHJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QC76ZEYUHVHDEQWE26TDLD5CHJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QC76ZEYUHVHDEQWE26TDLD5CHJ","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":"e6d6cea2ce36525047204477d68dcc4da87ad5c4f49de2f2862ec70df7176099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-16T14:36:43Z","title_canon_sha256":"9af1fc5429d653c1d988c63909f09c9f4cb0b092590e5813b16cab080aebdbf1"},"schema_version":"1.0","source":{"id":"1602.05033","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05033","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05033v2","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05033","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"QC76ZEYUHVHD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QC76ZEYUHVHDEQWE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QC76ZEYU","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:82e97f64de103502483d84a78de3e4ec57ddafe3028e92c08469a68012b90d85","target":"graph","created_at":"2026-05-18T00:51:34Z","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 the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the overall computational effort. When data are symmetric, we show that the Frobenius norm of the residual matrix can be computed at significantly lower cost than with available methods, without explicitly solving the reduced problem. For certain classes of problems, the new residual norm expression combined with a memory-reducing device make classical Krylov strate","authors_text":"Davide Palitta, Valeria Simoncini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-16T14:36:43Z","title":"Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05033","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":"sha256:5072e235f5394c3d14f8179475fee71c54ab60584cbfd0158b168c50fd4b537e","target":"record","created_at":"2026-05-18T00:51:34Z","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":"e6d6cea2ce36525047204477d68dcc4da87ad5c4f49de2f2862ec70df7176099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-16T14:36:43Z","title_canon_sha256":"9af1fc5429d653c1d988c63909f09c9f4cb0b092590e5813b16cab080aebdbf1"},"schema_version":"1.0","source":{"id":"1602.05033","kind":"arxiv","version":2}},"canonical_sha256":"80bfec93143d4e3242c4d7a6358fa23a5af78ed86f80d0f6b9d5a4b3d4e448b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80bfec93143d4e3242c4d7a6358fa23a5af78ed86f80d0f6b9d5a4b3d4e448b5","first_computed_at":"2026-05-18T00:51:34.175855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:34.175855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TjgDkRl7Q+DYjhCidhi8JCodoAeZY3RjXZZ2tcpbFK1BL5NJ+UTDLN0u7PFV0rff0Kv1JaBwUSxydm3rJDucBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:34.176340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05033","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5072e235f5394c3d14f8179475fee71c54ab60584cbfd0158b168c50fd4b537e","sha256:82e97f64de103502483d84a78de3e4ec57ddafe3028e92c08469a68012b90d85"],"state_sha256":"85527b9967b19696a376f669164bf58680ba32fa4925b26e7772379cd3facdfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N0wrELgenRbP47aWZeTx+XHROAzpGMw8sLBN39FqW7bEdv06kC2uoRSBrgtUk3I+PZ5cOV613whNgsRXyZQzDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:53:46.986043Z","bundle_sha256":"31c6a28f7dda1417b3ec6f09e186a7c9fba5ca11d2bdd504e99aed9634c57d71"}}