{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ITBXIDDVSFB2WMULUAQCVVR7EA","short_pith_number":"pith:ITBXIDDV","canonical_record":{"source":{"id":"1803.06306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T16:48:08Z","cross_cats_sorted":[],"title_canon_sha256":"402c4dff6cff26883d8c3b29e33ac5252246fac6216be0f8689e04f88b6ccc2f","abstract_canon_sha256":"ee6b374afef47e248e6fb536cb182061eb0af49bd7056a0e88165ee3a1704e24"},"schema_version":"1.0"},"canonical_sha256":"44c3740c759143ab328ba0202ad63f2026145469f9fadf04c42ffdab00702308","source":{"kind":"arxiv","id":"1803.06306","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06306","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06306v1","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06306","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"ITBXIDDVSFB2","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ITBXIDDVSFB2WMUL","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ITBXIDDV","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ITBXIDDVSFB2WMULUAQCVVR7EA","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T16:48:08Z","cross_cats_sorted":[],"title_canon_sha256":"402c4dff6cff26883d8c3b29e33ac5252246fac6216be0f8689e04f88b6ccc2f","abstract_canon_sha256":"ee6b374afef47e248e6fb536cb182061eb0af49bd7056a0e88165ee3a1704e24"},"schema_version":"1.0"},"canonical_sha256":"44c3740c759143ab328ba0202ad63f2026145469f9fadf04c42ffdab00702308","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:49.955824Z","signature_b64":"6V2GP8BmbgO/Q4OFCc3DGAO43llF69h79oeqpcBTmYVKUqeKWqV4GMGGoQCm0NYO3uAxcGMhY+R3Q97PxF2ODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44c3740c759143ab328ba0202ad63f2026145469f9fadf04c42ffdab00702308","last_reissued_at":"2026-05-18T00:20:49.955388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:49.955388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06306","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":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GsLqvtGM/FzXjAFSCN3gRZhqyorPwH7cMo4RIu/TIVGQQW9BYZfSo/Vo4BpEoZhtLJnpEl596skJriVe3C5vBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:29:24.856465Z"},"content_sha256":"1884557591b0ccc8ccd4730254c4e6e554958cd8faec756c3d4b669946b43033","schema_version":"1.0","event_id":"sha256:1884557591b0ccc8ccd4730254c4e6e554958cd8faec756c3d4b669946b43033"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ITBXIDDVSFB2WMULUAQCVVR7EA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Block minimal bases $\\ell$-ifications of matrix polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Froil\\'an M. Dopico, Javier P\\'erez, Paul Van Dooren","submitted_at":"2018-03-16T16:48:08Z","abstract_excerpt":"The standard way of solving a polynomial eigenvalue problem associated with a matrix polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil, known as a strong linearization. This process transforms the problem into an equivalent generalized eigenvalue problem. However, there are some situations in which is more convenient to replace linearizations by other low degree matrix polynomials. This has motivated the idea of a strong $\\ell$-ification of a matrix polynomial, which is a matrix polynomial of degree $\\ell$ having the same finite and infinite elementa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06306","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":""},"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":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"khi79IHXHeHxlzMRUtdCTszvz8CSfIMQOzcKaeNFEfi8DuszCUVAMGFagwJrrPnXtbwRHmq4FLDi5jA0mgfOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:29:24.856889Z"},"content_sha256":"095016e9bab96df7412b4f9a1150baa9304ef381acb4c470ded0ad6cf2c64a1d","schema_version":"1.0","event_id":"sha256:095016e9bab96df7412b4f9a1150baa9304ef381acb4c470ded0ad6cf2c64a1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITBXIDDVSFB2WMULUAQCVVR7EA/bundle.json","state_url":"https://pith.science/pith/ITBXIDDVSFB2WMULUAQCVVR7EA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITBXIDDVSFB2WMULUAQCVVR7EA/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":"2026-05-31T13:29:24Z","links":{"resolver":"https://pith.science/pith/ITBXIDDVSFB2WMULUAQCVVR7EA","bundle":"https://pith.science/pith/ITBXIDDVSFB2WMULUAQCVVR7EA/bundle.json","state":"https://pith.science/pith/ITBXIDDVSFB2WMULUAQCVVR7EA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITBXIDDVSFB2WMULUAQCVVR7EA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ITBXIDDVSFB2WMULUAQCVVR7EA","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":"ee6b374afef47e248e6fb536cb182061eb0af49bd7056a0e88165ee3a1704e24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T16:48:08Z","title_canon_sha256":"402c4dff6cff26883d8c3b29e33ac5252246fac6216be0f8689e04f88b6ccc2f"},"schema_version":"1.0","source":{"id":"1803.06306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06306","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06306v1","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06306","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"ITBXIDDVSFB2","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ITBXIDDVSFB2WMUL","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ITBXIDDV","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:095016e9bab96df7412b4f9a1150baa9304ef381acb4c470ded0ad6cf2c64a1d","target":"graph","created_at":"2026-05-18T00:20:49Z","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"},"paper":{"abstract_excerpt":"The standard way of solving a polynomial eigenvalue problem associated with a matrix polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil, known as a strong linearization. This process transforms the problem into an equivalent generalized eigenvalue problem. However, there are some situations in which is more convenient to replace linearizations by other low degree matrix polynomials. This has motivated the idea of a strong $\\ell$-ification of a matrix polynomial, which is a matrix polynomial of degree $\\ell$ having the same finite and infinite elementa","authors_text":"Froil\\'an M. Dopico, Javier P\\'erez, Paul Van Dooren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T16:48:08Z","title":"Block minimal bases $\\ell$-ifications of matrix polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06306","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":"sha256:1884557591b0ccc8ccd4730254c4e6e554958cd8faec756c3d4b669946b43033","target":"record","created_at":"2026-05-18T00:20:49Z","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":"ee6b374afef47e248e6fb536cb182061eb0af49bd7056a0e88165ee3a1704e24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T16:48:08Z","title_canon_sha256":"402c4dff6cff26883d8c3b29e33ac5252246fac6216be0f8689e04f88b6ccc2f"},"schema_version":"1.0","source":{"id":"1803.06306","kind":"arxiv","version":1}},"canonical_sha256":"44c3740c759143ab328ba0202ad63f2026145469f9fadf04c42ffdab00702308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44c3740c759143ab328ba0202ad63f2026145469f9fadf04c42ffdab00702308","first_computed_at":"2026-05-18T00:20:49.955388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:49.955388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6V2GP8BmbgO/Q4OFCc3DGAO43llF69h79oeqpcBTmYVKUqeKWqV4GMGGoQCm0NYO3uAxcGMhY+R3Q97PxF2ODg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:49.955824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1884557591b0ccc8ccd4730254c4e6e554958cd8faec756c3d4b669946b43033","sha256:095016e9bab96df7412b4f9a1150baa9304ef381acb4c470ded0ad6cf2c64a1d"],"state_sha256":"74700da10b4fcc8c6abd0060657e67e143cbea636cf439096a83d71b86ffc803"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LyoStozDD51/NjfFidoxdW4WXxXcwDRes+/sjdV6jdXC2Ia/JNOiCMLUxgInbNpyeSw97bpmx19Fxvp22+ciBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:29:24.860707Z","bundle_sha256":"eee150cb0c1089bc871a401214ce0f5c6fe2c9608637693881e4d1ea7275668b"}}