{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:N4KISNXXT6LMOKG76H2S5YCBKM","short_pith_number":"pith:N4KISNXX","canonical_record":{"source":{"id":"1311.3729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-15T05:24:06Z","cross_cats_sorted":[],"title_canon_sha256":"4c554a2aa7bc9b5bfcfaa26118bedf4f8681b31ff5d8809ab9cb4d2ec0c1a942","abstract_canon_sha256":"76f09a4e3cb5a31cebc89947ba4e9e19717488db86df032818a86aa689cfd059"},"schema_version":"1.0"},"canonical_sha256":"6f148936f79f96c728dff1f52ee04153214fa029a3b619a41d4eff7831a2a97f","source":{"kind":"arxiv","id":"1311.3729","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3729","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3729v1","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3729","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"pith_short_12","alias_value":"N4KISNXXT6LM","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N4KISNXXT6LMOKG7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N4KISNXX","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:N4KISNXXT6LMOKG76H2S5YCBKM","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-15T05:24:06Z","cross_cats_sorted":[],"title_canon_sha256":"4c554a2aa7bc9b5bfcfaa26118bedf4f8681b31ff5d8809ab9cb4d2ec0c1a942","abstract_canon_sha256":"76f09a4e3cb5a31cebc89947ba4e9e19717488db86df032818a86aa689cfd059"},"schema_version":"1.0"},"canonical_sha256":"6f148936f79f96c728dff1f52ee04153214fa029a3b619a41d4eff7831a2a97f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:03.171682Z","signature_b64":"XqXhfT95U9UOaDWQtl4KykMj1RdURzUeio3oDv4nyptd3u1GezXfzu0MPlTAw9ayjUOuhcDE9l6yUnjykX5YAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f148936f79f96c728dff1f52ee04153214fa029a3b619a41d4eff7831a2a97f","last_reissued_at":"2026-05-18T03:07:03.171099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:03.171099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3729","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":"2026-05-18T03:07:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3HFcr5AuxOBufzw1yZ6tpLLj0G3hSqAiI15ChCD28qII7Gbee/shCIZopmA4LzUll3KW16zNaKZ5V9yTPxUVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:30:44.760830Z"},"content_sha256":"f98dc43b4b1befa5996ef39500d420e0ec408c2fa96d54b1cbbbe0e2547b2366","schema_version":"1.0","event_id":"sha256:f98dc43b4b1befa5996ef39500d420e0ec408c2fa96d54b1cbbbe0e2547b2366"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:N4KISNXXT6LMOKG76H2S5YCBKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transformations of Matrix Structures Work Again II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Victor Y. Pan","submitted_at":"2013-11-15T05:24:06Z","abstract_excerpt":"Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computation. The four classes have distinct features, but in 1990 we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property to extend any successful algorithm that inverts matrices of one of these classes to inverting matrices of the three other classes. The power of this approach was widely recognized later, when novel numerically stable algorithms solved nonsingular Toeplitz linear systems of equations at first in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3729","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":"2026-05-18T03:07:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZoSS9H/Ldc12hYK9D4Gm79wsI/3O5aTXPcL3IM3P7u14UQZUTmtEyBkbbViJpE/2g5+bPy3TCZZhqqBgmqQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:30:44.761265Z"},"content_sha256":"78cc516dd0be4ad0722b448c7a8f7e70ab5b3b2c24210e3e60692e3ae5e983ad","schema_version":"1.0","event_id":"sha256:78cc516dd0be4ad0722b448c7a8f7e70ab5b3b2c24210e3e60692e3ae5e983ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4KISNXXT6LMOKG76H2S5YCBKM/bundle.json","state_url":"https://pith.science/pith/N4KISNXXT6LMOKG76H2S5YCBKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4KISNXXT6LMOKG76H2S5YCBKM/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":"2026-06-11T14:30:44Z","links":{"resolver":"https://pith.science/pith/N4KISNXXT6LMOKG76H2S5YCBKM","bundle":"https://pith.science/pith/N4KISNXXT6LMOKG76H2S5YCBKM/bundle.json","state":"https://pith.science/pith/N4KISNXXT6LMOKG76H2S5YCBKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4KISNXXT6LMOKG76H2S5YCBKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N4KISNXXT6LMOKG76H2S5YCBKM","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":"76f09a4e3cb5a31cebc89947ba4e9e19717488db86df032818a86aa689cfd059","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-15T05:24:06Z","title_canon_sha256":"4c554a2aa7bc9b5bfcfaa26118bedf4f8681b31ff5d8809ab9cb4d2ec0c1a942"},"schema_version":"1.0","source":{"id":"1311.3729","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3729","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3729v1","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3729","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"pith_short_12","alias_value":"N4KISNXXT6LM","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N4KISNXXT6LMOKG7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N4KISNXX","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:78cc516dd0be4ad0722b448c7a8f7e70ab5b3b2c24210e3e60692e3ae5e983ad","target":"graph","created_at":"2026-05-18T03:07:03Z","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":"Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computation. The four classes have distinct features, but in 1990 we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property to extend any successful algorithm that inverts matrices of one of these classes to inverting matrices of the three other classes. The power of this approach was widely recognized later, when novel numerically stable algorithms solved nonsingular Toeplitz linear systems of equations at first in","authors_text":"Victor Y. Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-15T05:24:06Z","title":"Transformations of Matrix Structures Work Again II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3729","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:f98dc43b4b1befa5996ef39500d420e0ec408c2fa96d54b1cbbbe0e2547b2366","target":"record","created_at":"2026-05-18T03:07:03Z","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":"76f09a4e3cb5a31cebc89947ba4e9e19717488db86df032818a86aa689cfd059","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-15T05:24:06Z","title_canon_sha256":"4c554a2aa7bc9b5bfcfaa26118bedf4f8681b31ff5d8809ab9cb4d2ec0c1a942"},"schema_version":"1.0","source":{"id":"1311.3729","kind":"arxiv","version":1}},"canonical_sha256":"6f148936f79f96c728dff1f52ee04153214fa029a3b619a41d4eff7831a2a97f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f148936f79f96c728dff1f52ee04153214fa029a3b619a41d4eff7831a2a97f","first_computed_at":"2026-05-18T03:07:03.171099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:03.171099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XqXhfT95U9UOaDWQtl4KykMj1RdURzUeio3oDv4nyptd3u1GezXfzu0MPlTAw9ayjUOuhcDE9l6yUnjykX5YAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:03.171682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f98dc43b4b1befa5996ef39500d420e0ec408c2fa96d54b1cbbbe0e2547b2366","sha256:78cc516dd0be4ad0722b448c7a8f7e70ab5b3b2c24210e3e60692e3ae5e983ad"],"state_sha256":"cdcc27850c78403f509d47ede706636213d75ed2ed582ff85f0f6a2bddc3764e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zQ1aBOivVRbXImY6T4kGXXzg0j08E2AE/T2AaStyB+7wuIjciaUKoNAACwvggbQz+ON1ixJvuXHQENngdNwDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:30:44.764475Z","bundle_sha256":"329f7ea72e7387a85ff9072aef3e8936f35b7eb7103507f29e53d8c1517014c4"}}