{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:F4UHTABTQ7PWPKYQXOYTY76T4N","short_pith_number":"pith:F4UHTABT","canonical_record":{"source":{"id":"1803.03124","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-06T14:10:22Z","cross_cats_sorted":[],"title_canon_sha256":"ecefc9236711b0d3c8004aaf43f90670efec9aeac1252e47388c701a0357ba6a","abstract_canon_sha256":"6a1b7e187d27e0ff898e1d1e7309db078977284d9a22b20ab69dddf4283bbb5e"},"schema_version":"1.0"},"canonical_sha256":"2f2879803387df67ab10bbb13c7fd3e342e11a558b78730461a78ffacd1a0d89","source":{"kind":"arxiv","id":"1803.03124","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03124","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03124v3","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03124","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"F4UHTABTQ7PW","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F4UHTABTQ7PWPKYQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F4UHTABT","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:F4UHTABTQ7PWPKYQXOYTY76T4N","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03124","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-06T14:10:22Z","cross_cats_sorted":[],"title_canon_sha256":"ecefc9236711b0d3c8004aaf43f90670efec9aeac1252e47388c701a0357ba6a","abstract_canon_sha256":"6a1b7e187d27e0ff898e1d1e7309db078977284d9a22b20ab69dddf4283bbb5e"},"schema_version":"1.0"},"canonical_sha256":"2f2879803387df67ab10bbb13c7fd3e342e11a558b78730461a78ffacd1a0d89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:03.719989Z","signature_b64":"BB2jHPvgJCZwl4IzhmcszdTGBxvbkjn9ig9x6BZo2X+X1fNeBdzzauNK8fqHA8Yvd4pbjHvWWFOZ5RtpvcK3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f2879803387df67ab10bbb13c7fd3e342e11a558b78730461a78ffacd1a0d89","last_reissued_at":"2026-05-18T00:18:03.719515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:03.719515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03124","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCEpMir9JEsu9YEFLQb6ytv3PuSkJV6w0LDPiblI5QUfYMm7VmgReQmnDYi1yXqoMJSwIXaiEgtk6jbuX5laAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:32:44.761246Z"},"content_sha256":"a6d201d89bc7183b043f5e160757b55b8264eb6c52dee4fc9f8840c34c98378b","schema_version":"1.0","event_id":"sha256:a6d201d89bc7183b043f5e160757b55b8264eb6c52dee4fc9f8840c34c98378b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:F4UHTABTQ7PWPKYQXOYTY76T4N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the transformation of the linear differential equation into a system of the first order equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"M. I. Ayzatsky","submitted_at":"2018-03-06T14:10:22Z","abstract_excerpt":"A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of first order equations that can be useful for analysis of the solutions of the N-th order differential equations. In particular, for the third-order linear equation the nonlinear second-order equation that plays the same role as the Riccati equation for second-order linear equation is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03124","kind":"arxiv","version":3},"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":"2026-05-18T00:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KGXHy8RKpMSOjBCvpYaNCTqwUk8HmVcZRahiaud3PYkaq4hNXfKnlfwrYlSawUsSHW/V2zJc50D9YXlF3snSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:32:44.761825Z"},"content_sha256":"d0b036c303e2e032f541b8b6c794590957b099349a74046bd96b577913c05c10","schema_version":"1.0","event_id":"sha256:d0b036c303e2e032f541b8b6c794590957b099349a74046bd96b577913c05c10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F4UHTABTQ7PWPKYQXOYTY76T4N/bundle.json","state_url":"https://pith.science/pith/F4UHTABTQ7PWPKYQXOYTY76T4N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F4UHTABTQ7PWPKYQXOYTY76T4N/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":"2026-08-13T18:32:44Z","links":{"resolver":"https://pith.science/pith/F4UHTABTQ7PWPKYQXOYTY76T4N","bundle":"https://pith.science/pith/F4UHTABTQ7PWPKYQXOYTY76T4N/bundle.json","state":"https://pith.science/pith/F4UHTABTQ7PWPKYQXOYTY76T4N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F4UHTABTQ7PWPKYQXOYTY76T4N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F4UHTABTQ7PWPKYQXOYTY76T4N","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":"6a1b7e187d27e0ff898e1d1e7309db078977284d9a22b20ab69dddf4283bbb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-06T14:10:22Z","title_canon_sha256":"ecefc9236711b0d3c8004aaf43f90670efec9aeac1252e47388c701a0357ba6a"},"schema_version":"1.0","source":{"id":"1803.03124","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03124","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03124v3","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03124","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"F4UHTABTQ7PW","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F4UHTABTQ7PWPKYQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F4UHTABT","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:d0b036c303e2e032f541b8b6c794590957b099349a74046bd96b577913c05c10","target":"graph","created_at":"2026-05-18T00:18:03Z","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":"A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of first order equations that can be useful for analysis of the solutions of the N-th order differential equations. In particular, for the third-order linear equation the nonlinear second-order equation that plays the same role as the Riccati equation for second-order linear equation is obtained.","authors_text":"M. I. Ayzatsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-06T14:10:22Z","title":"A note on the transformation of the linear differential equation into a system of the first order equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03124","kind":"arxiv","version":3},"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:a6d201d89bc7183b043f5e160757b55b8264eb6c52dee4fc9f8840c34c98378b","target":"record","created_at":"2026-05-18T00:18:03Z","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":"6a1b7e187d27e0ff898e1d1e7309db078977284d9a22b20ab69dddf4283bbb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-06T14:10:22Z","title_canon_sha256":"ecefc9236711b0d3c8004aaf43f90670efec9aeac1252e47388c701a0357ba6a"},"schema_version":"1.0","source":{"id":"1803.03124","kind":"arxiv","version":3}},"canonical_sha256":"2f2879803387df67ab10bbb13c7fd3e342e11a558b78730461a78ffacd1a0d89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f2879803387df67ab10bbb13c7fd3e342e11a558b78730461a78ffacd1a0d89","first_computed_at":"2026-05-18T00:18:03.719515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:03.719515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BB2jHPvgJCZwl4IzhmcszdTGBxvbkjn9ig9x6BZo2X+X1fNeBdzzauNK8fqHA8Yvd4pbjHvWWFOZ5RtpvcK3BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:03.719989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03124","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6d201d89bc7183b043f5e160757b55b8264eb6c52dee4fc9f8840c34c98378b","sha256:d0b036c303e2e032f541b8b6c794590957b099349a74046bd96b577913c05c10"],"state_sha256":"104f9fd773e5df6eecf884ee3ae51485c3148461a6af876430f7192722699857"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAY5eplSUiJl5mFagw5zlHUlbTLIkteYAUAR/v/u1UHtty6I09Hd5cZxR58upXD1Zv4UBed+ykzClDve91/NAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T18:32:44.773803Z","bundle_sha256":"d9ecf11794f5e7aef95f2aa5e070ececd8a050e932c85ec17ab839114b7ec01b"}}