{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XOW7YTZFMZP3W7RIULBAUWVGWB","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":"1d39d63992d50304b0fedb4df9ffd963b975e8ac6b009352705e6aa51348dec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-14T16:03:07Z","title_canon_sha256":"a85b587b4630f38d6fd012ec52677877f6ec49a90cb4071efbfe4490ad934470"},"schema_version":"1.0","source":{"id":"1305.3193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3193","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3193v1","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3193","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"pith_short_12","alias_value":"XOW7YTZFMZP3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XOW7YTZFMZP3W7RI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XOW7YTZF","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:5cba070602bda20ee1481957e6425cc473a250b195a5ee7a9aa8a94da9c26eac","target":"graph","created_at":"2026-05-18T03:25:44Z","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":"We consider the canonical fundamental systems of solutions of linear homogeneous Caputo fractional differential equations with continuous variable coefficients. Here we gained a series-representation of the canonical fundamental system by coefficients of the considered equations and the representation of solution to initial value problems using the canonical fundamental system. According to our results, the canonical fundamental system of solutions to linear homogeneous differential equation with Caputo fractional derivatives and continuous variable coefficients has different representations a","authors_text":"Hyong-Chol O, Myong-Ha Kim, Sun-Ae Pak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-14T16:03:07Z","title":"Representation of Solutions of Linear Homogeneous Caputo Fractional Differential Equations with Continuous Variable Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3193","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":"sha256:974e3ca072e0accd7acf4f344bb1953f63b0f47374de86c36c2097447ac143ce","target":"record","created_at":"2026-05-18T03:25:44Z","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":"1d39d63992d50304b0fedb4df9ffd963b975e8ac6b009352705e6aa51348dec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-14T16:03:07Z","title_canon_sha256":"a85b587b4630f38d6fd012ec52677877f6ec49a90cb4071efbfe4490ad934470"},"schema_version":"1.0","source":{"id":"1305.3193","kind":"arxiv","version":1}},"canonical_sha256":"bbadfc4f25665fbb7e28a2c20a5aa6b0661d61d8cb552a1123deece0c23908d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbadfc4f25665fbb7e28a2c20a5aa6b0661d61d8cb552a1123deece0c23908d1","first_computed_at":"2026-05-18T03:25:44.527743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:44.527743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WpoU9tu/k16zUVMm32MbeJMXHSGTCaU5251cB4vAPg7P9XXRt9Vj3QJGNgmthT1ykIcxBQcnqrihGrIflYF2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:44.528241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:974e3ca072e0accd7acf4f344bb1953f63b0f47374de86c36c2097447ac143ce","sha256:5cba070602bda20ee1481957e6425cc473a250b195a5ee7a9aa8a94da9c26eac"],"state_sha256":"587067bdc04f70a805b2326b7f3710c0b3170bd2a587a5bcc31df932ed363169"}