{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MKZFZSIGKRJCFFVVIK4BOCIJEN","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":"d8c4d3ef6d5d4ec11684c95774b9be32f4cc31616b0c1941f23d7251d07c58d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-17T21:05:21Z","title_canon_sha256":"10368b986d17f4639c513b8b9db3ee73fad9887a6207b2df8a5585a9e33df737"},"schema_version":"1.0","source":{"id":"1212.4163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4163","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4163v1","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4163","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"MKZFZSIGKRJC","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MKZFZSIGKRJCFFVV","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MKZFZSIG","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:94cd8bd516ae2979f954a3c0c6f9575fe36f12e8b9d87477a086bee1288c9220","target":"graph","created_at":"2026-05-18T03:38:13Z","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 establish the stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales in the sense of Hyers and Ulam. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there exists an exact solution to that dynamic equation that is close to the approximate one.","authors_text":"Douglas R. Anderson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-17T21:05:21Z","title":"Hyers-Ulam stability of higher-order Cauchy-Euler dynamic equations on time scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4163","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:e1a813854a062a1d048b6960b03ef611db4c6ca45f3ffcd9e38a7bb755690c23","target":"record","created_at":"2026-05-18T03:38:13Z","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":"d8c4d3ef6d5d4ec11684c95774b9be32f4cc31616b0c1941f23d7251d07c58d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-17T21:05:21Z","title_canon_sha256":"10368b986d17f4639c513b8b9db3ee73fad9887a6207b2df8a5585a9e33df737"},"schema_version":"1.0","source":{"id":"1212.4163","kind":"arxiv","version":1}},"canonical_sha256":"62b25cc90654522296b542b8170909234415c20466144bee20dbec0dc26c0727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62b25cc90654522296b542b8170909234415c20466144bee20dbec0dc26c0727","first_computed_at":"2026-05-18T03:38:13.638930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:13.638930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PkILRDJZxLGkI+ddphFMbNiD4e66gZlL6jUPpvcS1o8RCPgiQBoqA8yIOrboOP8cpHv8hb9LR6Tcud8kP9bCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:13.639339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1a813854a062a1d048b6960b03ef611db4c6ca45f3ffcd9e38a7bb755690c23","sha256:94cd8bd516ae2979f954a3c0c6f9575fe36f12e8b9d87477a086bee1288c9220"],"state_sha256":"52523a3313e03f5c3fad5bbb7f846eb25f3b100b971b7182e137db03a6b2469b"}