{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XPO4PANFIUNPQKZYVIMS5QPX6O","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":"0d42566ad45b4b95a47e4e591c53c57b9c5cd49ed7235578f9f418a8df9c22be","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-12T08:01:02Z","title_canon_sha256":"365855481f848bae569e3777e9548f50c9722df1bb637443e196b1c4d200ea85"},"schema_version":"1.0","source":{"id":"1604.03279","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03279","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03279v3","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03279","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"XPO4PANFIUNP","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XPO4PANFIUNPQKZY","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XPO4PANF","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:46f7b4b279a68ff03ef95180b449b72a946c85391500c3e98a448e33557e0394","target":"graph","created_at":"2026-05-18T00:43:43Z","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":"Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\\rightarrow B$ and any fixed complex number $\\lambda$, we study Hyers-Ulam stability of the global differential equation $Vy=\\lambda y+f$.","authors_text":"Maysam Maysami Sadr","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-12T08:01:02Z","title":"On the stability of first order PDEs associated to vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03279","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":"sha256:4b63f7e7ad389fbbe2d0ef4ac0fa9b9a784295de7202b3d9ae59aba6636a2197","target":"record","created_at":"2026-05-18T00:43:43Z","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":"0d42566ad45b4b95a47e4e591c53c57b9c5cd49ed7235578f9f418a8df9c22be","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-12T08:01:02Z","title_canon_sha256":"365855481f848bae569e3777e9548f50c9722df1bb637443e196b1c4d200ea85"},"schema_version":"1.0","source":{"id":"1604.03279","kind":"arxiv","version":3}},"canonical_sha256":"bbddc781a5451af82b38aa192ec1f7f3afa7bdb0acb0ac85232981a1b01fa49c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbddc781a5451af82b38aa192ec1f7f3afa7bdb0acb0ac85232981a1b01fa49c","first_computed_at":"2026-05-18T00:43:43.635636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:43.635636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OkKvcKPXBrIJu4tCUo56I0xuYTqq2Tugibi4pGITG8xB65KYTL8jGKyDcDshx+Pg+0BkNrkqZOGwbUFSyxCLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:43.636130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03279","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b63f7e7ad389fbbe2d0ef4ac0fa9b9a784295de7202b3d9ae59aba6636a2197","sha256:46f7b4b279a68ff03ef95180b449b72a946c85391500c3e98a448e33557e0394"],"state_sha256":"844932471ca769b24252cafee83d910463b022284b7005b4c1e2f22cc56b89f6"}