{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LS65FJFXRGCSV7UKMZYCB4H4AL","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":"a2a4857b15082274a6535c742b642a928ecbdf0922134d73bf9a4c0e94646b19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-28T11:50:37Z","title_canon_sha256":"98dd3e57db5ca63087622d03ce12039209fc744ecba911b171dd0e0916b5a766"},"schema_version":"1.0","source":{"id":"1801.09214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09214","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09214v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09214","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"LS65FJFXRGCS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LS65FJFXRGCSV7UK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LS65FJFX","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:f7db15f23aaa81b4dac33c2a14a9a4f00d2ec67f05585e39f4b5abde6dc54602","target":"graph","created_at":"2026-05-18T00:24:58Z","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":"For autonomous delay differential equations $x'(t)=f(x_t)$ we construct a continuous semiflow of continuously differentiable solution operators $x_0\\mapsto x_t$, $t\\ge0$, on open subsets of the Fr\\'echet space $C((-\\infty,0],\\mathbb{R}^n)$. For nonautonomous equations this yields a continuous process of differentiable solution operators. As an application we obtain processes which incorporate all solutions of Volterra integro-differential equations $x'(t)=\\int_0^tk(t,s)h(x(s))ds$","authors_text":"Hans-Otto Walther","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-28T11:50:37Z","title":"Delay differential equations with differentiable solution operators on open domains in $C((-\\infty,0],\\mathbb{R}^n)$, and processes for Volterra integro-differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09214","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":"sha256:3ef454b13761d61fbf57546481c3614347afcafe9c2fe8432822cd83234ec6e0","target":"record","created_at":"2026-05-18T00:24:58Z","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":"a2a4857b15082274a6535c742b642a928ecbdf0922134d73bf9a4c0e94646b19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-28T11:50:37Z","title_canon_sha256":"98dd3e57db5ca63087622d03ce12039209fc744ecba911b171dd0e0916b5a766"},"schema_version":"1.0","source":{"id":"1801.09214","kind":"arxiv","version":1}},"canonical_sha256":"5cbdd2a4b789852afe8a667020f0fc02cc89d5df63992b1e2d1651705d8ac5a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cbdd2a4b789852afe8a667020f0fc02cc89d5df63992b1e2d1651705d8ac5a7","first_computed_at":"2026-05-18T00:24:58.214684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:58.214684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YyyrgeHBl43nBgAiNBZ84VQDUAY4iDLi+56kPHKHl/8eXboj/+j4xII9xrc3VUZg/Ai0F6Aay8eY8NE0BDJVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:58.215415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ef454b13761d61fbf57546481c3614347afcafe9c2fe8432822cd83234ec6e0","sha256:f7db15f23aaa81b4dac33c2a14a9a4f00d2ec67f05585e39f4b5abde6dc54602"],"state_sha256":"5863216c06d5265039571563e7280380daf8791884940a3c8561d0d46797a423"}