{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KJOT6RTWO7WNM65NRMTKE6LED3","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":"b6d7ba3a6e3109c599449037202dd73ffed88967d3d04ef242f49fd0291f38b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-16T03:46:09Z","title_canon_sha256":"1235f368668652d593a8e1b597460686892099f820850b588c08c1b753c8d202"},"schema_version":"1.0","source":{"id":"1404.4131","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4131","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4131v2","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4131","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"KJOT6RTWO7WN","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KJOT6RTWO7WNM65N","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KJOT6RTW","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:cf60d5905943042cce0ad5503187f315b8313d2ad483f2078ce6b417c82bd0c0","target":"graph","created_at":"2026-05-18T01:20:03Z","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":"We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a parabolic character. Under appropriate Lipschitz-type and linear growth assumptions on the nonlinear terms we show that the unique mild solution is mean-$p$ H\\\"older continuous with values in an appropriate Sobolev space depending on the kernel and the data. In particular, we obtain pathwise space-time (Sobolev-H\\\"older) regularity of the solution together with a maximal type","authors_text":"Boris Baeumer, Matthias Geissert, Mihaly Kovacs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-16T03:46:09Z","title":"Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4131","kind":"arxiv","version":2},"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:ecf6ff881ce9259b2e1860c20c14c956efab95eafe61bcf38cd7ace088d77b00","target":"record","created_at":"2026-05-18T01:20:03Z","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":"b6d7ba3a6e3109c599449037202dd73ffed88967d3d04ef242f49fd0291f38b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-16T03:46:09Z","title_canon_sha256":"1235f368668652d593a8e1b597460686892099f820850b588c08c1b753c8d202"},"schema_version":"1.0","source":{"id":"1404.4131","kind":"arxiv","version":2}},"canonical_sha256":"525d3f467677ecd67bad8b26a279641ec34cfd48c0ce2bf2387b737b45fe0a44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"525d3f467677ecd67bad8b26a279641ec34cfd48c0ce2bf2387b737b45fe0a44","first_computed_at":"2026-05-18T01:20:03.885868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:03.885868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9YUkF0bl6b8wRP2uRSMuRfqoZn+fs42joMXfqGgtHjFW3rYrItm4qmVLV9aKWsORWzeXlR/01wa+nlp7zSj4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:03.886719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4131","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecf6ff881ce9259b2e1860c20c14c956efab95eafe61bcf38cd7ace088d77b00","sha256:cf60d5905943042cce0ad5503187f315b8313d2ad483f2078ce6b417c82bd0c0"],"state_sha256":"53b3612db372d39748efd845a3eb175970b4174bc05fac26ce909bf14ea737d8"}