{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MCPYT3S66H3S4NZQTIDBPKNSSB","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":"6b596d411bd3592bd7fe258302b3f19e6f5108d8baeb2654b5a344f085efccd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-26T10:30:53Z","title_canon_sha256":"7aa42e5215b8eacf799d8c66dbbd47abce8eb2995ca5a829b5c0c8c12209fcf2"},"schema_version":"1.0","source":{"id":"1505.06890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06890","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06890v1","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06890","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"MCPYT3S66H3S","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MCPYT3S66H3S4NZQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MCPYT3S6","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:9e7ffbc0f1fc93d04cdef18876387161d1f95db6243d3250f92490b3a8369623","target":"graph","created_at":"2026-05-18T02:03:27Z","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":"Existence, uniqueness and non-explosion of the mild solution are proved for a class of semi-linear functional SPDEs with multiplicative noise and Dini continuous drifts. In the finite-dimensional and bounded time delay setting, the log-Harnack inequality and $L^2$-gradient estimate are derived. As the Markov semigroup is associated to the functional (segment) solution of the equation, one needs to make analysis on the path space of the solution in the time interval of delay.","authors_text":"F.-Y. Wang, X. Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-26T10:30:53Z","title":"Functional SPDE with Multiplicative Noise and Dini Drift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06890","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":"sha256:9a1f794c5a5ac06b6112978bb1e68d900a55554296297a41e10a5b45217eb4ac","target":"record","created_at":"2026-05-18T02:03:27Z","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":"6b596d411bd3592bd7fe258302b3f19e6f5108d8baeb2654b5a344f085efccd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-26T10:30:53Z","title_canon_sha256":"7aa42e5215b8eacf799d8c66dbbd47abce8eb2995ca5a829b5c0c8c12209fcf2"},"schema_version":"1.0","source":{"id":"1505.06890","kind":"arxiv","version":1}},"canonical_sha256":"609f89ee5ef1f72e37309a0617a9b290647ba66b787eed243ff3e2f39aa72f56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"609f89ee5ef1f72e37309a0617a9b290647ba66b787eed243ff3e2f39aa72f56","first_computed_at":"2026-05-18T02:03:27.647374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:27.647374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qUUWjHYvk6eGuHvuzgZpU+Mpn69o7HMoX6FEVxNdijYwOgPd+Jd6XLwf616bKbjg1pA6h0sOkAuCcgt1qaKyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:27.647928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a1f794c5a5ac06b6112978bb1e68d900a55554296297a41e10a5b45217eb4ac","sha256:9e7ffbc0f1fc93d04cdef18876387161d1f95db6243d3250f92490b3a8369623"],"state_sha256":"3dedad602e2a05a3298327f45e43bc37584063c90d49cfef16b0af971465a2f6"}