{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X25SNFWI4K4Q45CKJGVOKUYCKY","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":"c9cb5e33222aa619d894b5580c304933ae8f06b1d33fe86d1028052fc1003588","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T11:45:35Z","title_canon_sha256":"3cc062eebf34a4802a68a09e083ad4b201a6af947abe96e80d11e9921ddbc697"},"schema_version":"1.0","source":{"id":"2506.04911","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04911","created_at":"2026-05-18T03:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04911v2","created_at":"2026-05-18T03:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04911","created_at":"2026-05-18T03:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"X25SNFWI4K4Q","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"X25SNFWI4K4Q45CK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"X25SNFWI","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:0f30e4dfa98e53cb8462e9a26e8591e12d4fb6ea968d329deb574103e30104be","target":"graph","created_at":"2026-05-18T03:09:35Z","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 new weak existence results for $d$-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution kernels. These results are obtained by introducing an approximation scheme and showing its convergence. A particular emphasis is made on the stochastic invariance of the solution in a closed convex set. To do so, we extend the notion of kernels that preserve nonnegativity introduced in \\cite{Alfonsi23} to non-convolution kernels and show that, under suitable stochastic invariance property of a closed convex set by th","authors_text":"Aur\\'elien Alfonsi, Eduardo Abi Jaber, Guillaume Szulda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T11:45:35Z","title":"Weak solutions of Stochastic Volterra Equations in convex domains with general kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04911","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:d31a22ebdbdbd80d6489abbb0ab4a97f58f28fc2f97de1fd443a05f25b0e106b","target":"record","created_at":"2026-05-18T03:09:35Z","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":"c9cb5e33222aa619d894b5580c304933ae8f06b1d33fe86d1028052fc1003588","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T11:45:35Z","title_canon_sha256":"3cc062eebf34a4802a68a09e083ad4b201a6af947abe96e80d11e9921ddbc697"},"schema_version":"1.0","source":{"id":"2506.04911","kind":"arxiv","version":2}},"canonical_sha256":"bebb2696c8e2b90e744a49aae553025628df9421b716d410b7dfa5d27894c0a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bebb2696c8e2b90e744a49aae553025628df9421b716d410b7dfa5d27894c0a6","first_computed_at":"2026-05-18T03:09:35.491025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:35.491025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kz0N13N8NTzjLZAFgOFe7fztW6NDVJdqUfLuGh7jI9hVWSs8Sz59vk/RDUX25ZaKSGlOz3UdQswPhRd2/M3pCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:35.491668Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04911","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d31a22ebdbdbd80d6489abbb0ab4a97f58f28fc2f97de1fd443a05f25b0e106b","sha256:0f30e4dfa98e53cb8462e9a26e8591e12d4fb6ea968d329deb574103e30104be"],"state_sha256":"e174730157dec7bd2ba1363709db45e105fa59e0f4f2f4cd52d804c85d453a13"}