{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DMB3SVYNFX5DOYTBBUQBSQCGIR","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":"e25d8530eb520aec0ac62d02a556e2213583bf09a423bc21d122c66121ea6555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T11:19:15Z","title_canon_sha256":"bfd1dffec601509c07f3b285cf3cbdddeba9a7f980ec6d20bcaef09a8c4b04c6"},"schema_version":"1.0","source":{"id":"1701.06155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06155","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06155v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06155","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"DMB3SVYNFX5D","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DMB3SVYNFX5DOYTB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DMB3SVYN","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:ad8a1f678fcaf58f5bbee051d9b0ca5670dbfebed37a209d255919ab42e34250","target":"graph","created_at":"2026-05-18T00:52:19Z","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 systems with memory represented by stochastic functional differential equations. Substantially, these are stochastic differential equations with coefficients depending on the past history of the process itself. Such coefficients are hence defined on a functional space. Models with memory appear in many applications ranging from biology to finance. Here we consider the results of some evaluations based on these models (e.g. the prices of some financial products) and the risks connected to the choice of these models. In particular we focus on the impact of the initial condition on th","authors_text":"David R. Ba\\~nos, Frank Proske, Giulia Di Nunno, Hannes Haferkorn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T11:19:15Z","title":"Stochastic functional differential equations and sensitivity to their initial path"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06155","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":"sha256:1dd4f71e9f649abe146025965fcec985a23e2900bc466866dc7a2a73bcd9ef63","target":"record","created_at":"2026-05-18T00:52:19Z","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":"e25d8530eb520aec0ac62d02a556e2213583bf09a423bc21d122c66121ea6555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T11:19:15Z","title_canon_sha256":"bfd1dffec601509c07f3b285cf3cbdddeba9a7f980ec6d20bcaef09a8c4b04c6"},"schema_version":"1.0","source":{"id":"1701.06155","kind":"arxiv","version":1}},"canonical_sha256":"1b03b9570d2dfa3762610d20194046447495cba65ff9a45fa0abaefd45f5b248","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b03b9570d2dfa3762610d20194046447495cba65ff9a45fa0abaefd45f5b248","first_computed_at":"2026-05-18T00:52:19.129152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:19.129152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Nf3JYwK1jubWNwmRDP3ur/VCLW/WFoGdfy9axFe4YWF7LC9YawLX2bf10bk3xXZY3jJsPNpCl/mnzgKzaW6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:19.129625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dd4f71e9f649abe146025965fcec985a23e2900bc466866dc7a2a73bcd9ef63","sha256:ad8a1f678fcaf58f5bbee051d9b0ca5670dbfebed37a209d255919ab42e34250"],"state_sha256":"c254070c9b16c115dd30d59c75cb81463f1f4ebc1f66ff947ee026aaf4932e11"}