{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BGGYAEFGIWZCBLVEUOPYE3E4JM","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":"1e6462e50286be643df0a8ed8ab1313e2daa87f6962a166cefca95485d448978","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-05T08:32:21Z","title_canon_sha256":"d40a893c7ed83f39c9d7a8b96ddecbbbf0cb23e711c83dd66cb7c69cad7b7185"},"schema_version":"1.0","source":{"id":"1305.0991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0991","created_at":"2026-05-18T03:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0991v2","created_at":"2026-05-18T03:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0991","created_at":"2026-05-18T03:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"BGGYAEFGIWZC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BGGYAEFGIWZCBLVE","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BGGYAEFG","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:e1f16f1791cba3870adf22a6f2d297701bc7fa07c4089d83a8a822db247fdd97","target":"graph","created_at":"2026-05-18T03:01:35Z","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":"Sufficient and necessary conditions are presented for the order-preservation of stochastic functional differential equations on $\\R^d$ with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency of the conditions extends and improves some known comparison theorems derived recently for one-dimesional equations and multidimensional equations without delay, and the necessity is new even in these special situations.","authors_text":"Feng-Yu Wang, Xing Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-05T08:32:21Z","title":"Order-Preservation for Multidimensional Stochastic Functional Differential Equations with Jump"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0991","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":"sha256:4f1f3b87b3e23429cc7f54790598365751fc260fe1a02f419e62df875f82bfb4","target":"record","created_at":"2026-05-18T03:01:35Z","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":"1e6462e50286be643df0a8ed8ab1313e2daa87f6962a166cefca95485d448978","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-05T08:32:21Z","title_canon_sha256":"d40a893c7ed83f39c9d7a8b96ddecbbbf0cb23e711c83dd66cb7c69cad7b7185"},"schema_version":"1.0","source":{"id":"1305.0991","kind":"arxiv","version":2}},"canonical_sha256":"098d8010a645b220aea4a39f826c9c4b041c565995558fed4eed1545a3a78d7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"098d8010a645b220aea4a39f826c9c4b041c565995558fed4eed1545a3a78d7b","first_computed_at":"2026-05-18T03:01:35.853914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:35.853914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kjsBexQadJPHJpF7kVry6/7uqaL8//C9daPjo9YjyRtZsFoxEbQDAs630dkecZMtq28bAWZYIdqPSEbVp6iCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:35.854537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f1f3b87b3e23429cc7f54790598365751fc260fe1a02f419e62df875f82bfb4","sha256:e1f16f1791cba3870adf22a6f2d297701bc7fa07c4089d83a8a822db247fdd97"],"state_sha256":"332d0e2df071d750dc0cabe61d5a96e6f3fabedd34773cd8e1d3ccbcbe597234"}