{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CFPB4URMGBWBCL5VPK5KAIHYRV","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":"96f5acd04351ac8f7da618acaeedbcc00b6cf272dac0b4574fe89e338176165b","cross_cats_sorted":["cs.AI","cs.LG","cs.NA","math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-03T14:17:58Z","title_canon_sha256":"cf5a8115667f899379989d6c8f2ec2e7df72c69a6412bcd9fde8d9d3bf29dd65"},"schema_version":"1.0","source":{"id":"2209.01432","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.01432","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"2209.01432v3","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.01432","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"CFPB4URMGBWB","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_16","alias_value":"CFPB4URMGBWBCL5V","created_at":"2026-07-05T08:54:00Z"},{"alias_kind":"pith_short_8","alias_value":"CFPB4URM","created_at":"2026-07-05T08:54:00Z"}],"graph_snapshots":[{"event_id":"sha256:c6c4d8be39c8c7654ce8e5b17ffc467b41943171bba2813e4ee9fcf3320c8f73","target":"graph","created_at":"2026-07-05T08:54:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.01432/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\\mathbb{R}^d$. We aim at two fundamental goals.\n  The first, and the most important, we show that the solution to Poisson equation can be numerically approximated in the sup-norm by Monte Carlo methods, and that this can be done highly efficiently if we use a modified version of the walk on spheres algorithm as an acceleration method. This provides estimates which are efficient with respect to the prescribed approximation error and with ","authors_text":"Arghir Zarnescu, Ionel Popescu, Iulian Cimpean, Lucian Beznea, Oana Lupascu-Stamate","cross_cats":["cs.AI","cs.LG","cs.NA","math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-03T14:17:58Z","title":"From Monte Carlo to neural networks approximations of boundary value problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.01432","kind":"arxiv","version":3},"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":"sha256:4cbc68a2412aab6f861365120a23a46873533474874e9355bf31314367b30ace","target":"record","created_at":"2026-07-05T08:54:00Z","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":"96f5acd04351ac8f7da618acaeedbcc00b6cf272dac0b4574fe89e338176165b","cross_cats_sorted":["cs.AI","cs.LG","cs.NA","math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-03T14:17:58Z","title_canon_sha256":"cf5a8115667f899379989d6c8f2ec2e7df72c69a6412bcd9fde8d9d3bf29dd65"},"schema_version":"1.0","source":{"id":"2209.01432","kind":"arxiv","version":3}},"canonical_sha256":"115e1e522c306c112fb57abaa020f88d4ba1195244df8e565578df34fbdd48ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"115e1e522c306c112fb57abaa020f88d4ba1195244df8e565578df34fbdd48ed","first_computed_at":"2026-07-05T08:54:00.370465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:54:00.370465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xCjXUlcCPfOaHwSc2fAIiIqFK42DLgJnH4RdGZGTYJeOvrGcnVz8fU+4BXsty9fjqzIXK+VghUcFKBiuTtZVDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:54:00.370978Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.01432","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cbc68a2412aab6f861365120a23a46873533474874e9355bf31314367b30ace","sha256:c6c4d8be39c8c7654ce8e5b17ffc467b41943171bba2813e4ee9fcf3320c8f73"],"state_sha256":"03c19d78e65ae4ea4314e3bc88cc8fbc903057b9fde88e2c1b7f0a7c9a2e5825"}