{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KEJTACUJBHPFDZ2PPKGSPYAFN5","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":"e7e699a9cd121a51fd39b77676d1e95f80be503156d059acfd86f14da225d634","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-25T16:44:07Z","title_canon_sha256":"15225251bd9f6f7e68e6660a7c395a19d8e9f3bb2e2003687b0136792027cb94"},"schema_version":"1.0","source":{"id":"2606.27259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27259","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27259v1","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27259","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"pith_short_12","alias_value":"KEJTACUJBHPF","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"pith_short_16","alias_value":"KEJTACUJBHPFDZ2P","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"pith_short_8","alias_value":"KEJTACUJ","created_at":"2026-06-26T01:16:16Z"}],"graph_snapshots":[{"event_id":"sha256:2d32409ae80d42d2b25d13393a91991a0eadc1b48d35cf1415cda56012a02411","target":"graph","created_at":"2026-06-26T01:16:16Z","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/2606.27259/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A sticky diffusion is a process that can stick to and detach from a lower-dimensional boundary. A challenge in simulating such a process is in capturing the change in dimension in a dynamically consistent way. We introduce a numerical algorithm to simulate a one-dimensional sticky diffusion, which sticks to and detaches from a point. Our method is a simple modification of the standard Euler-Maruyama scheme, which chooses with some probability between a reflected Euler-Maruyama update and a jump to the sticky point. We show how to choose this probability to be consistent with the generator of t","authors_text":"Chenqi Jiang, Miranda Holmes-Cerfon","cross_cats":["cs.NA","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-25T16:44:07Z","title":"A modified Euler-Maruyama method to simulate a one-dimensional sticky diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27259","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":"sha256:5b789c1b0f0330b3cec81475a058e67e33f9a0127c8c87ed48401c52bfb3ab06","target":"record","created_at":"2026-06-26T01:16:16Z","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":"e7e699a9cd121a51fd39b77676d1e95f80be503156d059acfd86f14da225d634","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-25T16:44:07Z","title_canon_sha256":"15225251bd9f6f7e68e6660a7c395a19d8e9f3bb2e2003687b0136792027cb94"},"schema_version":"1.0","source":{"id":"2606.27259","kind":"arxiv","version":1}},"canonical_sha256":"5113300a8909de51e74f7a8d27e0056f497ef07ba1e74cae1067c24d4e9962e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5113300a8909de51e74f7a8d27e0056f497ef07ba1e74cae1067c24d4e9962e9","first_computed_at":"2026-06-26T01:16:16.634807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:16.634807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fYxj0smykmjC0xniwKjvrwtK0UGPY87i8TGGmh8DPwi1Gb20L8VqwmzT4xZp/47OLpftDBa5ccNqGyosuhXlDg==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:16.635189Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b789c1b0f0330b3cec81475a058e67e33f9a0127c8c87ed48401c52bfb3ab06","sha256:2d32409ae80d42d2b25d13393a91991a0eadc1b48d35cf1415cda56012a02411"],"state_sha256":"ab319e9d21a0deee799d5fbc5e5f683808a414cdf0d39d02f5968393e20dd706"}