{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4Y3CQHLKMPDO5ZJVR3C7AFR5RF","short_pith_number":"pith:4Y3CQHLK","schema_version":"1.0","canonical_sha256":"e636281d6a63c6eee5358ec5f0163d8966548d04d1ad5b76708b30b4ce84139b","source":{"kind":"arxiv","id":"1111.6312","version":1},"attestation_state":"computed","paper":{"title":"Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS","math.PR","nlin.PS"],"primary_cat":"math.NA","authors_text":"Georgios T. Kossioris, Markos A. Katsoulakis, Omar Lakkis","submitted_at":"2011-11-27T22:51:03Z","abstract_excerpt":"We address the numerical discretization of the Allen-Cahn prob- lem with additive white noise in one-dimensional space. The discretization is conducted in two stages: (1) regularize the white noise and study the regularized problem, (2) approximate the regularized problem. We address (1) by introducing a piecewise constant random approximation of the white noise with respect to a space-time mesh. We analyze the regularized problem and study its relation to both the original problem and the deterministic Allen-Cahn problem. Step (2) is then performed leading to a practical Monte-Carlo method co"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.6312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-27T22:51:03Z","cross_cats_sorted":["math.AP","math.DS","math.PR","nlin.PS"],"title_canon_sha256":"5389c60b8e24a9e407f4e724c864434cc632790b91adceaa3045b1dfdb0db90b","abstract_canon_sha256":"db1ab4d6d7d07f81832f86c23ea57a160133e6ec84dd483ec0bdc172a4ffc535"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.084590Z","signature_b64":"jnKf/D/Mzh0E4Q7gUt8E1ZPvhxqcNFkIOFZd6A5wubgVtiaqK40Ib3C5TQBKY76nqMdQgi1BbRXWqgtqGTj5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e636281d6a63c6eee5358ec5f0163d8966548d04d1ad5b76708b30b4ce84139b","last_reissued_at":"2026-05-18T03:12:58.083949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.083949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS","math.PR","nlin.PS"],"primary_cat":"math.NA","authors_text":"Georgios T. Kossioris, Markos A. Katsoulakis, Omar Lakkis","submitted_at":"2011-11-27T22:51:03Z","abstract_excerpt":"We address the numerical discretization of the Allen-Cahn prob- lem with additive white noise in one-dimensional space. The discretization is conducted in two stages: (1) regularize the white noise and study the regularized problem, (2) approximate the regularized problem. We address (1) by introducing a piecewise constant random approximation of the white noise with respect to a space-time mesh. We analyze the regularized problem and study its relation to both the original problem and the deterministic Allen-Cahn problem. Step (2) is then performed leading to a practical Monte-Carlo method co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6312","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.6312","created_at":"2026-05-18T03:12:58.084047+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6312v1","created_at":"2026-05-18T03:12:58.084047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6312","created_at":"2026-05-18T03:12:58.084047+00:00"},{"alias_kind":"pith_short_12","alias_value":"4Y3CQHLKMPDO","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4Y3CQHLKMPDO5ZJV","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4Y3CQHLK","created_at":"2026-05-18T12:26:20.644004+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF","json":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF.json","graph_json":"https://pith.science/api/pith-number/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/graph.json","events_json":"https://pith.science/api/pith-number/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/events.json","paper":"https://pith.science/paper/4Y3CQHLK"},"agent_actions":{"view_html":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF","download_json":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF.json","view_paper":"https://pith.science/paper/4Y3CQHLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6312&json=true","fetch_graph":"https://pith.science/api/pith-number/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/graph.json","fetch_events":"https://pith.science/api/pith-number/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/action/storage_attestation","attest_author":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/action/author_attestation","sign_citation":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/action/citation_signature","submit_replication":"https://pith.science/pith/4Y3CQHLKMPDO5ZJVR3C7AFR5RF/action/replication_record"}},"created_at":"2026-05-18T03:12:58.084047+00:00","updated_at":"2026-05-18T03:12:58.084047+00:00"}