{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:56DHST7QQZRR33FKWXV7WAYVWS","short_pith_number":"pith:56DHST7Q","schema_version":"1.0","canonical_sha256":"ef86794ff086631decaab5ebfb0315b4818fb12e829d9788ee51ff57fba2bb0c","source":{"kind":"arxiv","id":"1005.3806","version":1},"attestation_state":"computed","paper":{"title":"SDDEs limits solutions to sublinear reaction-diffusion SPDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Hassan Allouba","submitted_at":"2010-05-20T19:51:22Z","abstract_excerpt":"We start by introducing a new definition of solutions to heat-based  SPDEs driven by space-time white noise: SDDEs (stochastic differential-difference equations) limits solutions. In contrast to the standard direct definition of SPDEs solutions; this new notion, which builds on and refines our SDDEs approach to SPDEs from earlier work, is entirely based on the approximating SDDEs. It is applicable to, and gives a multiscale view of, a variety of SPDEs.  We extend this approach in related work to other heat-based SPDEs  (Burgers, Allen-Cahn, and others) and to the difficult case of SPDEs with  "},"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":"1005.3806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-20T19:51:22Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"948b060ee289332f3c0ef3d5787a2143da523c9db34b455691830f4a289a6e3f","abstract_canon_sha256":"f1848dca04a682a7f21d6d5f90e414e2beb24f38c6b0122f1d17924130d88b5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.235411Z","signature_b64":"M/4oCmhr5gz+Ve0Zu9oHDUN4gM1ca/xnjZm16Xy3kCytLEHqAQvIfXfvU8HtUbY4Fh+XWO9wNjS+G6QQU5e9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef86794ff086631decaab5ebfb0315b4818fb12e829d9788ee51ff57fba2bb0c","last_reissued_at":"2026-05-18T04:36:51.235022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.235022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SDDEs limits solutions to sublinear reaction-diffusion SPDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Hassan Allouba","submitted_at":"2010-05-20T19:51:22Z","abstract_excerpt":"We start by introducing a new definition of solutions to heat-based  SPDEs driven by space-time white noise: SDDEs (stochastic differential-difference equations) limits solutions. In contrast to the standard direct definition of SPDEs solutions; this new notion, which builds on and refines our SDDEs approach to SPDEs from earlier work, is entirely based on the approximating SDDEs. It is applicable to, and gives a multiscale view of, a variety of SPDEs.  We extend this approach in related work to other heat-based SPDEs  (Burgers, Allen-Cahn, and others) and to the difficult case of SPDEs with  "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3806","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":"1005.3806","created_at":"2026-05-18T04:36:51.235079+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.3806v1","created_at":"2026-05-18T04:36:51.235079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3806","created_at":"2026-05-18T04:36:51.235079+00:00"},{"alias_kind":"pith_short_12","alias_value":"56DHST7QQZRR","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"56DHST7QQZRR33FK","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"56DHST7Q","created_at":"2026-05-18T12:26:04.259169+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/56DHST7QQZRR33FKWXV7WAYVWS","json":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS.json","graph_json":"https://pith.science/api/pith-number/56DHST7QQZRR33FKWXV7WAYVWS/graph.json","events_json":"https://pith.science/api/pith-number/56DHST7QQZRR33FKWXV7WAYVWS/events.json","paper":"https://pith.science/paper/56DHST7Q"},"agent_actions":{"view_html":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS","download_json":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS.json","view_paper":"https://pith.science/paper/56DHST7Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.3806&json=true","fetch_graph":"https://pith.science/api/pith-number/56DHST7QQZRR33FKWXV7WAYVWS/graph.json","fetch_events":"https://pith.science/api/pith-number/56DHST7QQZRR33FKWXV7WAYVWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS/action/storage_attestation","attest_author":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS/action/author_attestation","sign_citation":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS/action/citation_signature","submit_replication":"https://pith.science/pith/56DHST7QQZRR33FKWXV7WAYVWS/action/replication_record"}},"created_at":"2026-05-18T04:36:51.235079+00:00","updated_at":"2026-05-18T04:36:51.235079+00:00"}