{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:A5LGNET66WKOXLM4MTVCUTIRHW","short_pith_number":"pith:A5LGNET6","schema_version":"1.0","canonical_sha256":"075666927ef594ebad9c64ea2a4d113dbaf9b7092ba5531923edf611f29dc124","source":{"kind":"arxiv","id":"2605.28677","version":1},"attestation_state":"computed","paper":{"title":"Weak universality for stochastic reaction-diffusion models with long-range correlated noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Markus Tempelmayr, Simon Gabriel","submitted_at":"2026-05-27T16:10:47Z","abstract_excerpt":"We study the large-scale behaviour of a family of stochastic reaction-diffusion equations driven by long-range correlated noise in a weakly nonlinear regime. Depending on the decay of correlations of the noise and the strength of the nonlinearity, the universal behaviour is governed by a version of the dynamical $\\Phi^p$ model with long-range correlated noise, and with a coupling constant determined by the reaction term of the microscopic model. Our main result establishes the stochastic estimates and convergence of models required in the theory of regularity structures. We adapt the multiinde"},"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":"2605.28677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-27T16:10:47Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"4833b35d373dca8ace18b14d434cd758212aa0df8fedabec05173f5ed1b6effa","abstract_canon_sha256":"d8ba0b90745fa140f840210914590f8aa856d4f5053dfaa367e0a4ffbce36a20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:59.600285Z","signature_b64":"rsXm2dz2+QD5PYQ9wLm4a1Xd5/HxVXlPYvSlUrOtOS3c7nwhmw+0EZ2cfvgbT8yEdFWBUoQvJaoD7qouubILBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"075666927ef594ebad9c64ea2a4d113dbaf9b7092ba5531923edf611f29dc124","last_reissued_at":"2026-05-28T02:04:59.599867Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:59.599867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak universality for stochastic reaction-diffusion models with long-range correlated noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Markus Tempelmayr, Simon Gabriel","submitted_at":"2026-05-27T16:10:47Z","abstract_excerpt":"We study the large-scale behaviour of a family of stochastic reaction-diffusion equations driven by long-range correlated noise in a weakly nonlinear regime. Depending on the decay of correlations of the noise and the strength of the nonlinearity, the universal behaviour is governed by a version of the dynamical $\\Phi^p$ model with long-range correlated noise, and with a coupling constant determined by the reaction term of the microscopic model. Our main result establishes the stochastic estimates and convergence of models required in the theory of regularity structures. We adapt the multiinde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28677","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.28677/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.28677","created_at":"2026-05-28T02:04:59.599927+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.28677v1","created_at":"2026-05-28T02:04:59.599927+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28677","created_at":"2026-05-28T02:04:59.599927+00:00"},{"alias_kind":"pith_short_12","alias_value":"A5LGNET66WKO","created_at":"2026-05-28T02:04:59.599927+00:00"},{"alias_kind":"pith_short_16","alias_value":"A5LGNET66WKOXLM4","created_at":"2026-05-28T02:04:59.599927+00:00"},{"alias_kind":"pith_short_8","alias_value":"A5LGNET6","created_at":"2026-05-28T02:04:59.599927+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/A5LGNET66WKOXLM4MTVCUTIRHW","json":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW.json","graph_json":"https://pith.science/api/pith-number/A5LGNET66WKOXLM4MTVCUTIRHW/graph.json","events_json":"https://pith.science/api/pith-number/A5LGNET66WKOXLM4MTVCUTIRHW/events.json","paper":"https://pith.science/paper/A5LGNET6"},"agent_actions":{"view_html":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW","download_json":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW.json","view_paper":"https://pith.science/paper/A5LGNET6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.28677&json=true","fetch_graph":"https://pith.science/api/pith-number/A5LGNET66WKOXLM4MTVCUTIRHW/graph.json","fetch_events":"https://pith.science/api/pith-number/A5LGNET66WKOXLM4MTVCUTIRHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW/action/storage_attestation","attest_author":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW/action/author_attestation","sign_citation":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW/action/citation_signature","submit_replication":"https://pith.science/pith/A5LGNET66WKOXLM4MTVCUTIRHW/action/replication_record"}},"created_at":"2026-05-28T02:04:59.599927+00:00","updated_at":"2026-05-28T02:04:59.599927+00:00"}