{"paper":{"title":"Symmetries for the gKPZ equation via multi-indices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Multi-indices compute the exact dimensions of the two symmetry spaces for the generalised KPZ equation by avoiding over-parametrization of renormalised terms.","cross_cats":["math.AP","math.RA"],"primary_cat":"math.PR","authors_text":"Carlo Bellingeri, Yvain Bruned","submitted_at":"2024-10-01T16:14:21Z","abstract_excerpt":"In this work, we study the two main symmetries for the one-dimensional generalised KPZ equation (gKPZ): the chain rule and the It\\^o Isometry. We consider the equation in the full-subcritical regimes and use multi-indices that avoid an over-parametrization of the renormalised equation to compute the dimension of the two spaces associated with these two symmetries. Our proof is quite elementary and shows that multi-indices provide in this case a simplification in comparison to the results obtained via decorated trees. It also completes the program on the study of the chain rule initiated in arx"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We consider the equation in the full-subcritical regimes and use multi-indices that avoid an over-parametrization of the renormalised equation to compute the dimension of the two spaces associated with these two symmetries. Our proof is quite elementary and shows that multi-indices provide in this case a simplification in comparison to the results obtained via decorated trees.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Multi-indices can be defined and manipulated so that they label renormalized terms without introducing over-parametrization, allowing direct dimension counts of the symmetry spaces that match the structure of the gKPZ equation (abstract, paragraph on multi-indices).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Computes dimensions of symmetry spaces for the gKPZ equation via multi-indices that avoid over-parametrization, providing an elementary proof that simplifies prior decorated-tree results and completes the chain-rule program.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Multi-indices compute the exact dimensions of the two symmetry spaces for the generalised KPZ equation by avoiding over-parametrization of renormalised terms.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b5881e13aa9779cd0d4c5df65270b3b3f3bdf3e31dc75c139afd7c75fe6875a9"},"source":{"id":"2410.00834","kind":"arxiv","version":3},"verdict":{"id":"8184b37e-d76d-4bc7-a268-ef4f363b1463","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T20:06:16.395570Z","strongest_claim":"We consider the equation in the full-subcritical regimes and use multi-indices that avoid an over-parametrization of the renormalised equation to compute the dimension of the two spaces associated with these two symmetries. Our proof is quite elementary and shows that multi-indices provide in this case a simplification in comparison to the results obtained via decorated trees.","one_line_summary":"Computes dimensions of symmetry spaces for the gKPZ equation via multi-indices that avoid over-parametrization, providing an elementary proof that simplifies prior decorated-tree results and completes the chain-rule program.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Multi-indices can be defined and manipulated so that they label renormalized terms without introducing over-parametrization, allowing direct dimension counts of the symmetry spaces that match the structure of the gKPZ equation (abstract, paragraph on multi-indices).","pith_extraction_headline":"Multi-indices compute the exact dimensions of the two symmetry spaces for the generalised KPZ equation by avoiding over-parametrization of renormalised terms."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.00834/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":42,"sample":[{"doi":"","year":null,"title":"I. Bailleul, Y. Bruned Locality for singular stochastic PDEs. arXiv:2109.00399","work_id":"40b187e0-1289-4d92-8648-cf1a850824a7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"I. Bailleul, Y. Bruned Random models for singular SPDEs. arXiv:2301.09596","work_id":"0c065b3c-c8ad-472e-9c66-15eeff62b7e8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1214/19-ejp404/25","year":2020,"title":"Bellingeri An Itˆo type formula for the additive stochastic heat equation","work_id":"3ffaf3bf-75c3-4b3d-9b69-c0045bf746d0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Y. Bruned, A. Chandra, I. Chevyrev, M. Hairer. Renormalising SPDEs in regularity structures. J. Eur. Math. Soc. (JEMS), 23, no. 3, (2021), 869-947. doi:10.4171/ JEMS/1025","work_id":"4016f12f-f658-44d1-bc3b-7b49622cc27a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Y. Bruned, V. Dotsenko. Novikov algebras and multi-indices in regularity structures arXiv:2311.09091","work_id":"31e6f6e9-67be-4d19-b327-f8617144e107","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":42,"snapshot_sha256":"a298f353238cc127365d7bd3e2736a84a72c0efb320811fe00986bff73e0c5dc","internal_anchors":3},"formal_canon":{"evidence_count":2,"snapshot_sha256":"b3dabc459273d38811476af5718d63cb5d448047f9643113ac99333e09577fb8"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}