What was already known
Caravenna, Sun and Zygouras constructed the critical 2D stochastic heat flow in 2023. The new work constructs and characterizes the centred logarithmic field at criticality. It does not claim the same result for every microscopic growth model or all forms of the two-dimensional KPZ equation.
AI involvement
Appendix C identifies AI-derived covariance/tightness bounds, a new simpler conditional-Gaussian-convexity route completing convergence, and a Gaussian-rigidity argument for non-Gaussianity. The human authors supplied structural inputs, rejected a flawed switch-off construction and revised the retained approach with AI. Inclusion concerns the surviving arguments, not the abandoned proposal.
Importance
Provides a precise critical logarithmic scaling limit and identifies non-Gaussian structure in a central stochastic-growth model.
Limitations
Gaussian directed-polymer disorder, the critical-window scaling and the stated initial-data class are essential. Armstrong’s separate formalization records corrections and deliberate changes of conventions, including precise SHF predicates and topology. Its identification with the earlier literature’s SHF is a literature comparison, not established by Comparator alone. His four additional results are separately credited and are outside this contribution.
Technical verification
Armstrong reports Lean kernel checking of the principal formal counterparts using only the three standard Lean axioms. The source documents 126 deliberate deviations and corrections for the main paper. Exact identification of the artifact’s SHF predicate and topology with the original literature has not been fully reconciled in this review, so the original mathematical claim remains Partial rather than inferring full checking from registration.
Human understanding
The named authors explain the convergence decomposition and non-Gaussianity mechanism in Section 2 and Section 9 and document the strategy changes in Appendix C. Armstrong’s formalization and later four-results note retain separate credit.
Correction and publication history
Lists the original paper once while retaining the specific checking and provenance references. Research claims and rating levels are unchanged.
Read this published revisionClarifies that the source reports completed checking but does not supply its exact completion date. Research claims and rating levels are unchanged.
Read this published revisionNewly reviewed source-backed research contribution with contribution-specific AI attribution and checking limits.
Read this published revision