{"id":"c7258de7-0565-49d4-9369-de1f35e74dc3","arxiv_id":"2604.03062","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A proper smooth fourfold over a perfect field of characteristic p>0 is constructed with asymmetric Hodge-Witt numbers in total degree 3 via computation of the Hodge-Witt cohomology of the classifying stack B alpha_p.","lead":"The authors construct a proper smooth fourfold over a perfect field of positive characteristic with asymmetric Hodge-Witt numbers in total degree 3. This is the smallest possible dimension and degree for such an example, derived from explicit calculations on the classifying stack of the group scheme alpha_p.","discovery_kind":"new_application","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"Hodge-Witt cohomology computation for Bα_p yields asymmetry counterexample in dim-4/deg-3; no overlap with RS cost/φ/period forcing","alignment":"orthogonal","rationale":"Paper's core objects (graded R-modules, domino numbers T_{i,j}, slope numbers m_{i,j}, Ekedahl diagonal t-structure on DGr_c(R), de Rham-Witt totalization) are standard Illusie-Raynaud-Ekedahl homological algebra in char-p AG. RS forcing chain (reality_from_one_distinction, J-cost uniqueness, φ-ladder, 8-tick/3D emergence) has no theorems or predicates about Hodge-Witt numbers, domino filtrations, or classifying-stack approximations. Dimension-4 example does not contradict RS 3D forcing (mathematical variety vs. physical spacetime). No J(ρ), cosh identities, or parameter-free constants appear. Hence orthogonal.","tokens_in":65132,"confidence":"high","tokens_out":213,"duration_ms":18898,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-05-13T17:49:06.802106+00:00","model_set":{"reader":"grok-4.3"},"falsifier":null,"supporting_citations":[],"review_version":1}