The proposal is not semantically faithful. It omits k >= 2: for k=1 and x=(1), coordinatewise annihilation forces y=(0), contradicting y != 0. It also replaces the dot product by coordinatewise products. For k=2, x=(1,1) and y=(1,-1) give x dot y=0 with y nonzero, while the coordinate products are (1,-1), not both zero. This audit does not assess whether either Lean declaration compiles.
RESULT_JSON: {"semantic_status":"NOT_EQUIVALENT","defects":["MISSING_DIMENSION_PREMISE","DOT_PRODUCT_REPLACED_BY_COORDINATEWISE_ZERO"],"missing_premise_certificate":{"dimension":1,"x":[1],"forced_y":[0]},"operator_mismatch_certificate":{"dimension":2,"x":[1,1],"y":[1,-1],"dot_product":0,"coordinate_products":[1,-1]}}
