Explanation of JcostN_unit in IndisputableMonolith.Cost.Ndim.Core
(1) In plain English, the theorem states that for any positive integer number of dimensions n and any weight vector α (a function from Fin n to reals), the n-dimensional cost JcostN α evaluated at the constant vector whose every component is 1 equals exactly 0.
(2) In Recognition Science this matters because it identifies the uniform (all-ones) configuration as the zero-cost fixed point of the multi-component reciprocal cost. This supplies the baseline against which any distinction or recognition event incurs positive cost, consistent with the scalar J-cost minimum at unity and the overall forcing of recognition from cost structure.
(3) The formal statement is read as: theorem JcostN_unit {n : ℕ} (α : Vec n) : JcostN α (fun _ => 1) = 0. Here Vec n abbreviates Fin n → ℝ; JcostN α x is defined as JlogN α (logVec x) where JlogN applies the scalar cost to the weighted log-sum aggregate; the proof reduces the claim by simplification to the scalar unit case.
(4) Visible dependencies inside the supplied module are the definitions JcostN, JlogN, dot, logVec together with the simplification tactic that invokes Jcost_unit0. Related declarations present in the same module are JcostN_eq_Jcost_aggregate (which rewrites JcostN to scalar Jcost of the aggregate) and JcostN_nonneg (which derives non-negativity from the same aggregate form).
(5) The declaration does not prove uniqueness of the zero, any global minimization property, reciprocity beyond the componentwise case already shown in the module, or any link to physical constants, spacetime emergence, or the forcing chain.