Conjecture on the Topological Invariants of the Fibres of the v-Calculus in Dimension n: Numerical Evidence and Precise Formulation

The v-calculus on ℂⁿ establishes a dimensional reduction theorem: the v-calculus in dimension n is always isomorphic to a one-dimensional calculus in the coordinate Φ, with the genuine n-dimensional novelty concentrated in the topology of the fibres F_c = {Φ(z) = c}. In dimension 1, the fibre is a point — trivial. This note formulates a precise conjecture for n ≥ 2: the fibres have non-trivial fundamental group, producing topological invariants additional to Ω_γ, all invisible to every operation of the v-calculus. The conjecture k(n) = n−1 is verified numerically up to dimension n = 100 with zero exceptions, with monodromy error exactly 0.000 × 10⁰ at each tested dimension.