This paper presents a preliminary study on the P-space within the seven-space framework. The P-space iteration is p_{n+1} = p_n^{1/s} e^{π p_n / s^2}, with s = σ + iω ∈ ℂ \ {0,1}, where σ = Re(s) and ω = Im(s). The fixed point is p* = e^{-W_0(-π/(s(s-1)))} and the multiplier is λ = 1/s + π p*/s^2. Five initial values (0.5, 1.0, -0.5, 1.0j, 0.5+0.5j) were tested with a maximum of 200,000 iterations and a convergence tolerance of 10^{-12}. At ω = 0, for the initial value 0.5, convergence occurs for σ ∈ (-∞, -2.46475] ∪ [3.46475, ∞). At the four tested σ values with ω > 0, the minimum ω required for convergence is systematically lower in the P-space than in the U-space. On the line σ = 1/2, the P-space fixed point is real for all tested ω, which is proved analytically. At σ = -2.0, ω = 0, all five tested initial values fail to converge; logarithmic-domain tracking confirms super-exponential growth of the modulus. The convergence boundary of the P-space is defined implicitly by |λ| = 1 and admits no closed-form analytic solution. All conclusions are strictly limited to the tested range of parameters and initial values. This study is preliminary and its conclusions may be revised in future work.