In this new paper, I establish a no-hair theorem for static black holes in a conformally coupled scalar-tensor theory, motivated by a fundamental geometric reinterpretation: the ratio π between circumference and diameter is not a universal constant but a spacetime-dependent variable π(x) = f[g_μν(x)]. This geometric variability naturally leads to the conformal coupling Π²R/12, where the scalar field Π encodes the local deviation of geometric proportions from Euclidean values. We prove analytically, via a virial argument in the Einstein frame, that static black holes with regular horizons admit no scalar hair—the field Π asymptotically approaches a constant, meaning π recovers its Euclidean value at infinity. Numerical verification confirms this through Einstein-frame energy diagnostics: all attempted hair configurations have I_φ/V ~ 10^-8, indicating φ ≡ 0. We identify and eliminate a spurious numerical branch (p≈1.02) through global consistency checks. The theorem implies that **spacetime geometry actively resists π-variation**, maintaining geometric proportion constancy as a dynamical equilibrium condition. Implications for modified gravity, observational signatures, and minimal symmetry-breaking scenarios are discussed.
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