Solar-System-Calibrated Geometric Upper Bound for Planetary Multiplicity and Inclination Correlation

Conventional planetary formation theory attributes planetary multiplicity primarily to primordial nebula mass, initial density fluctuations, and stochastic collisional accretion history. Such material-determined paradigms cannot provide a strict upper limit for long-term stable planetary systems and fail to yield deterministic statistical correlations between planetary number and orbital architecture (Winn & Fabrycky, 2015). Under the continuous-medium dynamical framework, stellar systems are governed by background potential gradient cascading locking rather than nebula material abundance. This study derives a geometric upper bound for stable major planet multiplicity controlled by the perturbation-bearing capacity of the stellar background potential field. The theoretical upper limit follows a base-2 logarithmic scaling relation determined by the ratio of the outer locking cutoff radius to the inner stable locking radius. A paradigm-exclusive falsifiable prediction: within stable limits, system-averaged mutual orbital inclination increases monotonically with major planet number, originating from cumulative secondary perturbation distortion. For Solar-like G-type stars, calibrated with observed boundary parameters, the theoretical stable upper multiplicity range is approximately 8 to 10 major planets. We further discuss the physical implications of the radial thermodynamic gradient, which dictates planetary compositional zonation and establishes a narrow rocky habitability window essential for the emergence of complex dissipative structures. This statistical signature is testable with PLATO, extended TESS catalogs, and the Vera C. Rubin Observatory.