Discovery of Pi, sqrt(3), and Perfect Gravitational Torque Balance in the Solar System's Planetary Architecture

This paper presents the Hasan Dipole Model — an original theoretical framework proposing that the Solar System operates as a closed thermodynamic dipole system. Using NASA planetary data normalized to Earth = 1 unit, seven independent analyses reveal hidden mathematical constants:Pi (π = 3.14159) emerges from the Mass/Radius ratio of Group 1 (Mercury–Jupiter) divided by Group 2 (Saturn–Pluto)Near-perfect volume balance (~1.04) between the two groupsDensity ratio of 2.420 between inner and outer groupsPi appears again independently in the Jupiter/Saturn emitted energy ratio (107.209 / 34.109 = 3.142)Perfect 50/50 energy balance (49.98% vs 50.02%) in adjacent planet energy division tablesNear-perfect thermodynamic equilibrium (99.43%) across the entire Solar SystemPerfect gravitational torque balance — Group 1 and Group 2 torques equal 750.928 exactly, calculated from the system fulcrum at 7.522 AUAdditionally, this research proves that Pluto — reclassified as a dwarf planet by the IAU in 2006 — is the gravitational balance pin of the Solar System. Its removal immediately breaks the 6-decimal-place torque balance, despite representing only 0.00045% of total system mass.