Modern physics faces fundamental dilemmas, including dozens of free parameters that cannot be derivedfrom first principles, the hierarchy problem, the black hole information paradox, and the absence ofmagnetic monopoles. This paper constructs the Topological Residual Entropy Theory based on a single firstprinciple axiom: the "right-handed cylindrical helical motion of space at the speed of light" (). Through a three-layer topological geometric expansion ( ),we rigorously derive the fine-structure constant , the gravitationalconstant , and the core formula for the Planck constant:h = (μu2080 αu2075 / c²) × ln(10) × Factor_hHere,has the dimension of , serving as a residual bridge between geometric topology andelectromagnetic dimensions, ensuring complete self-consistency among the four fundamentaldimensions of mass, length, time, and electric current in the SI system. This paperdemonstrates that the underlying logic of physics originates entirely from geometrictopological bootstrapping and residual entropy increase: characterizes the energy densityof the divergent motion of the helical fluid, with its dimension precisely matching humanbiological energy consumption; the reciprocal of , , represents the observer'scognitive residual of the decimal base; the residual frequency iterates five times by from themaximum rigidity of to reach the Planck limit, aligning with the six degrees of separationnetwork protection mechanism. The Planck scale marks the end of continuous topology andthe "near-perfection" of the discrete quantum world. Brain-Computer Interface (BCI)experiments directly verify the observer closed loop from the dimensional perspective of. The universe exhibits an infinite, Matryoshka-style hierarchical nesting, whereobservers deeply participate in the creation of physical laws. The theoretical errors (aresidual for and a residual for ) are in high agreement with experiments, providinga purely geometric and philosophical pathway for the Grand Unified Theory.