Resolution of the Continuous Line via Entropy Bound and Asymmetry

Because structural asymmetry definitively separates the roles of wholes and parts; Parthood establishes its independence by naturally aligning with point symmetry metrology. A framework that natively handles completeness via discrete state sequences converging to individual points. Also, we use constructive real arithmetic via the Integer Shield Equation (ISE) which ablates infinite continuities while inside a bounded manifold. Specifically, we first show employing Cantor's diagonal argument, there are irreversible metric holes in the indexed continuum which ultimately implies an unyielding asymmetry between the discrete and irrational numbers. Then, under live execution constraints, we demonstrate that attempting to evaluate the indexed continuum triggers a non-terminating loop hang and total processing freeze, identified as the Successor-Stoppage Paradox. This initiates an infinite entropy expenditure delineated by Brillouin's macro state thermodynamic entropy bound Delta S >= Delta I_r. This is resolved safely by truncating the irrational tails at the hardware unit step size of the Planck Wall O(h) built into the ISE, collapsing them to solitary stable points. At the same time providing a logarithmic sink to channel the entropy explosion. Consequently, this metrological overhaul redirects computational and physical energy away from the indexed continuum and directly into active resolution layers of the power set cardinality |P(S)| = 2^n bounded manifold. Making continuity a resolution choice with the discrete as the antecedents and irrational numbers as the progenitors. Hence, securing a stabilized system across physical scaling horizons such as aerospace processing environments via Dyadic Asymmetry.