Abstract

We present a comprehensive construct wherein nature organizes by pairs (parity, bipartition, entangled duals) while macroscopic asymmetry emerges from small differences (infinitesimal deviations, symmetry breaking, representational obstructions). The paper unifies (i) a parity and pair-based worldview in which evenness encodes constraint and definiteness, and oddness encodes obstruction and imbalance, (ii) a rigorous account of decimal expansions, including termination criteria, multiplicative order, and the identity 0.999... = 1, (iii) a mathematically precise treatment of nonzero but negligible differences via hyperreals and the standard-part map, and (iv) multiple worked physical models demonstrating how minute biases accumulate into macroscopic drift, namely pair-constrained dynamics, baryogenesis toy kinetics with freeze-out, entanglement stabilization under noise, diffusion-abrasion with cumulative loss, quantization error propagation, graph-theoretic frustration, and Ising parity constraints. We correct the literal arithmetic claim that division by even denominators is definite while odd denominators are indefinite, reframing it as a symmetry metaphor grounded in base-dependent factor compatibility, while preserving the philosophical thesis that pairs govern balance and small differences power becoming. We close by situating the framework within broader discussions of identity under symmetry, impermanence, and scale-relative equivalence.

Keywords

Baryogenesis, Hyperreals, Infinitesimals, Parity Symmetry, Symmetry Breaking.

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