Irrational Phase Topology as the Origin of the Cosmic Baryon Asymmetry

This paper proposes a minimal, first-principles explanation for the observed baryon–antibaryon asymmetry of the universe, derived from a topological obstruction in scalar field phase dynamics. Building on the Origin Axiom — a mathematical condition that forbids exact cancellation of irrational exponentials — the theory introduces a complex scalar field with a non-linear, irrationally modulated potential. The resulting field structure generates an intrinsic, time-dependent chemical potential: μ_eff(t) = (1 / ħ) · dS/dt, which biases baryon production in thermal equilibrium without the need for external CP-violating interactions. Through ergodic averaging over irrational phase modulations, the model yields a universal suppression factor on the order of ~10⁻⁹, matching the observed baryon-to-entropy ratio η_B ≈ 6 × 10⁻¹⁰. The suppression is statistical, not fine-tuned, and arises solely from the topology of the scalar field’s vacuum structure. The mechanism satisfies all three Sakharov conditions, including thermodynamic irreversibility, without invoking speculative particles or beyond-Standard-Model physics. Key insights and predictions: Matter–antimatter asymmetry emerges as a geometrical residue, not a stochastic accident. Oscillon structures may act as asymmetry carriers, embedding spatial baryon gradients during early-universe evolution. Observable imprints may include subtle non-Gaussian signatures in the cosmic microwave background (CMB) or matter clustering patterns. The mechanism is falsifiable via deviation patterns in η_B(z), residual field relics, and baryon number transport features. This work reframes the origin of matter as a structural consequence of irrational topology in a unified scalar field framework — an irreducible remainder of forbidden cancellation. Keywords: Baryon Asymmetry, Origin Axiom, Scalar Field, Irrational Phase Dynamics, CP Violation, Chemical Potential, Thermal Bias, Oscillons, Topological Field Theory, Cosmology