The Koch-Rindler Vacuum: Topological Mass Quantization, Biomorphic Rhythms, and the Binary Source Code of Spacetime

We present the Asymmetric Convergence Sequence (ACS), a self-generating algebraic framework derived fromfirst principles. The framework defines a sequence Zₙ = 1/(2n+1) that governs the kinematic phase θ = (pT,2 / pT,1) of bipartite states, predicting a strict convergence towards the irrational geometric constant π/4 as the iteration parameter n → ∞. We empirically validate this mathematical attractor using open-source high-energy physics data from the CMS detector at CERN (Run2011A DoubleMu dataset). By mapping the scaling parameter n to the invariant mass M of fundamental dimuon resonances, we observe a monotonic decrease in the mean absolute phase deviation from π/4. While light resonances (J/ψ, M ≈ 3.1 GeV) exhibit significant structural asymmetry, the phase of the heavy Z-boson (M ≈ 91.2 GeV) collapses strictly onto the predicted π/4 geometric attractor (mean phase = 0.7866). This paper provides the formal mathematical proofs for the ACS framework, including a structural binary decomposition of the fine-structure constant's inverse (α⁻¹ ≈ 137), and the accompanying Python analytical codebase for reproducing the empirical validation on public CERN datasets.