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 = (pₓ, ₂ / pₓ, ₁) of bipartite states, predicting a strict convergence towards the irrational geometric constant /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 /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 /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 (^-1 137), and the accompanying Python analytical codebase for reproducing the empirical validation on public CERN datasets.