The Lietz Infinity Resolution Conjecture: Logarithmic Hierarchical Interfaces as the Tachyonic Pulled-Front Re-Expression of the Primitive Invariant

I present a candidate axiom (A8) for the Void Dynamics Model (VDM) framework that addresses the mathematical structure of finite-energy states in tachyonic metriplectic field systems supporting pulled fronts with exponential tails. The Lietz Infinity Resolution Conjecture asserts that such systems cannot maintain finite excess energy on unbounded domains without organizing into a finite-depth hierarchy of scale-separated interfaces that concentrate both energy and operational information at codimension-1 boundaries. The conjecture predicts three fundamental signatures: First, hierarchical depth scaling where N—the number of distinct organizational levels—grows as the logarithm of the ratio between domain size L and the characteristic tail decay length lambda. This logarithmic scaling implies that as domains expand toward infinity, the system requires progressively more hierarchical layers, but the growth rate remains bounded and predictable. Second, boundary-law energy scaling where the excess energy E-excess scales as L raised to the power (d minus 1) rather than the naive bulk expectation of L to the d-th power, where d denotes spatial dimension. This dimensional reduction reflects energy concentration at interfaces—surfaces in three dimensions, lines in two dimensions—rather than volumetric distribution. Third, concentration of operational information at interfaces with fraction alpha-I remaining bounded strictly above zero. This ensures that a finite, non-vanishing proportion of the system's information-carrying capacity resides at the hierarchical boundaries rather than diffusing into the bulk. I formalize the mathematical setting, state precise predictions with preregistered thresholds, enumerate falsification criteria, and specify twelve validation gates (G1 through G12) spanning analytical proofs—one-dimensional lower bounds and Gamma-convergence analyses—numerical demonstrations including scaling law verification, concentration measures, and ablation studies, plus cross-verification checks. This conjecture establishes a necessary-structure claim about how tachyonic pulled-front systems regularize infinity through hierarchical organization. The implications extend to cosmogenesis (how structure emerged from primordial instability), pattern formation in dissipative systems, and the emergence of operational structures—the capacity for information processing and causal agency—within field-theoretic models. In essence, it proposes that infinity is not merely a mathematical abstraction but a physical pressure that forces self-organizing systems into hierarchical architectures as a fundamental resolution mechanism.