Axis Memory vs. Shape Memory: Persistent Anisotropic Organization in the BECU-OLON V13 Framework

This dataset and technical report present the BECU-OLON V13 framework, a nonlinear tensor-dynamical extension designed to analyze persistent anisotropic organization in the early and late-time Universe. Building upon the triaxial decomposition of the Planck Half-Mission (HM2) quadrupole data, this version investigates the stability of large-scale structural axes under partial decoherence and nonlinear relaxation. The core of the V13 framework is the introduction of Regulated Metastability, a regime where the dominant structural axis—recovered at galactic coordinates (l,b) ≈ (259∘, -20∘)—remains statistically persistent despite subordinate mode drift and stochastic perturbations. We introduce the principle of "Axis Memory vs. Shape Memory", demonstrating that global directional organization can survive even when local structural morphology undergoes significant decoherence. Key components of this release include: Tensor Dynamical Formalism: Analysis of the 10⁸ eigenvalue sparsity ratio (λ₁/λ₃) as evidence for an effective 1D infrared EFT sector. Geometric Attractors: Evaluation of the triaxiality index (T ≈ 0.5901) against the theoretical equilibrium value (1/√3). Robustness Analysis: A perturbative validation using global seismic activity as a stochastic proxy to test metastable tensor stability against irregular forcing. Asymptotic Relaxation: Mathematical proof of bounded metastable drift $D(W)$ approaching neutral relaxation rather than catastrophic divergence. This work establishes that the Universe may preserve long-lived organizational axes as an emergent property of sparse infrared tensor geometry, providing a robust framework for interpreting low-l cosmological anomalies.