BERNA: Boundary-Encoded Resonance Network Architecture

Financial markets exhibit abrupt regime transitions—breaks, volatility explosions, and squeezes—that are typically identified ex post but rarely explained as necessary outcomes of an internal state law. Most existing approaches rely on price moments, efficiency ratios, or regime-duration counters, implicitly framing regime change as a detection problem rather than a mechanical consequence. As a result, price paths with similar volatility and momentum may display radically different survivability without a structural explanation.<br><br>This paper introduces BERNA (Boundary-Encoded Resonance Network Architecture), a structural failure framework in which market regimes are modeled as boundaries with finite capacity. BERNA defines three primitive state variables—accumulated structural stress (Σ), structural capacity (Θ), and remaining capacity (Λ = Θ − Σ)—that are not derived from price moments, volatility, or temporal persistence. Regime change occurs when accumulated stress exhausts capacity, formalized as a deterministic threshold event (rupture), rather than as an ex post statistical classification.<br><br>A central methodological challenge concerns reducibility to existing lifetime- or duration-based regime measures. This is addressed by demonstrating reset-invariance violation: duration counters reset by construction at regime boundaries, whereas BERNA continues to accumulate structural stress until rupture. This incompatibility precludes functional derivation or hierarchical embedding and establishes a strict direction of explanation from endogenous capacity depletion to observed regime persistence.<br><br>Empirical validation employs a broad test suite including principal component separation, permutation-based null tests, event-aligned analyses, rupture hazard modeling, structural and Markov comparisons, ablation studies, Granger causality, out-of-sample prediction, multi-asset evaluation, and robustness analyses. Across all tests, BERNA exhibits sequence-dependent behavior orthogonal to classical indicators, accumulates prior to regime failure, and remains robust to parameter and sample perturbations.<br><br>BERNA does not propose trading rules nor claim universal predictive dominance. Its contribution is diagnostic: to quantify remaining structural capacity within a regime and to explain why continuation becomes mechanically unsustainable. By replacing time-based persistence with endogenous capacity depletion, BERNA reframes regime change as a failure process rather than a detection problem.<br><br>In the empirical implementation, the capacity parameter Θ is treated as an exogenous, regime‑dependent constraint and is not inferred from price moments; a fully reproducible reference implementation is provided in Appendix A.