BERNA:Boundary-Encoded Resonance Network Architecture

BERNA:Boundary-Encoded Resonance Network Architecture A Structural Failure Theory of Financial Regimes Based on Endogenous Capacity Depletion Author:Bülent Duman Affilitiation:Independent Researcher Abstract: Canonical Definition (BERNA)BERNA (Boundary-Encoded Resonance Network Architecture; DUMAN,BÜLENT January 18, 2026) models financial regimes as bounded systems with finite structural capacity. Accumulated structural stress (Σ) depletes regime capacity (Θ), leaving remaining capacity Λ = Θ − Σ. A regime transition occurs when Σ reaches Θ, constituting a deterministic rupture event rather than a statistically detected break. BERNA defines a capacity-based structural state variable independent of price moments, volatility, and time. Financial markets exhibit abrupt regime transitions—breaks, volatility explosions, squeezes—that are routinely identified ex post but rarely explained as necessary outcomes of an internal state law. Existing approaches rely on price moments, efficiency ratios, or regime-duration counters, implicitly treating regime change as a detection problem rather than a mechanical consequence. As a result, price trajectories with similar volatility and momentum may exhibit radically different survivability without a principled explanation. 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 detection. A central methodological challenge is reducibility to existing lifetime-based regime measures. We address this explicitly by demonstrating reset invariance violation: duration counters reset by construction at regime changes, while BERNA continues to accumulate structural stress until rupture. This incompatibility precludes functional derivation, extension, or hierarchical embedding, establishing a strict direction of explanation from capacity depletion to observed regime persistence. Empirical validation employs a comprehensive test suite including principal component separation, permutation-based null hypothesis tests, event-aligned analyses, rupture hazard modeling, structural and Markov comparisons, ablation studies, Granger causality, out-of-sample prediction, multi-asset evaluation, walk-forward and Monte Carlo robustness, sensitivity analysis, and scientific audit procedures. Across all tests, BERNA exhibits sequence-dependent behavior orthogonal to classical indicators and efficiency measures, accumulates prior to regime failure, and remains robust to parameter and sample perturbations. BERNA does not propose trading rules nor claim universal predictive dominance. Its contribution is diagnostic: to quantify how much structural capacity remains within a regime and to explain why continuation becomes mechanically unsustainable. By replacing time-based persistence with endogenous capacity depletion, BERNA introduces a new class of structural state variable for financial dynamics, reframing regime change as a failure process rather than a detection problem. 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. Key Contents Capacity-Centric Regime OntologyFinancial regimes are modeled as bounded structures with finite capacity, replacing time-based persistence with a capacity coordinate. Structural State Primitives (Σ, Θ, Λ)Introduction of accumulated structural stress (Σ), structural capacity (Θ), and remaining capacity (Λ), none of which are derived from price moments, volatility, or duration. Deterministic Rupture MechanismRegime transitions occur through a threshold-based rupture event when Σ reaches Θ, not via ex post statistical detection. Reset-Invariance ViolationDemonstration that BERNA accumulates structural stress across regime transitions where lifetime-based measures reset, proving non-equivalence to duration counters such as LEVENT. Non-Derivability from Price MomentsPermutation-based null hypothesis tests show BERNA depends on temporal ordering rather than marginal price distributions. Orthogonality to Classical IndicatorsPCA and correlation analyses confirm BERNA is orthogonal to momentum, volatility, trend-following, efficiency, and exhaustion indicators. Sequence-Dependent Structural DynamicsBERNA encodes ordered internal events, distinguishing structural failure processes from distributional or statistical market descriptions. Θ Scaling Invariance and Rank StabilityCapacity scaling affects magnitude but preserves event timing and ordering, rejecting calibration-driven explanations. Empirical Robustness Across Assets and SamplesValidation through multi-asset testing, out-of-sample prediction, walk-forward analysis, Monte Carlo simulations, and scientific audit procedures. Diagnostic Rather Than Prescriptive ContributionBERNA does not propose trading rules; it provides a diagnostic framework to quantify remaining structural capacity and explain why regimes become mechanically unsustainable. Citation (BERNA) Duman, Bülent (2026).BERNA: Boundary-Encoded Resonance Network Architecture – A Structural Failure Theory of Financial Regimes Based on Endogenous Capacity Depletion.Preprint, Zenodo.