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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18641322 |
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Table of Contents:
- <p>Gaussian and non-Gaussian distributions are typically treated as distinct statistical forms without a unified structural interpretation. This paper develops a framework interpreting these distributional regimes as structural phases of reality corresponding to Being and Becoming, respectively. Gaussian distributions emerge when structural openness resolves into stabilized configurations, producing equilibrium conditions in which variation remains constrained and symmetrical. Non-Gaussian distributions arise when structural openness remains active, allowing rare events and discontinuities capable of reorganizing system structure. Crucially, these regimes are not separate domains but alternating structural phases within evolving systems. Systems stabilize locally into Gaussian equilibrium yet remain susceptible to structural transformation, during which non-Gaussian dynamics re-emerge.</p> <p>Building on the interpretation of probability as structural openness situated between potentiality and actuality, this paper proposes a Distributional Signature Principle: distributional form reflects the degree to which structural openness remains operative within a system. Gaussian regimes correspond to stabilized actuality; non-Gaussian regimes correspond to active becoming. By integrating probabilistic theory with structural dynamics, this account clarifies the significance of distributional form and extends the structural interpretation of probability into a general framework for understanding equilibrium and transformation in nature.</p>