Alysis as a Guardian of Theoretical Integrity and Filter for Hypotheses

Scope and Intent of this Preprint This preprint introduces alysis as both a guardian of theoretical integrity and a filtering mechanism for selecting meaningful hypotheses from less robust ones. The Alysis Coefficient (AC) is defined as a scalar quantity that quantifies the collapse of a model’s relational structure under boundary operations such as coarse-graining, decoherence, compactification, or dimensional reduction. The primary purpose of this work is to offer alysis as a filtering mechanism for selecting hypotheses based on their ability to maintain relational coherence. The paper does not propose new physical laws or reconstruction algorithms but instead provides a framework for applying alysis to theoretical models in quantum mechanics, thermodynamics, relativity, and string theory. The framework evaluates when models retain their relational structure and when they collapse into degenerate forms, ensuring only structurally meaningful models are retained for further exploration. This is demonstrated through concrete toy examples, including a Bell state in quantum mechanics (where partial tracing leads to complete relational collapse, yielding AC = 1) and coarse-graining in a 2×2 Ising model (yielding AC = 0.67), providing a practical basis for the heuristic threshold of significant collapse (AC ≈ 0.6–0.8). Relation to Existing Concepts Alysis is complementary to traditional diagnostic tools in theoretical physics but focuses specifically on structural integrity rather than entropy or probabilistic uncertainty. While entropy measures the loss of information or statistical uncertainty under coarse-graining processes, alysis quantifies structural collapse—when relational data that define the system's model lose coherence due to boundary operations. Unlike probabilistic tools that rely on statistical measures (e.g., entropy, uncertainty), alysis offers a model-independent criterion that detects the degradation of hierarchical relationships within theoretical models. This sets alysis apart from statistical methods like bootstrapping, which aims to estimate model uncertainty based on resampled empirical data. Alysis, in contrast, applies to theoretical models that rely on relational structures (e.g., entanglement in quantum mechanics or geometry in string theory), providing a clear distinction from purely probabilistic frameworks. Thus, the Alysis Coefficient (AC) extends the existing theoretical toolbox by focusing on structural collapse and offering a direct, objective measure to distinguish between meaningful and degenerate hypotheses. This makes alysis an essential tool in theoretical model selection, ensuring that only models with coherent relational structures remain within consideration. Conclusion for Zenodo This preprint introduces alysis as a diagnostic tool for assessing theoretical models’ structural integrity and provides a method for filtering valid hypotheses from those that fail to maintain relational coherence. The Alysis Coefficient (AC) has broad applications across quantum mechanics, thermodynamics, relativity, and string theory, as well as potential uses in other scientific domains dealing with hierarchical relational structures and boundary aggregation. This framework contributes to ensuring the robustness and consistency of theoretical models across multiple disciplines.