From Causality to Containment: Empirical Testing of Structural Determination and Its Implications for the Structural Depth Framework

Abstract

From Causality to Containment: Empirical Testing of Structural Determination and Its Implications for the Structural Depth Framework This research article presents an empirical investigation of the containment-based determination architecture developed within the Structural Depth Research Program. The study examines whether a structural quantity derived from containment relations can be computationally defined, observed, reproduced, and empirically evaluated on a selected market-microstructure representation. The theoretical starting point is the transition from causality to containment. Rather than treating observed market outcomes as primary explanatory objects, the study begins with containment as the primitive structural relation. A directed containment graph is constructed, valid containment paths are identified, and the shortest and longest valid structural depths are defined as Θ_min and Θ_max. Structural Dispersion (Ψ) is then derived from these path-depth measures and operationalized as an observable structural state/event. The computational core was subjected to fifteen independent validation tests (T1–T15), covering linear containment, unequal and equal-depth paths, closure, representation resolution, controlled perturbation, random DAG validation, cycle-boundary rejection, exhaustive reachable-pair validation, path-length consistency, independent oracle comparison, and metamorphic edge-addition and edge-removal behavior. All fifteen computational validation tests passed. The empirical component uses market microstructure as a selected measurement representation rather than as an ontological definition of the market. Five visible order-book levels provide the operational containment representation, while execution-derived shortcut relations are incorporated when aggressive trades penetrate visible levels. The observer records structural depth, Structural Dispersion (Ψ), path multiplicity, spread, mid-price, volume and count measures, execution depth, penetrated-layer count, order imbalance, and realized volatility. Four empirical campaigns were conducted. Campaign I is retained as pilot/discovery evidence, while Campaigns II–IV constitute the main dual-side empirical corpus. The final Campaign IV corpus contains 8,019,919 observation rows and 80,817 Ψ>0 events. Event/log matching, timestamp integrity checks, contamination diagnostics, and strict one-to-one non-overlapping matched-control procedures were applied before forward comparisons. The empirical evidence indicates that Structural Dispersion (Ψ) can be computed and repeatedly observed as a structural state/event within the selected market representation. Ψ>0 observations are measurably separated from Ψ=0 matched controls in subsequent market-microstructure behavior. The study therefore provides empirical support for the operational measurability and observability of containment/path-based structural depth and Structural Dispersion within the tested representation. The study deliberately maintains a strict epistemic boundary. It does not establish causality, universal price direction, out-of-sample prediction, alpha, profitability, or a complete empirical validation of the broader Structural Depth framework. Spectral accessibility, representation-independent invariance, quantum/non-commutative topology, entropy unification, and the quantitative waiting-time formulation of the Structural Depth Law of Time remain outside the tested scope. The research is designed as a reproducible computational empirical study. The accompanying source-code archive provides the implementation used for the computational and empirical analysis, while the manuscript documents the definitions, validation procedures, data-integrity controls, matched-control design, robustness analyses, result-artefact structure, and epistemic boundaries required for interpretation. Related research and computational infrastructure: This study forms part of the Structural Depth Research Program and the broader Market Alchemy Research architecture developed by Halil İbrahim Güven. The research program connects theoretical work on Structural Determination and Structural Depth with computational experimentation, empirical validation, and market-microstructure observation. Research program: Market Alchemy Research — marketalchemy.io Related software archive: Zenodo DOI 10.5281/zenodo.22062622 Keywords: Structural Determination; Structural Depth; Structural Dispersion; containment; containment graph; market microstructure; order book; structural observability; matched controls; empirical robustness; computational validation; quantitative finance; reproducible research; structural measurement; Market Alchemy.