Structuristics: A Formal Field for the Study of Constructive and Decompositional Dynamics Across Domains, Substrates, and Scales

This work introduces Structuristics as a research program concerned with identifying the structural conditions required for organized persistence across domains. The central hypothesis is that coupled operations of Construction and Decomposition (C/D) constitute a necessary structural condition for systems that produce and maintain organized structure, independent of substrate, scale, or domain. The framework emerges from a traceable derivation chain: CAMAF establishes criteria for distinguishing fact from opinion in representational systems; the Fundamental Principle of Intelligence (FPI) identifies C/D as a minimal condition in systems considered intelligent; Structuristics extends this question to persistence itself, treating intelligence as a special case within a broader structural class. A formal metric, Decompositional Integrity (I_D), is defined as the normalized distance between a structure and its reconstruction after decomposition. From this, a three-regime structure is derived using domain-calibrated thresholds. The framework is instantiated across multiple domains, including physical dissipative systems, morphogenetic processes, ecosystems, legal corpora, scientific fields, pedagogical systems, musical structures, linguistic systems, and large language models. An independently developed result, the EML operator (Odrzywolek, arXiv:2603.21852), provides a formal confirmation within a closed domain that the absence of a decomposition-equivalent component leads to structural incompleteness. This constitutes a confirmed instance of Prediction 0 of this program, without implying a general proof of C/D duality. A defining methodological feature of this work is the requirement that every operational formal expression is accompanied by algorithmic prose. This consists of explicit procedural descriptions of what each expression computes, what each term represents, how the operation is applied step by step, and how its output is interpreted. This requirement is not motivated by accessibility alone, but by three structural conditions: (1) compliance with the CAMAF principle of traceability, which requires that no transformation remain implicit; (2) the transdomain scope of the framework, which includes fields that do not rely on mathematical notation; and (3) a methodological commitment that the ability to decompose a knowledge structure should not depend on prior credentialing in any formal system. This work is positioned within a broader effort to promote the structural opening of knowledge. It argues that the value of a scientific work lies not in its institutional context of production, but in the degree to which its claims are traceable, auditable, and reconstructible by independent agents. The availability of open-access infrastructures enables the publication of works that prioritize these criteria, even when they diverge from conventional editorial standards. The objective is not to replace existing scientific institutions, but to propose stricter structural criteria for knowledge production, in which formal compression and procedural decomposability are treated as epistemologically equivalent representations of the same operations.