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

This work introduces Structuristics as a formal research programme investigating whether coupled Construction and Decomposition operations (C/D) constitute a necessary structural condition for organized persistence across domains, substrates, and scales. 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 coupled C/D operations as a necessary structural condition for systems recognized as intelligent. Structuristics generalizes the question further, asking whether the same condition governs persistence and organization themselves, independently of intelligence attribution. Formally, the relationship is expressed as: FPI Structuristics meaning that the FPI is treated as the intelligent-systems subset of a broader structural field. The central metric of the framework is Decompositional Integrity: ID = 1 - d (y, yₕat) / Z, with yₕat = C (D (y) ) where ID measures the normalized fidelity between a structure and its reconstruction after decomposition. From this metric emerges a regime-based framework consisting of Homeostatic, Corrigible, and Reconstitutable structural states governed by domain-calibrated thresholds τ and τ₀. Version 1. 4. 3 expands the original field proposal with the formalization of the Structural Spectrum, defining the upper and lower boundary conditions of organized persistence. The framework establishes: ID = 0 as the dissolution limit, ID = 1 as the closure limit, and organized persistence constrained to the interval ID ∈ [τ, 1). The document also formalizes over-reconstruction regimes (ID > 1), interpreted either as projection artefacts or as indicators of structural stress under recursive compression. A major addition in this version is the N–E–E (Newton–Einstein–Eddington) model of temporal regime competition. The model introduces competing logistic structural curves, Eddington transition events, and the Limiting Approximation Principle as a substrate-independent mechanism for analysing paradigm replacement and structural hegemony transitions across scientific, symbolic, political, and economic systems. The framework is instantiated across multiple domains, including: physical dissipative structures, morphogenesis, ecosystems, jurisprudence, pedagogy, scientific replication, musical systems, large language models, galactic rotation curves, recursive narrative systems, and political social systems. Prediction 0, concerning D-type necessity in closed formal domains, now includes a confirmed weak-form instance through the independently developed EML operator (Odrzywołek 2026), where the absence of decomposition-equivalent operators produces structural incompleteness in a closed mathematical domain. The document also incorporates: the RENS framework (Solazzo 2026) as an independently derived candidate convergence case, the Babel Argument for political social systems, and an expanded methodological architecture including epistemic labels, validation criteria, and explicit falsifiability conditions. A defining methodological feature of Structuristics is the requirement that all formal expressions be accompanied by algorithmic prose: explicit procedural descriptions of what each expression computes, what each term represents, how the operation is performed, and how the result should be interpreted. This requirement reflects: CAMAF traceability standards, the cross-domain scope of the framework, and the principle that the ability to decompose knowledge structures should not depend on prior credentialing in a specific formal notation system. Structuristics is explicitly presented as a research programme rather than a confirmed theory. The work defines its own epistemological status, validation conditions, falsifiability requirements, and declared limits. The decisive validation condition proposed for Structuristics as a unified field is the simultaneous confirmation of cross-domain Predictions 8, 9, and 10. This document was produced under the CAMAF Scientific Production Methodology framework. Keywords: Structuristics; decompositional integrity; structural regimes; constructive-decompositional dynamics; CAMAF; Fundamental Principle of Intelligence; recursive systems; structural spectrum; NEE model; recursive decomposition; galactic rotation curves; RENS; Babel argument; political social systems; algorithmic prose; epistemology; recursive reconstruction; cross-domain systems; structural persistence; regime transitions.