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

# Structuristics v2.0.0: A Formal Framework for Coupled Construction and Decomposition as a Necessary Structural Condition **Version 2.0.0** – Major revision introducing axiom system D0–D6, the promotion of D3 to a theorem, and the N-E-E model applied to the corpus itself. ## Abstract This paper proposes **Structuristics** as a formal field of inquiry investigating whether coupled **Construction (C)** and **Decomposition (D)** operations constitute a necessary structural condition for any process that produces and maintains organised structure, independently of substrate, scale, or domain. The central metric is **Decompositional Integrity**, *ID* ∈ [0,1]*, defined as the normalised distance between a structure and its reconstruction under a domain-appropriate distance function. A three-state regime framework (**Homeostatic**, **Corrigible**, **Reconstitutable**) provides the basis for cross-domain comparison and prediction. ## Key Innovations in v2.0.0 - **Axiom System D0–D6**: A formally structured description of operators providing greater logical resolution than the inherited Core Operators definition. - **D3 as Theorem**: The non-injectivity of D is derived by pigeonhole argument – a mathematical consequence of the structural domain being infinite and the image of D being finite, requiring no symmetry and no triangle inequality. - **N-E-E Model Applied**: Sections 2.1 and 2.6 coexist as a declared instance of the N-E-E model applied to the corpus itself, with the Eddington event identified and dated, the criterion of hegemony declared, and the current state stated as post-Eddington but pre-hegemony. ## Admissible Instantiation Definitions – Three Additions - **(L)** Asymmetric distance functions - **Organisational complexity measure *K(y)*** derived from the fibre structure of D - **Constructive Expansion Factor (CEF)** – a declarable condition for instantiations invoking the **Amplification Hypothesis (H-Amp)**, which is formalised as a conditional hypothesis dependent on CEF (not derivable from D1–D6 alone). ## Falsifiability and Predictions - **Meta-level prediction P-Meta** – a falsifiable prediction derived from D6. - **Universality Falsifiability Criterion** stated with two independent thresholds: proportional and absolute. - **Five non-circular validation tests** reported with verdicts (Test 4 deliberately deferred). - **Fifteen predictions** stated with explicit falsification conditions. ## Interpretation of *ID* Explicitly reestablished as measuring the behaviour of the operator over objects, not intrinsic properties of the objects. ## Domain-Specific Instantiations Developed for: - Physical dissipative structures - Morphogenetic systems - Ecosystems - Legal corpora - Scientific fields - Pedagogical systems - Musical works - Language systems (including large language models) - The EML mathematical operator - Galactic rotation curves ## Compliance Produced under **CAMAF CS2 compliance** and follows the **CAMAF Author's Manual v0.5.0** standards for structural transparency, falsifiability declaration, and epistemic labelling.