Schrödinger's Cat as a Three-Regime Structural Transition: A Structuristics Instantiation in the Quantum Measurement Domain

This working paper instantiates the Structuristics framework (DOI: 10. 5281/zenodo. 19636897, v2. 0. 0) in the quantum measurement domain, reinterpreting the Schrödinger cat paradox as a three-regime structural transition governed by Decompositional Integrity ID (t) rather than a binary collapse event. The central argument is that wave-particle duality is the shadow of a ternary structure projected onto a binary observational frame: two regimes are structurally insufficient to describe a genuine transition, and the absent intermediate regime produces the apparent paradox. The paper formalises a modified Schrödinger equation with an entropic trigger gamma (t) driven by the time-averaged integrity IDbar (t), which carries memory of the initial state and activates only under accumulated structural drift, not under reversible oscillations. Norm conservation is proved explicitly for the deterministic part; a stochastic extension recovers Born-rule statistics via the Ito convention; a scale estimate tau₀ (N, alpha) derives the empirical invisibility of the Corrigible regime for macroscopic systems. The mechanism is traced to its origin in CAMAF 2. 0. 3 (DOI: 10. 5281/zenodo. 19076532) via the Newton-Einstein-Eddington logistic model, of which this paper is the fourth domain instantiation. The paper is fully compliant with CAMAF CS2 (Standards 1-10 declared, Standard 6 satisfied at claim level via inline epistemic labels). Five falsifiable predictions are stated (Q1-Q5). The primary discriminating test of Q5 is the Akaike Information Criterion comparison between logistic and exponential decay models on individual quantum trajectory records of IDbar (t): the ternary framework predicts logistic decline with an identifiable inflection point tC > 0, whereas standard exponential decoherence has its inflection at t = 0. Simulation against the validated Bayesian model of Chantasri et al. (2016, Physical Review X 6, 041052) shows mathematical consistency with the logistic structure; analytic confirmation is provided by the exact parity-meter solution of that paper, which is the logistic function ID (t) = 2/ (1 + exp (t/tauₘ) ), derived independently of this framework. The Englert complementarity relation V² + D² <= 1 is identified as the existing experimental signature of the ternary structure, with IDbar (t) proposed as its natural parametrisation. The paper introduces the Evolutionary Fractal concept and the cross-domain prediction P-FE1. The Evolutionary Fractal mechanism was not derived from the Structuristics framework: it was discovered empirically during the galactic rotation curves work (DOI: 10. 5281/zenodo. 19872381) through the author's active search beyond the RAR baseline, subsequently formalised in Structuristics v2. 0. 0, and applied here as the first deliberate framework-guided test in an independent domain. Two confirmed instances are documented: the galactic domain (Delta R² = 0. 033 over RAR baseline, circularity = 0%, permutation p = 0. 000) and the quantum domain (Q5 simulation result). A third instance is identified within the Structuristics corpus itself via the declared N-E-E transition between Core Operators and Axiom System D0-D6 in Structuristics v2. 0. 0. A condensed three-class residue taxonomy (R1 structural, R2 indeterminate, R3 genuinely stochastic) is introduced; full treatment is reserved for a dedicated paper. The paper is updated to full Structuristics v2. 0. 0 compliance: ID reframed as operator behaviour metric per D0-D6 interpretation; D3 (non-injectivity) declared in the quantum domain as a theorem via Born rule and pigeonhole argument; rho (t) = 1 - ID (t) introduced as a first-class residual object; Admissible Instantiation compliance declared (Conditions 1-5, Condition L, K (y), CEF, H-Amp). The relationship between the Evolutionary Fractal and H-Amp is explicitly distinguished. The Bohr-Einstein debate is reanalysed as a projection artefact: Copenhagen, Everett, GRW/CSL, and Lindblad decoherence each describe a valid projection of the ternary structure onto a binary screen. Files are restricted pending confirmation of Q5 against raw experimental data. Use of AI assistance is declared.