Structural-State Mathematical Economics 

This paper proposes a Structural-State Mathematical Economics framework for stockmarket research. Its central claim is simple but consequential: the primary object of modeling should not be prices, returns, or isolated indicators, but rather a structure system jointly determined by multiple structural dimensions and their intrinsic constraints. Within this view, a stock market is represented as the structure object S stock = (D, F, R, Φ), where D denotes the set of structural dimensions-quality, growth, valuation, trend, momentum, volatility, volume-price, and macro constraints. The library R collects intrinsic cross-dimensional constraints, Ω ⊂ ∏ d∈D X d is the feasible set of admissible structural states induced by these constraints, and Φ is a manifestation operator that maps structural states to observable market outcomes (e.g., trend manifestation and regime-shift risk). Accordingly, a market state is defined as an admissible configuration (a structural state), and market dynamics are interpreted as transitions in a constrained state space, including boundary reconstructions when feasibility shrinks or constraints are reshaped. This unified language allows us to characterize structural consistency, structural mismatch, and structural collapse, while clarifying the hierarchy between price signals and structural causes. Our contribution is methodological and representational rather than predictive. We do not aim to deliver a trading strategy or to improve forecasting accuracy. Instead, we provide an extensible structure-first representation that diagnoses the structural changes behind model breakdowns and supplies structural priors and applicability boundaries for factor models, technical analysis, and machine-learning approaches. As an illustrative application, we use NVDA as a case study to describe its structural-state path under the coupling of technology cycles, expectation expansion, and macro constraints. The case demonstrates how the structural-state framework can explain phase stability, rising tension, mismatch manifestation, and the subsequent divergence into repair versus collapse, without relying on heavy econometric regressions.