成功概率动态模型的数学表达与完整论述

This paper establishes a formal mathematical framework for the Dynamic Success Probability Model, the second of the three core methodological pillars of the "Productive Political Philosophy" system. Utilizing a multiplicative structure combining four variables—Structural Completeness (S), Leadership (L), Kernel Inheritability (H), and Historical Opportunity (O)—along with two coefficients—Subjective Agency Coefficient (α) and Objective Constraint Coefficient (β)—the model strictly separates subjective agency from objective conditions. Within the objective variables, H is further distinguished into core ideological inheritability (H_core) and carrier inheritability (H_carrier), and its modes of inheritance are divided into complete and selective inheritance. O is distinguished into long-term structural opportunities and short-term event-driven opportunities. Within subjective variables, S encompasses the dual criteria of logical consistency and historical validity, and its completion is categorized into deep-level structural completion versus surface-level completion. The model reveals a dynamic weighting mechanism: under normal competition, objective conditions dominate; during "Founding Moments" and "Turning Points," subjective agency sharply rises. Crucially, it makes a precise distinction regarding the constraint of H: during Founding Moments, H acts as a broad, diffuse directional constraint shaped by material production modes and survival experience; during Turning Points, H acts as a concrete, highly textualized, and institutionalized constraint of specific options. Consequently, L plays a creative role during Founding Moments (constructing a structurally complete S in the direction set by H), and a confirmatory role during Turning Points (making the final confirmation among the options set by H, thereby slightly advancing or delaying the historical process). Through numerical simulations of three classic cases—Mohism, Early Confucianism, and the Zhou Rites—the model intuitively demonstrates how multiplicative relationships lead to drastically different historical outcomes. Finally, it derives four core principles and elucidates the model's philosophical implications and boundaries. Keywords: This paper establishes a formal mathematical framework for the Dynamic Success Probability Model, the second of the three core methodological pillars of the "Productive Political Philosophy" system. Utilizing a multiplicative structure combining four variables—Structural Completeness (S), Leadership (L), Kernel Inheritability (H), and Historical Opportunity (O)—along with two coefficients—Subjective Agency Coefficient (α) and Objective Constraint Coefficient (β)—the model strictly separates subjective agency from objective conditions. Within the objective variables, H is further distinguished into core ideological inheritability (H_core) and carrier inheritability (H_carrier), and its modes of inheritance are divided into complete and selective inheritance. O is distinguished into long-term structural opportunities and short-term event-driven opportunities. Within subjective variables, S encompasses the dual criteria of logical consistency and historical validity, and its completion is categorized into deep-level structural completion versus surface-level completion. The model reveals a dynamic weighting mechanism: under normal competition, objective conditions dominate; during "Founding Moments" and "Turning Points," subjective agency sharply rises. Crucially, it makes a precise distinction regarding the constraint of H: during Founding Moments, H acts as a broad, diffuse directional constraint shaped by material production modes and survival experience; during Turning Points, H acts as a concrete, highly textualized, and institutionalized constraint of specific options. Consequently, L plays a creative role during Founding Moments (constructing a structurally complete S in the direction set by H), and a confirmatory role during Turning Points (making the final confirmation among the options set by H, thereby slightly advancing or delaying the historical process). Through numerical simulations of three classic cases—Mohism, Early Confucianism, and the Zhou Rites—the model intuitively demonstrates how multiplicative relationships lead to drastically different historical outcomes. Finally, it derives four core principles and elucidates the model's philosophical implications and boundaries.