Reset Dynamics, Paper 2: Structural Closure and Generative Rupture

This paper presents the formal core of Reset Dynamics (RD) as a constrained generative system over well-founded structures. It provides a complete, operational answer to the foundational questions raised in the first RD paper (Pan, 2026a, Zenodo 19373151). Two primitive notions drive the framework:1. Structural Closure (1): The minimal unit of structural closure, defined up to isomorphism, satisfying internal completeness, boundary definability, minimality, and iterative stability.2. Generative Rupture (÷_rupture): A novel operator defined as Gen(R, Γ, x), which maps a structure x to the set of all structures reachable under rule set R within resource budget Γ. Six core theorems establish structural duality, contradiction-freedom, information expansion, paradox-as-rupture, state space closure, and the fixed-point property of the closure unit under generation. The framework is a conservative extension of classical arithmetic and includes executable pseudocode. THIS FILE: main.tex (LaTeX source). Compile to reproduce the PDF.