CNVS Extended Formal Theory: Emergent Security, Dependent Collusion, and Probabilistic Verification Dynamics

This work presents the extended formal development of the CNVS framework, including probabilistic security dynamics, dependent-collusion models, asymptotic reconstruction bounds, and emergent security scaling behavior. The document extends the core CNVS theoretical structure with:- threshold reconstruction probability models;- dependent and correlated collusion analysis;- Chernoff-style asymptotic security bounds;- information-density constraints;- epistemically restricted verification dynamics;- reconstruction consistency theorems;- emergent security scaling conditions;- critical-threshold collapse regimes. The framework is formulated as a formal distributed verification architecture based on recursive information fragmentation, local admissibility constraints, relational consistency, and verification-dependent state reconstruction. This version also integrates:- AI-assisted Lean 4 formalization workflows;- Mathlib-compatible verification modules;- probabilistic security formalization experiments;- asymptotic verification structures;- Monte Carlo compatibility analyses for emergent security behavior. The repository associated with this work contains:- Lean 4 proof modules;- formal verification experiments;- probabilistic security tests;- theorem outcome reports;- reconstruction-security integration tests;- asymptotic scaling verification artifacts. This document should be interpreted as a formal theoretical and verification-oriented preprint rather than a peer-reviewed finalized publication.