CNVS, Formal Mathematical Synthesis.
Year: 2026
Type: preprint
Abstract: This document constitutes the compact and definitive mathematical formalization of the Closed Native Verification Systems (CNVS) theory. The manuscript synthesizes the topological, probabilistic, and thermodynamic foundations that allow a distributed network to transcend the classical limits of Byzantine Fault Tolerance (BFT). By unifying the combinatorial calculus of graphs with Shannon's Information Theory, the CNVS framework demonstrates how the security of a global secret can be transformed into an emergent property of the topological space, guaranteeing the epistemic isolation of nodes even under scenarios of dependent collusion and massive corruption. Core Contributions Emergent Security Scaling Theorem (Theorem 4): Mathematically proves that the global probability of compromise ({P}(Rec*)) decays exponentially toward zero as the structural fragmentation depth (m) increases, overwhelmingly neutralizing the adversary's inference capacity regardless of their computational power. Thermodynamic Equivocation Limit (Remark 18a.2): Integrates probabilistic security equations with Shannon's dynamic residual entropy (H(S(t)|W(t))), proving that the combinatorial explosion of the orthogonal topology unconditionally dominates the temporal erosion of global uncertainty. Topological Underdetermination & Entropy Separation (Lemmas 8 and 10): Proves the orthogonal separation between verification metadata and payload entropy (I_{payload}), ensuring that the physical accumulation of fragments does not equate to a semantic gain. Global Veto Property (Corollary 19a): Replaces traditional majority-based consensus mechanisms with a zero-tolerance cryptographic veto paradigm against state manipulations. Release Notes - Version 6.2 (Changelog) Version 6.2 represents a formal and epistemological major revision of the framework, featuring the following critical updates: Dynamic Thermodynamic Transition: Introduced temporal parameterization (t) to model the dynamic decay of residual entropy during a progressive attack. The heuristic inference probability has been completely replaced with an exact analytical function based on Shannon's equivocation. Unification of Equations 36 and 37: The combinatorial impact of corrupted nodes (q) and the entropic inference driven by accumulated information ({E}(W(t))) are now fused into a single, mathematically unassailable operator. Rigorous Mathematical Typesetting: Definitive and rigorous typographic distinction among the Structural Universe ({S}), Power Set / Complexity Classes ({P}), and Probability Measures ({P}). Refinement of Decidable Limits: Optimization of the boundary conditions for Lemma 9 (Decidability Constraint) and formalization of the initial equivalence at time t_0 (H(S(t_0)|W(t_0)) \equiv H(S_{max})).
Author: Comitato, Massimo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162115278
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