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[3] ai.viXra.org:2601.0077 [pdf] submitted on 2026-01-19 20:15:09
Authors: Tzanko Golemanov, Emilia Golemanova
Comments: 13 Pages.
The digitization of democratic processes faces a persistent trilemma: achieving strong voter anonymity, endu2011tou2011end verifiability, and resilience against coercion and credential loss. Existing eu2011voting systems typically sacrifice recovery mechanisms to preserve anonymity or rely on persistent digital identities that introduce privacy and insideru2011threat risks. This paper presents Arcaunt (from "ARC" and "Accountability"), a scalable eu2011voting architecture that resolves these tensions through a hybrid design combining airu2011gapped physical credential distribution with an Anonymous Recovery Channel (ARC). ARC enables voters to autonomously revoke and replace compromised tokens without revealing personally identifiable information. We provide a comprehensive security analysis under a modified Dolev—Yao model, demonstrating resistance to coercion, insider attacks, clientu2011side compromise, and voteu2011selling incentives. The architecture integrates SHAu20113 hashing, ECCu2011based verification, and zku2011SNARK proofs to ensure efficient revoting integrity. A performance evaluation shows that credential generation and ledger validation scale to national deployments, while a 10u2011year economic model indicates an over 85% cost reduction compared to traditional paperu2011based elections. A functional web prototype is under development to assess usability and realu2011world performance of the ARC and sequential validation mechanisms. Arcaunt offers a practical and accountable blueprint for globalu2011scale digital democracy.
Category: Data Structures and Algorithms
[2] ai.viXra.org:2601.0062 [pdf] submitted on 2026-01-16 11:18:17
Authors: Joshua Christian Elfers
Comments: 9 Pages.
We demonstrate that the carry-coupled skew-product extension of the Collatz map over finite fields Z_p contains a computationally universal subsystem. By identifying a "Transistor Interval" where arithmetic magnitude constraints function as logical switches, we construct a universal NAND gate from pure number-theoretic operations. This establishes that modular arithmetic dynamics are Turing Complete. Our proof proceeds by exhaustive verification over Z_p, demonstrating that the invariant set W_4 (defined by integers n where 4n < p) forms a Local Identity Monoid capable of exact information storage (RAM), and that signal interactions within this set implement universal Boolean logic (CPU). We classify the system as a Piecewise Isometry, distinguishing it from stretching-based chaotic systems and placing it within the framework of reversible computing.
Category: Data Structures and Algorithms
[1] ai.viXra.org:2601.0017 [pdf] replaced on 2026-06-01 20:18:04
Authors: Mirko Netz
Comments: 357 Pages.
This work presents a formal proof of the functional identity P = NP using differential geometric complexity theory within a non-classical framework of hypercomputation. By employing an adaptive axiomatic system embedded within a finite-dimensional pseudo Euclidean vector space V, which induces a continuous hyperbolic space H^2, the classical partitioning of P != NP is reinterpreted as a projection effect of an insufficient geometric embedding.We show that primordial symmetry breaking acts as a fundamental system invariant, reducing combinatorial complexity to the geometric necessity of an O(1) process. Driven by the gravity of geometry, the system forces complexity to converge into a self-regulating "Equilibrium State", where the global solution manifests as a stable geodesic trajectory (M, N). This paradigm shift demonstrates that the ultimate collapse of the complexity classes within a quotient space (NP/P) is driven by the physical necessity of maintaining a continuous relativistic equilibrium. Within this periodically and axiomatically condensed metric, the traditionally chaotic and temporal non-deterministic search process is entirely replaced by the structured, deterministic geometric embedding of the Adaptive Axiomatic System operating as a native model of hypercomputation. Within the framework of ZFC, this treatise establishes this equivalence as a cosmological law of transcendence, providing a unified resolution for the P versus NP problem under hypercomputational conditions and demonstrating how the Collatz conjecture is structurally integrated into the geometric dynamics of the spacetime matrix. This foundational mechanism is formalized as the "Axiom of Constant Existence", which dictates that the fundamental length of existence — the invariant hypotenuse — remains structurally conserved throughout all relativistic transformations. By demonstrating the trivial Collatz cycle (4; 2; 1) as a manifestation of universal scale invariance, we establish a quantitative fact: the convergence of discrete numerical sequences is a topological necessity within the gravitationally condensed manifold.Ultimately, guided by this Axiom, the spatial metric stabilizes at a constant, non-zero state of pulsating excitation (1 + ε). The resulting quantifiable comparison serves as final evidence for the mechanical equivalence between computational complexity and relativistic geometric dynamics.
Category: Data Structures and Algorithms