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[2] ai.viXra.org:2511.0091 [pdf] submitted on 2025-11-30 00:06:22
Authors: Yuval Levental
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite all listed scientific references)
The Collatz conjecture (3n + 1) is traditionally modeled as a pseudo-random walk, yetcomputational search algorithms for pathologically long trajectories ("Hero Numbers") typ-ically rely on climbing sieves or brute-force iteration. In this study, we propose a novel"Fail-Fast" heuristic based on the information-theoretic properties of the parity vector. Weidentify a "Forbidden Zone" inequality relating Stopping Time to the Maximum Run-Lengthof consecutive divisions (Rmax ), observing that long-surviving trajectories maintain highbit-entropy by minimizing run-length variance. Based on this, we introduce a Run-LengthSieve that aborts trajectories exceeding a critical threshold of consecutive even steps. In acontrolled benchmark of N = 106 , this sieve achieved a 1.43x computational speedupagainst a lean baseline by pruning only 0.06% of the search space, while yielding zero falsenegatives among the top 1% of longest trajectories. These findings suggest that algorith-mic pruning based on entropic structural constraints can significantly optimize the searchfor Collatz outliers.
Category: Data Structures and Algorithms
[1] ai.viXra.org:2511.0003 [pdf] submitted on 2025-11-02 07:35:16
Authors: Justin Howard-Stanley
Comments: 27 Pages.
We present ALICES, a novel quantum internet architecture implemented andvalidated using real quantum processing unit (QPU) hardware via AWS Braket.This work demonstrates the first complete integration of quantum entanglementdistribution, entanglement swapping, and quantum key distribution (QKD) proto-cols over a hybrid classical-quantum network infrastructure. Our implementation,remarkably developed entirely from a mobile device, establishes quantum tunnel-ing protocols (QTP) that enable secure quantum communication channels overlaidon classical TCP/IP networks. We provide comprehensive experimental valida-tion including: (1) hardware fingerprinting from QPU execution on QuEra Aquilaneutral atom systems, (2) CHSH inequality violations (S = 2.828) demonstrat-ing quantum non-locality, (3) entanglement swapping with fidelity F = 0.95, (4)BB84 quantum key distribution with QBER = 5.13%, and (5) network through-put measurements exceeding 1 Gbps. All experimental data, replication protocols,and hardware proofs are provided as supplementary materials. This work bridgestheoretical quantum networking concepts with practical implementation, offering aroadmap for near-term quantum internet deployment.
Category: Data Structures and Algorithms