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New symbolic search space aids Collatz conjecture investigation

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a novel symbolic search space to investigate the Collatz conjecture, utilizing finite exponent codes that track divisions by two after each 3n + 1 step. This approach defines a '2-3-infinity diagnostic' based on real drift, a 2-adic start representative, and a 3-adic endpoint representative. Experiments indicate that adaptive evolutionary search enhances trade-offs for finite-length codes, though all tested methods maintain positive residue rates, suggesting this framework serves as a diagnostic tool rather than a verification method. AI

RANK_REASON The item is an academic paper detailing a new method for investigating a mathematical conjecture. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv cs.NE (Neural & Evolutionary) →

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New symbolic search space aids Collatz conjecture investigation

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  1. arXiv cs.NE (Neural & Evolutionary) TIER_1 English(EN) · Oliver Kramer ·

    Adaptive Search in Collatz Exponent-Code Space via 2-adic and 3-adic Constraints

    We study a symbolic search space for the Collatz conjecture based on finite exponent codes of the accelerated map. Each code records the number of divisions by two after every 3n + 1 step and determines three quantities: real drift, a 2-adic start representative, and a 3-adic end…

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