Number Theory

    

Symbolic Collapse Grammar and the Convergence of the Collatz Function

Authors: Travis Shane Taylor

We propose a symbolic gateword encoding of the Collatz transformation, demonstrating that all positive integers reduce to the fixed point 1 via finite symbolic collapse. By reformulating the Collatz function as a compressible grammar and defining collapse as a symbolic entropy-reduction process, we offer a constructive resolution to the conjecture and frame it as a computational attractor with implications for number theory, complexity, and information physics.

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[v1] 2025-05-14 19:46:41

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