Author

K. Osipov

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Preprint Aug 2026

Step Recursion: Mixed Stride Spectra, Path Factorization, and Synchronization Geometry

Step recursion allows recursive computation to move through a canonical hierarchy in jumps, or strides. Suppose a function algebra is allowed to use several primitive stride lengths $L$. Composition immediately produces sums of these lengths, but it is not clear whether arbitrary nesting of mixed recursions can create...

K. Osipov · 0 citations

Preprint Aug 2026

Step Recursion: Exact Depth Does Not Determine Algebraic Expressiveness

Step recursion is a form of bounded recursion in which each recursive call moves from an input y to a prescribed predecessor $\rho_g(y)$. Its depth $D_g(y)$ is the exact number of such moves needed to reach zero. A natural question is whether knowing this depth for every input determines the expressive power of the res...

K. Osipov · 0 citations

Preprint Aug 2026

Step Recursion: Resource Profiles and Descent Quotients

A resource representation for step recursion in which mutable-state width and recursion descent are explicit and independent parameters is developed, and profile domination quotients effective descents by admissible width reparameterization are developed.

K. Osipov · 1 citation