Scalar recurrence sequences with finitely repairable power subsequences

Henry Zweiman — September 8, 2026

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A finite algebraic classification for scalar power subsequences of integral recurrences. It includes repeated roots, periodic cancellations, and finite transients; identifies the exact coefficient-field exponent in the nondegenerate case; proves eventual periodicity of the admissible exponents; and gives a terminating least-multiplier computation for sampling powers greater than one.

Status: complete manuscript with internal proof, source, and artifact checks. It is a proposed research contribution, not externally peer reviewed. Historical priority and journal-level significance remain provisional. The problem is formulated as a classification question here, not attributed to an invented named conjecture.

• Source and significance assessment
• Proof and artifact audit
• Exact finite checks and results
• Artifact manifest

Run the standalone consistency checks with python3 check.py. Compile manuscript.tex with Tectonic or an appropriate LaTeX installation. The full Markdown was converted with the research program's Pandoc/AUX-numbering workflow and syntax checked with MathJax 3.2.2; the adjacent reports record the exact source and output hashes.

This is one consolidated paper. Its classification, corollaries, examples, and algorithm are not counted as separate papers.