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Releases: ipitchford/cyclicity-root-span-low-rank

v0.1.0-candidate — Fixed-seed cyclic rank as reduced inverse-root span

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@ipitchford ipitchford released this 09 Aug 21:59

Plain-English summary

An exponential integral can generate a differential equation when it is
differentiated repeatedly. This candidate asks how many genuinely different
directions one chosen starting form produces.

Conditional on the fixed-seed stationary-phase bridge established in the
parent release,
the answer is obtained by counting the independent inverse-root functions of
the polynomial after removing their common average.

For indecomposable polynomial phases, powers have rank one, Chebyshev phases
have rank two, and indecomposable quartics have rank three. The package also
contains a finite exact calculator. A degree-twelve example shows why the
decomposable case remains open: symmetry can make separate root blocks
coincide.

Assurance boundary

This is an anonymous, unrefereed candidate. Producer-side replay passes.
Independent reproduction, formal verification, external specialist review,
editorial peer review, and novelty or priority determination have not
occurred.

DOI: 10.5281/zenodo.21864884