The WKB Geometry of Newton Polygons: A Functorial Classification Theory

This release publishes the camera-ready manuscript The WKB Geometry of Newton Polygons: A Functorial Classification Theory together with its full Phase I–V computational atlas, refereed Round-1 and Round-2 revision packages, and submission-ready arXiv and journal bundles. For a scalar local linear operator L (differential, difference, or q-difference) with one irregular singularity at x = ∞ whose Newton polygon has a unique dominant edge of slope −p/q with r + 1 lattice points, the WKB ansatz on that edge produces a characteristic polynomial χ ∈ C[c]. Our central algebraic identity is χ(c) = χw(cq), where χw ∈ C[w] is the classical edge-indicial polynomial of degree r. The exponent constellation C(L) ⊂ C is therefore a μq-equivariant union of r fibres of c → cq over Roots(χw). This factorisation organises a finite stratified atlas: a computational sweep yields 23 single-edge classes for −p/q ∈ {1/2, 1/3, 1/4, 2/3, 3/2} and r ≤ 3, refining to 39 classes once multi-edge, nested-ramification, and prime-q arithmetic strata are tracked. We prove a per-edge factorisation along the slope filtration, an iterated μq′-pullback law for nested inner polynomials, a block-diagonal pullback for systems, and a prime-q Kummer dichotomy separating the algebraically independent stratum from the cyclotomic stratum. The analytic input attaching anti-Stokes directions is classical (Levelt–Turrittin, Sibuya, Wasow); on the q-fold cover the rays of a generic single-edge operator satisfy arg Δij + pφ ≡ π/2 (mod π). One explicit consequence: the slope numerator p, invisible to C(L), is visible to the cover-side ray pattern. The analytic statements (Theorems AT1, AT3, AT5, AT7) are μq/μq′-equivariant repackagings of classical formal-classification theory. Release contents. Camera-ready LaTeX manuscript (26 pp, 898 KB PDF, byte-identical compile across all bundles), the full Phase I–V computational atlas (19 JSON artifacts, ~2.6 MB), the arXiv-ready and journal-ready submission bundles, the eight in-manuscript theorem proofs (M1, N1, D2, S1, AT1, AT3, AT5, AT7), the agent-pipeline scripts (fleet.py … fleet5.py), the phase reports, and the Round-1 + Round-2 refereed revision packages. Repository. A stable, versioned public GitHub mirror of this Zenodo release is at https://github.com/papanokechi/wkb-newton-polygons; the manuscript points to it from the Reproducibility paragraph of the Computational and AI Disclosure section. Dual licensing. All text, figures, and the JSON atlas are released under CC-BY-4.0; all code and fleet scripts are released under MIT. See LICENSE-TEXT and LICENSE-CODE in the record.