Published August 23, 2026
| Version 0.1.0-candidate
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Effective Fourier certificates for the full e=4 Polydegree column
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Description
Anonymous unrefereed three-paper candidate bundle. The principal paper proves the full e=4 Polydegree containment for every integer d >= 2 using published low-degree input, an exact residue class, 14,985 outward-rounded FLINT/Arb certificates, and an explicit eventual analytic branch. Companion papers provide a Lean-checked universal bordered-Jacobian identity over arbitrary commutative rings and a conditional finite-pencil boundary-norm transfer theorem. Producer-side replay and internal AI editorial review are recorded. Independent reproduction, external specialist review, journal peer review, Furter R(3), JC2, and HC4 are not claimed.
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boundary-norm-finite-pencil-v0.1.0-candidate.pdf
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Additional details
References
- Lewis, D., Perry, K., & Straub, A. (2019). An algorithmic approach to the Polydegree Conjecture for plane polynomial automorphisms. Journal of Pure and Applied Algebra, 223(12), 5346--5359. https://doi.org/10.1016/j.jpaa.2019.04.002
- Perry, K. A. (2016). Polydegree properties of polynomial automorphisms. Doctoral dissertation, The University of Alabama. https://ir.ua.edu/items/f71aa1b3-0dbc-42a2-9f59-3f01eb1a5529
- Furter, J.-P. (2009). Plane polynomial automorphisms of fixed multidegree. Mathematische Annalen, 343, 901--920. https://doi.org/10.1007/s00208-008-0296-2
- Anonymous. (2026). A Jacobian smooth-point criterion and the full e=3 column of the Polydegree Conjecture (Version 0.1.0-candidate). https://doi.org/10.5281/zenodo.21909085