Part II Article: every fiber of the marked-root Keller family.
GPT‑5.6‑Sol performed the main mathematical derivation in an investigation I prompted and directed.
For Kₙ: ℂⁿ → ℂⁿ, n ≥ 3, we determine every fiber, the exact image, omitted-locus codimension ⌈n/2⌉, and the precise nonproperness locus.
Main formula: |Kₙ⁻¹(P)| = (n−2)s(P) − (n−3)𝟙[P(0)=0].
Self-contained proof, public code and exact symbolic verification. Independent review welcome.
https://t.co/hpJhasRMpw
@jdlichtman, @tszzl, @polynoamial, @QiaochuYuan, @littmath, @AndrewCurran_
New article: An Explicit Infinite Family of Counterexamples to the Jacobian Conjecture
Starting from the ℂ³ map announced by @alpoge, we construct non-injective Keller maps in every dimension n ≥ 3 with det J(Kₙ) = (n−2)/2 and generic degree n(n−2).
These are not identity-coordinate paddings of the original map.
Independent mathematical review is strongly welcomed.
https://t.co/yGvfvu7uT9
@jdlichtman, @tszzl, @polynoamial, @QiaochuYuan, @AcerFur, @chetaslua, @AndrewCurran_