What question did this study set out to answer?

This work aims to establish a new quotient-Jacobian identity and classify (1,-1,-2)-equivariant Keller maps up to degree four.

July 23, 20260 citationsOpen Access

Quotient-Jacobian Identity and Classification of (1,-1,-2)-Equivariant Maps

A quotient-Jacobian identity for the full (1,−1,−2)-equivariant class containing the July 2026 counterexample to the Jacobian conjecture, with an unconditional classification through degree four

View Full Paper

Ask AI

Bookmark

Authors

MSMinus T Squared

Discussion

Member takes

Overview

Randomized trial classifies (1,-1,-2)-equivariant Keller maps, indicating clear polynomial automorphisms.

Key Points

This work aims to establish a new quotient-Jacobian identity and classify (1,-1,-2)-equivariant Keller maps up to degree four.
Introduced a new explicit quotient-Jacobian identity for equivariant polynomial maps.
Classified (1,-1,-2)-equivariant Keller maps of polynomial degree at most four through computational reproduction.
Utilized exact-arithmetic certificates for verification without reliance on AI reasoning.
Every (1,-1,-2)-equivariant Keller map of degree at most four is proven to be a polynomial automorphism.
Explicit polynomial inverses and verification of compositions were provided for all classified maps.
The classification is the first of its kind for degree at most four in this equivariance class.

Cite This Study

Minus T Squared (2026) studied this question.

synapsesocial.com/papers/6a61b004faa9903c5116ab06 https://doi.org/10.5281/zenodo.21479447

View Full Paper

Ask AI

Bookmark

July 23, 20260 citationsOpen Access

Quotient-Jacobian Identity and Classification of (1,-1,-2)-Equivariant Maps

A quotient-Jacobian identity for the full (1,−1,−2)-equivariant class containing the July 2026 counterexample to the Jacobian conjecture, with an unconditional classification through degree four

View Full Paper

Ask AI

Bookmark

Authors

MSMinus T Squared

Discussion

Member takes

Overview

Randomized trial classifies (1,-1,-2)-equivariant Keller maps, indicating clear polynomial automorphisms.

Key Points

This work aims to establish a new quotient-Jacobian identity and classify (1,-1,-2)-equivariant Keller maps up to degree four.
Introduced a new explicit quotient-Jacobian identity for equivariant polynomial maps.
Classified (1,-1,-2)-equivariant Keller maps of polynomial degree at most four through computational reproduction.
Utilized exact-arithmetic certificates for verification without reliance on AI reasoning.
Every (1,-1,-2)-equivariant Keller map of degree at most four is proven to be a polynomial automorphism.
Explicit polynomial inverses and verification of compositions were provided for all classified maps.
The classification is the first of its kind for degree at most four in this equivariance class.

Cite This Study

Minus T Squared (2026) studied this question.

synapsesocial.com/papers/6a61b004faa9903c5116ab06 https://doi.org/10.5281/zenodo.21479447

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

View Full Paper

Ask AI

Bookmark