What does this research mean for the field?

The extension structure of the full linear stabilizer of a specific configuration of 1,024 six-dimensional subspaces over the binary field is a nonsplit special 2-group governed by four copies of the 2×2 matrix-multiplication tensor. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine the exact extension structure and geometric properties of the full linear stabilizer for a configuration of 1,024 six-dimensional binary subspaces.

August 24, 2026Open Access

A Nonsplit Special 2-Group Extension Governed by the 2×2 Matrix-Multiplication Tensor

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To determine the exact extension structure and geometric properties of the full linear stabilizer for a configuration of 1,024 six-dimensional binary subspaces.
Characterized linear stabilizers, flag kernels, and quotient group actions over the binary field.
Utilized the CARMA-Math AI-assisted workflow and deterministic verification software to perform exact algebraic computations over binary and integer fields.
Proved the stabilizer extension is nonsplit, identifying the inverse image of the translation subgroup as a special 2-group of order 2^43 with a faithful quotient of order 2^36.
Demonstrated that the structural mechanism is governed by four copies of the 2x2 matrix-multiplication tensor, explaining the operator rank distribution and Segre geometry.
Resolved the involution-liftability distribution for all 65,536 translation cosets while computing the conjugacy-class number and commuting probability.

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Implication

Mathematical analysis demonstrates a nonsplit special 2-group extension across 1,024 binary subspaces, revealing algebraic structure governed by matrix-multiplication tensors.

Cite This Study

Akihiro Koide (2026) studied this question.

synapsesocial.com/papers/6a8c0086bca056c88e6df41f https://doi.org/10.5281/zenodo.22053804

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Implication

Mathematical analysis demonstrates a nonsplit special 2-group extension across 1,024 binary subspaces, revealing algebraic structure governed by matrix-multiplication tensors.

A Nonsplit Special 2-Group Extension Governed by the 2×2 Matrix-Multiplication Tensor

Key Points

Discussion

Implication

Cite This Study

A Nonsplit Special 2-Group Extension Governed by the 2×2 Matrix-Multiplication Tensor

Key Points

Discussion

Implication

Cite This Study

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