What does this research mean for the field?

A direct structural link exists between the low-rank Segre geometry and the complement cohomology of a specific forty-three-dimensional two-step nilpotent associative algebra over the binary field, governed by a shared character of the dihedral group. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine the intrinsic geometry, symmetry structure, and complement cohomology of a specific forty-three-dimensional two-step nilpotent associative algebra over the binary field.

August 24, 2026Open Access

Low-Rank Segre Geometry, Automorphism Groups, and Complement Cohomology of a Binary Two-Step Algebra

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AKAkihiro Koide

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Implication

Mathematical analysis uncovers Segre geometry and symmetry groups in a 43-dimensional binary two-step algebra, establishing structural links to complement cohomology.

Key Points

To determine the intrinsic geometry, symmetry structure, and complement cohomology of a specific forty-three-dimensional two-step nilpotent associative algebra over the binary field.
Analyzed the contraction ranks and polarization of the quadratic map induced by the 43-dimensional binary algebra.
Computed pseudo-isometry groups, automorphism groups, and module decompositions over the dihedral group using exact finite calculations.
Implemented the CARMA-Math AI-assisted mathematical research workflow for proof development and computational verification.
Identified a rank-three gap in contraction ranks, where the low-rank locus contains a canonical 5-dimensional subspace and forty-nine rank-4 points forming a finite Segre configuration.
Characterized full pseudo-isometry, automorphism, and outer automorphism groups via a single character of the dihedral group.
Demonstrated that a unique nonsplit pullback block and resulting cohomological obstruction are governed by the same dihedral character that controls geometric gluing.

Cite This Study

Akihiro Koide (2026) studied this question.

synapsesocial.com/papers/6a8c00d0bca056c88e6dfd6a https://doi.org/10.5281/zenodo.22062973

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Implication

Mathematical analysis uncovers Segre geometry and symmetry groups in a 43-dimensional binary two-step algebra, establishing structural links to complement cohomology.

Low-Rank Segre Geometry, Automorphism Groups, and Complement Cohomology of a Binary Two-Step Algebra

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Low-Rank Segre Geometry, Automorphism Groups, and Complement Cohomology of a Binary Two-Step Algebra

Discussion

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