What does this research mean for the field?

Exactly five probes are necessary and sufficient to separate all 3,568 dual orbits of the studied binary quadratic tensor, yielding a complete classification of 2,078,105 effective minimum systems characterized by a one-exchange graph with a unique giant component. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To classify the dual orbits of a 20-dimensional binary quadratic tensor and determine the minimum probe systems required to completely separate them.

August 27, 2026Open Access

Rank-One Syndrome Fibers, Minimum Orbit Separation, and Reconfiguration Geometry for a Binary Tensor Code

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To classify the dual orbits of a 20-dimensional binary quadratic tensor and determine the minimum probe systems required to completely separate them.
Assembled rank-one contraction fibers into a complete invariant to distinguish 3,568 dual orbits across 3,039 effective probe columns.
Constructed a finite blocking-core certificate to prove probe minimality and executed AI-assisted combinatorial search routines to exhaust all 198 residual search branches.
Proved that four probes can never suffice and identified exactly 2,078,105 effective minimum five-probe systems (3,173,771 raw lifts) that separate every dual orbit.
Mapped the complete one-exchange graph of 11,946,710 edges and 177,469 connected components, identifying a dominant giant component containing 1,824,449 systems.

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Implication

Computational analysis reveals minimum five-probe orbit separation in a binary quadratic tensor code, demonstrating complete reconfiguration graph connectivity.

Cite This Study

Akihiro Koide (2026) studied this question.

synapsesocial.com/papers/6a8fea0110c91c1e92621ede https://doi.org/10.5281/zenodo.22101934

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Implication

Computational analysis reveals minimum five-probe orbit separation in a binary quadratic tensor code, demonstrating complete reconfiguration graph connectivity.

Rank-One Syndrome Fibers, Minimum Orbit Separation, and Reconfiguration Geometry for a Binary Tensor Code

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Implication

Cite This Study

Rank-One Syndrome Fibers, Minimum Orbit Separation, and Reconfiguration Geometry for a Binary Tensor Code

Key Points

Discussion

Implication

Cite This Study

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