What does this research mean for the field?

Every finite complete Steiner triple system can be realized as bounded full-dimensional strictly convex compact sets in 23-dimensional Euclidean space. Novelty: ClaimNovelty.CONTRADICTORY. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

To determine whether every finite complete Steiner triple system can be geometrically realized as a convex code in a fixed, low-dimensional Euclidean space.

September 14, 2026Open Access

A universal 23-dimensional realization of Steiner triple codes

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To determine whether every finite complete Steiner triple system can be geometrically realized as a convex code in a fixed, low-dimensional Euclidean space.
Constructed bounded, full-dimensional, strictly convex compact sets in 23-dimensional Euclidean space using three simultaneous quadratic coefficient relations to reduce a sextic construction.
Established uniform face estimates, rational residual bounds, and an all-point rational ball construction with O(n^3) total binary description length verified by polynomial-time integer certificates.
Demonstrated that every finite complete Steiner triple system has an exact convex realization in 23 dimensions, contradicting Conjecture 16 by Jeffs, Siegel, Staudinger, and Wang.
Constrained the optimal universal realization dimension for Steiner triple codes to strictly between 4 and 23.

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Implication

Theoretical study demonstrates universal 23-dimensional convex realizations in finite Steiner triple systems, disproving a prominent conjecture and bounding optimal dimensions.

Cite This Study

Byungwoong Yoo (2026) studied this question.

synapsesocial.com/papers/6aa7b3d00926e14a848b2f99 https://doi.org/10.5281/zenodo.22728409

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Implication

Theoretical study demonstrates universal 23-dimensional convex realizations in finite Steiner triple systems, disproving a prominent conjecture and bounding optimal dimensions.

A universal 23-dimensional realization of Steiner triple codes

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Implication

Cite This Study

A universal 23-dimensional realization of Steiner triple codes

Key Points

Discussion

Implication

Cite This Study

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