What question did this study set out to answer?

The focus is to explore the six-direction affine plank covering problem for a triangle and establish a certified lower bound for the corresponding covering constant.

August 13, 2026Open Access

Boundary Certificates and an Information Barrier for a Six-Direction Affine Plank Problem on a Triangle

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The focus is to explore the six-direction affine plank covering problem for a triangle and establish a certified lower bound for the corresponding covering constant.
Developed a cevian boundary-certificate framework and proved a general three-arm support theorem.
Obtained a closed-form evaluation for the cyclic three-cevian family relevant to the covering problem.
Combined certificates with a location-sensitive linear relaxation to derive a certified rational lower bound for the covering constant.
Proved the certified rational lower bound C ≥ 13505875189/14039754651 ≈ 0.9619737327844277 for the six-direction covering constant C of the triangle.
Demonstrated that the self-overlap coefficient is sharp, equal to 1, with an induced rescue coefficient of 576, both having rational witnesses.
Identified an information barrier theorem indicating that improvements must leverage unexplored information beyond the established framework.

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Implication

Studies a six-direction affine plank covering for a triangle, demonstrating certified rational bounds and structural barriers.

Cite This Study

Maximiliano Lucius (2026) studied this question.

synapsesocial.com/papers/6a7d769b2b0e0cff3f640025 https://doi.org/10.5281/zenodo.21895464

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Boundary Certificates and an Information Barrier for a Six-Direction Affine Plank Problem on a Triangle

Key Points

Discussion

Implication

Cite This Study

Boundary Certificates and an Information Barrier for a Six-Direction Affine Plank Problem on a Triangle

Key Points

Discussion

Implication

Cite This Study

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