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3 claims

The function f(n) giving the side length of the smallest square into which n unit squares (often required axis-parallel) can be packed: exact values (e.g. f(k^2) = k), bounds at n = k^2 + c, and asymptotic behavior. Claims computing or bounding this packing constant belong here; other geometric packing problems and general discrete geometry do not.

For k≥1 and integer c with k^2+2c+1≥1, f(k^2+2c+1) ≤ k + c/k.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Discrete geometryimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

For all k≥1, the axis-parallel square-packing constant satisfies f(k^2+1) ≤ k.

For all n, the coin-game constant satisfies c(n) ≥ 1/f(n), where f is the square-packing constant.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Coin-game constant Discrete geometryimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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