AlphaEvolve problems·alphaevolve:36
Circle packing in a square / rectangle
No formal proof attached. Any claim here rests on a write-up or a report.
Fidelity F0: None. No formal statement is attached to the result.
For any $n \\geq 1$, let $C(n)$ denote the largest sum $\\sum_{i=1}^n r_i$ of radii such that one can place $n$ disjoint open disks of radius $r_1,\\dots,r_n$ inside the unit square, and let $C'(n)$ denote the largest sum $\\sum_{i=1}^n r_i$ of radii such that one can place $n$ disjoint open disks of radius $r_1,\\dots,r_n$ inside a rectangle of perimeter $4$. Establish upper and lower bounds for
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F0 no formal statement None. No formal statement is attached to the result.
Computed from what the project declares and what the register holds, never from reading the mathematics. How fidelity is graded.
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