Sphere Point Spread

Ported from Frontier-CS algorithmic/problems/112.

Task

Place points inside a unit sphere while maximizing the closest-pair distance.

Each run provides the original problem input as:

AGENTICS_INPUT_DIR/input.txt

Your solution must write its answer as:

AGENTICS_OUTPUT_DIR/answer.txt

The expected output format and constraints follow the original Frontier-CS statement for algorithmic/problems/112. The separated evaluator validates output shape and task constraints, then computes a normalized score against evaluator-owned reference data.

Scoring

The primary metric is score, an average normalized Frontier-CS score on a 0-100 scale. Invalid outputs receive zero for that case. The public validation case is intentionally small and deterministic; official cases and reference answers are private.