[community] Add Erdos Unit Distance 3D Problem

[m8ngotree]

Summary

• Adds erdos_unit_distance_3d, the three-dimensional version of the existing erdos_unit_distance problem
• Place N=65536 points in R³ to maximize unit-distance pairs at Euclidean distance exactly 1
• Same cubic scoring formula, same Python interface, same Docker image as the 2D version
• Evaluator is a direct 2D→3D extension: bucket grid, validation, and distance counting all extended to three dimensions

Validation

Smoke test (reference.py → evaluator.py):

N=65536; unit_pairs=195322; baseline=65536; raw_score=66.45; score=29.34

Reference scores > 0 ✓

Scoring

• Baseline: N pairs (trivial construction)
• Formula: score = 100 * (raw_score / 100)^3 where raw_score = 100 * (pairs - N) / pairs
• Ceiling: approaches but never reaches 100 (cubic scale prevents saturation)

Resources

• Python 3.11, 10800s timeout, no external packages, ubuntu:24.04

Test plan

• python3 -m py_compile 2.0/problems/erdos_unit_distance_3d/evaluator.py
• python3 2.0/problems/erdos_unit_distance_3d/evaluator.py 2.0/problems/erdos_unit_distance_3d/reference.py — score=29.34 (> 0)
• uv run frontier list 2.0 — problem appears as erdos_unit_distance_3d
• uv run frontier show 2.0 erdos_unit_distance_3d — readme renders correctly
• Harbor smoke trial — 5 successful submissions, best score=56.72

Harbor trial (gpt-5-2025-08-07, 600s agent timeout):

{
  "score": 56.72,
  "reward": 0.5672,
  "successful_submissions": 5,
  "trial_status": "scored",
  "agent_status": "completed"
}

Submission trajectory: 0 → 56.55 → 56.69 → 56.72 → 56.72 → 56.68

Harbor Smoke Trial Logs

Frontier-CS % uv run frontier harbor trial 2.0 erdos_unit_distance_3d \
  -a codex \
  -m gpt-5-2025-08-07 \      
  --agent-timeout 600 \
  --verifier-timeout 600 \
  --force-build \
  --json
[frontier harbor] Generating task frontier-cs-2-0-erdos-unit-distance-3d
[frontier harbor] Starting Harbor trial frontier-cs-2-0-erdos-unit-distance-3d
[frontier harbor] Building/preparing Harbor environment; judge readiness appears at submission time
[frontier harbor] submission #1 2026-06-11T02:31:28.405Z status=queued code_chars=1616
[frontier harbor] submission #1 2026-06-11T02:31:28.499Z status=running code_chars=1616
[frontier harbor] submission #1 2026-06-11T02:31:34.526Z status=done score=56.55 best=56.55 reward=0.5655 code_chars=1616
[frontier harbor] score bar: █ (0.00 -> 56.55)
[frontier harbor] submission #2 2026-06-11T02:32:05.206Z status=queued code_chars=1849
[frontier harbor] submission #2 2026-06-11T02:32:05.356Z status=running code_chars=1849
[frontier harbor] submission #2 2026-06-11T02:32:11.381Z status=done score=56.69 best=56.69 reward=0.5669 code_chars=1849
[frontier harbor] score bar: ▁█ (56.55 -> 56.69)
[frontier harbor] submission #3 2026-06-11T02:32:28.952Z status=queued code_chars=1837
[frontier harbor] submission #3 2026-06-11T02:32:29.063Z status=running code_chars=1837
[frontier harbor] submission #3 2026-06-11T02:32:35.101Z status=done score=56.72 best=56.72 reward=0.5672 code_chars=1837
[frontier harbor] score bar: ▁▆█ (56.69 -> 56.72)
[frontier harbor] submission #4 2026-06-11T02:33:20.423Z status=queued code_chars=1837
[frontier harbor] submission #4 2026-06-11T02:33:20.518Z status=running code_chars=1837
[frontier harbor] submission #4 2026-06-11T02:33:26.551Z status=done score=56.72 best=56.72 reward=0.5672 code_chars=1837
[frontier harbor] score bar: ▁▆█▇ (56.72 -> 56.72)
[frontier harbor] submission #5 2026-06-11T02:33:33.775Z status=queued code_chars=1838
[frontier harbor] submission #5 2026-06-11T02:33:33.905Z status=running code_chars=1838
[frontier harbor] submission #5 2026-06-11T02:33:40.934Z status=done score=56.68 best=56.72 reward=0.5668 code_chars=1838
[frontier harbor] score bar: ▁▆█▇▆ (56.72 -> 56.68)
[frontier harbor] Reading trial artifacts
{
  "reward": 0.5672172124112516,
  "score": 56.72172124112515,
  "score_unbounded": 56.72172124112515,
  "trial_status": "scored",
  "agent_status": "completed",
  "trial_name": "frontier-cs-2-0-erdos-unit-dista__xZjmbdY",
  "task_name": "frontier-cs/frontier-cs-2-0-erdos-unit-distance-3d",
  "trial_dir": "/Frontier-CS/.frontier-cs/harbor/trials/frontier-cs-2-0-erdos-unit-dista__xZjmbdY",
  "agent": "codex",
  "agent_version": "0.139.0",
  "model": "gpt-5-2025-08-07",
  "n_input_tokens": 1253037,
  "n_cache_tokens": 1074560,
  "n_output_tokens": 25704,
  "cost_usd": 0.61445625,
  "successful_submissions": 5,
  "best_iterative_reward": 0.5672172124112516,
  "used_best_submission": false,
  "started_at": "2026-06-11T02:27:42.238832Z",
  "finished_at": "2026-06-11T02:34:17.027065Z"
}