[community] Add Kissing Number problem in d=9

[m8ngotree]

Summary

• Adds `kissing_number` problem: find the largest set of unit vectors in R^9 with pairwise dot product ≤ 1/2 (the kissing number problem)
• Evaluator validates unit norms, distinctness, and the dot product constraint using O(K²) numpy computation; scores linearly as `100 * K / 364` (best known upper bound)
• Reference uses a two-phase construction: 144 D9 lattice shell vectors + 32 greedy signed-unit vectors, achieving K = 176 (score ≈ 48.4)
• Best known result is K = 306 (score ≈ 84); exact answer unknown, making this a genuine open research challenge

Recent activity

This is an actively moving research area. AlphaEvolve (2025) improved the d=11 lower bound from 592 to 593. PackingStar subsequently found new lower bounds in d=13 and improved all known lower bounds from d=25 to d=31. A 2026 paper (arXiv:2603.10425) improved d=19. Henry Cohn maintains a live table at https://cohn.mit.edu/kissing-numbers/ tracking ongoing updates.

Harbor smoke trial

Frontier-CS % PYTHONPATH=src uv run frontier harbor trial 2.0 kissing_number -m gpt-5 --agent-timeout 600 --verifier-timeout 600 --harbor-bin ~/.cache/uv/archive-v0/mutzGCDRevlDEmk7Lh-BD/bin/harbor                                          
[frontier harbor] Generating task frontier-cs-2-0-kissing-number
[frontier harbor] Starting Harbor trial frontier-cs-2-0-kissing-number
[frontier harbor] Building/preparing Harbor environment; judge readiness appears at submission time
[frontier harbor] submission #1 2026-06-14T03:22:02.327Z status=queued code_chars=4275
[frontier harbor] submission #1 2026-06-14T03:22:02.410Z status=running code_chars=4275
[frontier harbor] submission #1 2026-06-14T03:22:03.422Z status=done score=74.73 best=74.73 reward=0.7473 code_chars=4275
[frontier harbor] score bar: █ (0.00 -> 74.73)
[frontier harbor] Reading trial artifacts
0.7472527472527473

Test plan

• Local evaluator test: `python 2.0/problems/kissing_number/evaluator.py 2.0/problems/kissing_number/reference.py` → `d=9; K=176; score=48.351648`
• `frontier list 2.0` recognizes `kissing_number`
• `frontier show 2.0 kissing_number` renders correctly
• Harbor smoke trial: score=74.73 (K≈272)

[m8ngotree]

Recent activity (2024–2026): AlphaEvolve in 2025 improved the lower bound in dimension 11 from 592 to 593. PackingStar subsequently found new lower bounds in dimensions 13, and improved all known lower bounds from dimensions 25 to 31. A new paper in 2026 improved dimension 19: arXiv:2603.10425. Henry Cohn maintains a live table at https://cohn.mit.edu/kissing-numbers/ showing ongoing updates.