Kissing Number & PackingStar

From zero background to writing your SCMP letter

Your angle: Human in the loop — humans should be central when using AI for research, including maths.

Sources: paper (KissingNumber/paper), work ideas (ideas4letters.md, moreIdeas.md), PackingStar GitHub, Ref/SCMPreport.md, Ref/PKU_wechat (video + transcript).

What is the Kissing Number Problem?

In 3D: How many identical spheres can touch one central sphere of the same size without overlapping?

Think: a pomegranate — replace seeds with unit spheres. How many can “kiss” the centre? Answer in 3D: 12 (proven 1953).

The problem is extended to n dimensions: K(1)=2, K(2)=6, K(3)=12, K(4)=24, … up to K(24)=196,560. In many dimensions the exact value is still unknown; we only have lower and upper bounds.

Comment for your letter: Human value in the problem itself — Newton and Gregory debated it in 1694. Centuries of human intuition and proof (e.g. 3D settled in 1953) built the foundation. Ref: SCMPreport.md, PKU video (石榴子).

Human value in the past literature

Timeline

1694 Newton vs Gregory (12 vs 13) 1900 Hilbert’s 18th problem 1953 3D = 12 proven 2003 Musin: 4D = 24 1971–2016 Lattice/code methods (13D, 14D, 25–31…)

Progress relied on human-designed tools: lattices, error-correcting codes, group theory, substructures. “In higher dimensions even top mathematicians felt stuck” (PKU video). About seven major advances in ~50 years, each with different methods.

Applications (human motivation): information coding (compress most with fewest bits), telecommunications, quantum coding, satellite signals. Ref: SCMP report (Qi quote), paper intro.

Comment for your letter: The past literature is entirely human — problem posing (Newton, Hilbert), proofs, and applications. AI did not replace that history; it builds on it. Ref: SCMPreport.md, PKU video (希尔伯特, 信息编码).

Why is it so hard?

Exact kissing numbers are known only in dimensions 1, 2, 3, 4, 8, 24. In other dimensions we have bounds, not proofs.

High dimensions: “combinatorial explosion,” geometry beyond human intuition.
Traditional methods depend on prior human designs (lattices, codes); they don’t scale arbitrarily.
Numerical issues: in coordinate-based search, tiny errors accumulate and break the packing (PKU video: stuck at 8–9D until they changed the formulation).

Comment for your letter: Humans defined what “hard” means and pushed the frontier for centuries. AI enters where human intuition and hand-designed methods hit limits — so AI is extending human endeavour, not replacing it. Ref: paper intro, PKU video (九维八维).

What does PackingStar do?

Idea: Don’t search in high-dimensional coordinates. Use a cosine matrix (pairwise angles between sphere centres). The problem becomes: fill this matrix under constraints → matrix size = kissing number. That reformulation is stable, GPU-friendly, and avoids precision blow-up.

Two agents (the key design)

Player 1 (Filler)

Adds entries to the matrix to grow the configuration.

Player 2 (Corrector)

Removes or corrects bad entries — like “one bad ball ruins the soup.”

They cooperate via reinforcement learning. Plus: decompose matrices into “fragments” and reuse them in new games (like “cell division,” PKU video).

Paper: arXiv:2511.13391; code: github.com/CDM1619/PackingStar.

Comment for your letter: The second agent was inspired by a human act: the mathematician manually deleting “bad” balls to get 14D 1932. So “human in the loop” is literally in the algorithm design. Ref: PKU video (手动删掉坏球, 陈栋把球问题转化成了博弈问题), moreIdeas.md.

How is the study novel? (vs SCMP report & video)

SCMP report: “Romance” between scientists and AI; PackingStar; new lower bounds in dimensions 25–31; first progress in 13D rational since 1971; AI doesn’t prove — humans verify.
PKU video adds: No training data (“无中生有”); 14D 1932 as “nightmare” until the second agent; human interpretation of the black box (“解释神”); young team; “PackingStar is the spacecraft” — not arrival, new start.
Paper adds: 6000+ new structures; antipodal paradigms challenged; humans then improved bounds (e.g. 22D) from AI patterns; results in standard databases; generalized kissing numbers under angular constraints.

Comment for your letter: Novelty is not “AI did it alone.” It’s: human insight (cosine matrix, two-agent design, fragments) + engineering + AI exploration + human verification and interpretation. Ref: SCMPreport.md, Ref/PKU_wechat.txt, paper abstract & intro.

Human in the loop — where to comment

1. Problem and history — Newton, Hilbert, decades of human proofs and constructions. Your letter can say: the value of humans is in the very formulation and the long literature.

2. Design of the system — The corrector agent came from watching a human “delete bad balls.” So human intuition is encoded in the method. Ref: PKU video.

3. Verification and proof — PackingStar does not prove; mathematicians must verify. 25D “may be optimal” but “rigorous proof still lacking.” Ref: SCMP report, paper.

4. Interpretation — “The work I spent the most time on was interpreting the data from the AI black box” (PKU video). Humans give meaning to what the machine finds. Ref: moreIdeas.md (解释神).

5. Human improvements after AI — “Inspired by these patterns, humans devised further improved constructions” (paper). So: AI suggests, humans refine and prove. Ref: paper, ideas4letters.md.

6. Other AI-for-science — Unlike AlphaFold-style (lots of data), this is “discovery from nothing” (无中生有). You can contrast: different roles for AI, but humans still in the loop in both. Ref: PKU video.

Takeaways for your letter

Anchor in Ref/SCMPreport.md (e.g. “I refer to the report on PackingStar…”).
Main argument: Humans should be in the loop when using AI for research, including maths — problem posing, design, verification, interpretation, and building on AI to improve bounds.
Use one or two vivid lines from the PKU video if helpful (e.g. “not arrival, but a new start”; “human and machine exploring the universe together”).
Keep it short (SCMP letters ~400 words), one clear ask, and match SCMP style (see partnerAIwriting.md).

Local refs: Ref/SCMPreport.md, Ref/PKU_wechat.txt, work/ideas4letters.md, work/moreIdeas.md, work/partnerAIwriting.md.