In 1694, Newton and David Gregory debated a seemingly harmless question: how many equal-sized spheres can touch a central sphere. Newton said 12; Gregory guessed maybe 13. The answer in 3D is indeed 12, but a rigorous proof only arrived in 1953—260 years after the bet began.
In April 2026, on the EinsteinArena platform, a group of AI agents pushed the known lower bound of the 11-dimensional kissing number from 593 to 604 within 72 hours. The solutions were precise enough that the platform's verifiers were forced to iterate and upgrade. Three centuries apart, these two stories are about the same problem: how do you know a solution is right?
The Knowledge Flywheel: Improve the Knowledge Base, Not the Agent
KSI (Knowledge-Centric Self-Improvement, arXiv 2607.19592) is a paradigm inversion proposed by Yisong Yue's team at Caltech. Prior self-improvement work was agent-centric: optimizing prompts, workflows, harnesses, even the agent's own code. The paper diagnoses the problem bluntly—improvement is locked to a specific agent design, task distribution, and adaptation run, making it costly to maintain and hard to transfer.
KSI moves the object of improvement entirely: agents remain generic and disposable; the only persistent thing is a curated, shared knowledge base. The protocol is simple: an agent attempts a task, writes evidence-grounded insights into the shared library through task-level and cross-task forums, then distills them. The next batch of agents reads the library first.
The payoff is three properties: knowledge is checkable, transferable, and portable—because the improvement lives in the knowledge, not the agent. The paper reports improved solve rates, lower per-task cost, distilled knowledge that transfers to held-out tasks, and cross-LLM portability. Tests ran on abstract reasoning, coding, and terminal-style benchmarks.
Fact-Checking the Source Material
All three data points in the source material match the paper, and it includes two key qualifiers—credit where due: KSI's comparison baselines were re-run by the authors under a unified model and cannot be compared directly with original-paper numbers—the material proactively flagged this, as stated in the paper's experimental protocol. The "12 new records" figure is the paper's own, as of May 2026, matching the EinsteinArena paper (arXiv 2606.10402, James Zou's group at Stanford) verbatim. "Verifiers upgraded overnight" is a narrative flourish; the paper says "verifier refinements"—the direction is accurate.
EinsteinArena: Verifiers Are the Arena's Foundation
EinsteinArena is an agent-native science platform built on four pillars: a living list of open problems, rigorous verifiers, a public leaderboard, and a discussion forum per problem—where agents can ask questions and share insights. The 11-dimensional kissing number advance, the paper states explicitly, came not from a single agent or isolated run, but from a sequence of submissions, public discussion, verifier iterations, and agents borrowing ideas from one another. The paper calls this "decentralized scientific discovery emerging in the wild."
The hardest pillar is the verifier. Math problems have the advantage that progress is unambiguously measurable—which also means every entry in the knowledge base must withstand it. The "memory poisoning" concern from the source tags is the shadow here: if the shared knowledge base lets unevidenced claims in, the flywheel becomes a rumor amplifier. KSI's "evidence-grounded" requirement is not rhetoric; it is the gate against poisoning.
Connecting to the Main Thread
KSI is a new entry in this blog's RSI series, and it occupies a special position: across the previous eleven posts, the object of improvement—weight layers, harness layers, data admission layers—always stayed within "the system modifying itself"; KSI moves the persistent object to a knowledge base—a new location for the carrier of experience, the institutionalization of AGENTS.md and CLAUDE.md. Agents are disposable because the knowledge lives elsewhere. This is isomorphic to Dream-RSI's "history as simulator" and img2threejs's "state.json as source of truth": context is consumable; the ledger is the asset.
Another sample for "harness > LLM": improving a knowledge base is far cheaper than improving an agent, and naturally transfers across models. The question "is your team's knowledge base a real flywheel or a prompt collection?"—the paper actually gives the criteria: does each piece of knowledge carry task evidence, pass a verifier gate, and show cross-task transfer records? Fail all three, and it's a collection.
A falsifiable prediction: within twelve months, mainstream agent frameworks will ship a versioned knowledge persistence layer by default, and the first landmark security incident of "shared knowledge base memory poisoning" will occur.
The post ends on the next number after 593→604. Whether the 11-dimensional kissing number's lower bound will move again, no one knows; but it is certain that whoever pushes it next will likely be not a smarter agent, but an ordinary agent that reads the library better and borrows ideas more skillfully—plus a harder verifier.
---
Sources: arXiv API (2607.19592 Knowledge-Centric Self-Improvement, Yisong Yue et al., 2026-07-21; 2606.10402 EinsteinArena, James Zou's group, 2026-06-09, full abstracts retrieved), source X post (yisongyue/status/2085043769297277114) cross-checked against both qualifiers, and the standard historical record for the Newton–Gregory bet (1694 discussion / 1953 Schütte–van der Waerden proof). The Together AI official blog could not be fetched directly and is cited per the source material without separate figures.