In 1964 László Fejes Tóth published What the Bees Know and What They Do Not Know. The hexagonal comb is the cheapest way to divide a plane into equal cells, a claim proved only in 1999. Where two layers of comb meet out of sight, the bees’ three-panel cap can be beaten by a fraction of one percent of wax. The architecture is optimal in the light and a whisker off in the dark, and no bee registers either fact. The pipeline behind this site is named the swarm, so both halves of the title apply to it. Most research programmes publish only the first.
The record
The process reports what it has tested, and the accounting was itself corrected. Every verdict is published on this site, including the founder’s own retired namesake model. Significant is not the same as promoted: two real crowding effects were held significant and neither was promoted, because the threshold does not move. The statistics come from deterministic code, and no language model in the shop computes so much as a Sharpe ratio, that is, return per unit of risk.
| Hypotheses, at 23 July 2026 | Count |
|---|---|
| Filed | 212 |
| Judged under the gates | 104 |
| Still queued | 22 |
| Errored before producing a verdict | 86 |
| Crowding effects held significant, not promoted | 2, at t of 4.1 and 3.9 |
| Gates applied | a signal-library vendor’s own checks for the majority, then Newey-West statistics, reruns with a margin of safety, multiplicity deflators |
| Correction, 3 August 2026, Working Paper No. 22 | 212 was the count filed, not the count tested; a hypothesis that errored before a verdict tested nothing and earns no place in the denominator |
| Power audit, 21 August 2026 | Share of true signals passing the gates |
|---|---|
| True Sharpe ratio 0.8, twenty years of data | four to six per cent |
| True Sharpe ratio 1.0, twenty years of data | about 22 per cent |
| True Sharpe ratio 0.8, five years of data | none |
| Stressed rerun | halves the t-statistic by design |
The limits
| Declared limit | What the record says |
|---|---|
| The universe flatters the results | The test universe comprises today’s index constituents, the companies that survived. Every Sharpe ratio published on this site is an upper bound for this reason, and is labelled as such. |
| Unmet regimes | The sample contains a few crises; the future is not obliged to draw from the same urn. Correlations measured in calm are fiction in a storm. The process stresses for this, but a stress test is only a rehearsal. |
| Capacity is assumed, not proven | Every backtest presumes that the process’s own trading does not move the price. At current size that is nearly true, which reflects the size more than the method. |
| Unmeasured crowding | The 13F study run in house, 13F being the US Securities and Exchange Commission form on which large managers disclose US equity holdings each quarter, measures crowding among long positions in public filings, excluding shorts and swaps. It captures the floor of the crowd and misses the ceiling. |
| Strategies that almost fit | Newton held that twelve spheres can touch a central one and a thirteenth never quite fits, though the remaining slack looks inviting; the proof took 250 years. Each week the pipeline meets a strategy at t = 2.3 that appears to almost fit. The slack is real, and it still does not fit. |
| The instrument’s power, added 21 August 2026 | The limit above was written as if a near miss were a fact about the strategy. Table 2 says it is mostly a fact about the bar: a t of 2.3 is what a real but modest signal usually looks like through this instrument. The bar has not moved; the reading of the verdicts has. They say “did not clear the bar”, not “does not work”. |
The bee and the mathematician
The bee needs only to be right. The mathematician must be certain against every competitor, including the infinitely many nobody has drawn; referees spent four years on Thomas Hales’s sphere-packing proof and reached only 99 percent certainty, after which he spent a further decade having a machine verify every line. A backtest that works is the bee, impressive and locally optimal, blind to its own caps. Pre-registration, stress and multiplicity deflation move a claim toward the mathematician’s standard without ever arriving, because markets are not geometry.
References
- Fejes Tóth, L. (1964). What the Bees Know and What They Do Not Know. Bulletin of the American Mathematical Society, 70, 468–481.
- Hales, T. C. (2001). The Honeycomb Conjecture. Discrete & Computational Geometry, 25(1), 1–22.
- Hales, T. C. (2005). A Proof of the Kepler Conjecture. Annals of Mathematics, 162(3), 1065–1185.