ADR-056: capability-thresholds: whether a capability arrives abruptly is a claim, not a method

Context

luria #311 made unbound relations a lint class, which put the practice chain’s one unbound line in front of a reader for the first time:

SOTA-036, SOTA-037, SOTA-038, SOTA-279, SOTA-280, SOTA-281
share no `tags` across the whole line

Reading it did not produce a tag for that line — the diagnosis there is a relation carrying two senses, and is separate work. It produced a different finding. Two of the six, SOTA-037 (“LM in-context learning emerges at scale”) and SOTA-279 (“…and only once the model is large enough; below ~100B it does nothing or hurts”), make a claim the vocabulary has no word for, and a sweep for its siblings found nineteen documents across all three schemes:

• the emergence debate itself — LIT-470 Emergent Abilities of Large Language Models and LIT-471 Are Emergent Abilities a Mirage?, with THEORY-040 (a metric that composes or thresholds per-token error turns a smooth curve into a sharp one) and SOTA-200 (check before believing it);
• the grokking line — LIT-537, LIT-538, LIT-539, LIT-540, LIT-085 and THEORY-069 through THEORY-072;
• the singular-learning-theory account of stagewise development — LIT-543, LIT-544, THEORY-073 and THEORY-074.

All nineteen carry analysis-and-evaluation, and for most it is the primary. That is the measurement: one topic absorbed an entire subject.

Its blurb is “how to find out whether something worked — what to measure, what a measurement cannot tell you, and which comparisons are unsound.” That is a word for methods. “A capability appears above 100B parameters”, “a network generalises long after it has memorised”, “the posterior changes phase at n≈600” are claims about what happens. The dispute over whether an emergent ability is real is a methodological argument, so analysis-and-evaluation fits LIT-471 and SOTA-200 — it does not fit the phenomenon they argue about, and filing both under one word makes the disagreement invisible, which is the opposite of what this record is for.

Decision

A nineteenth topic: capability-thresholds.

a capability that arrives abruptly rather than smoothly — emergence at scale, grokking after long training, phase transitions in learning — which axis it turns on, and whether the discontinuity is real or an artefact of how it was measured

One word, not three, and the axis is the reason. Emergence turns on model scale, grokking on training time, and an SLT phase transition on dataset size. Three axes, and it is tempting to call them three subjects. They are not: in every case the claim is that a curve has a knee, the argument is whether the knee is in the phenomenon or in the plot, and the literature already borrows across them — THEORY-074 exists precisely to say that a Bayesian and a dynamical transition are different events, a distinction that is unstatable if each axis has its own topic. Naming the axis is the document’s job; naming the shape of the claim is the topic’s.

Nineteen documents retagged, appended in every case but four. The four primary moves are documents that are this claim and nothing else:

document	why the primary moved
LIT-470	Emergent Abilities of LLMs — the paper that named the phenomenon
LIT-471	Are Emergent Abilities a Mirage? — the paper that disputed it
LIT-538	Power et al., the paper that named grokking
THEORY-069	the one Active grokking explanation; its whole content is that grokking is a regime

Everywhere else capability-thresholds is appended, because primary_topic derives {tags[0]} and a prepend silently refiles a document (ADR-055).

What it does not take. SOTA-150 (“make the feed-forward layers a sparse mixture of experts once the model is large enough to be compute-bound”) is conditioned on scale and is not this: the condition is an engineering economics crossover, not a capability arriving. LIT-542 (the Local Learning Coefficient) and SOTA-325 (measure degeneracy when the loss has saturated) are the instrument and the method, and stay where they are. THEORY-076 (width scaling under the standard parametrization) is a training-dynamics claim about a limit, not about a knee. Writing these down is the point: a topic whose boundary is not tested is a topic that will absorb its neighbours, which is how analysis-and-evaluation got here.

The line that started this

It does not fix the line. SOTA-037 and SOTA-279 take the new tag; SOTA-036, SOTA-038, SOTA-280 and SOTA-281 correctly do not, so the intersection is still empty. That is the honest outcome and it is worth stating, because the tempting move — reach for a word that makes the warning go away — is the failure the vocabulary’s own alert names. The line’s actual defect is that extends licenses three senses, one of which (“a rule that only exists because the earlier one is followed”) cannot preserve subject by construction; that is its own decision and its own work.

Alternatives considered

• Leave them in analysis-and-evaluation. Status quo, and the cost is measurable rather than theoretical: the record holds the field’s largest live controversy about learning dynamics — three independent accounts of grokking, an emergence claim and its rebuttal, and a formal theory of staged development — and a reader browsing by topic cannot find it, because it is filed under the same word as “state the token count beside any reconstruction FID”.
• emergence. The obvious name, and it smuggles in the answer. The whole dispute is whether “emergent” describes the model or the metric (LIT-471), and a topic asserting the contested reading would put the record on one side of an argument it is supposed to hold both sides of. capability-thresholds is neutral about whether the threshold is real, and the blurb says so explicitly.
• Three topics, one per axis. Splits THEORY-074 — whose entire claim is that two of the axes are different events — across two topics that then cannot state the relation. It would also file the metric-artefact argument three times, once per axis, when it is one argument.
• A broader learning-dynamics. It would take these nineteen and another sixty besides — edge of stability, loss curves, warmup, the whole training half of the corpus — which is training-optimization with a different name. A topic most of the corpus could hold asserts nothing.
• Wait for the domain/kind vocabulary split. LU-#298 would let topics be a union of sub-vocabularies, and a reasonable reading is that all of this should wait for it. It should not: capability-thresholds is a kind of claim, so it belongs in the kinds vocabulary whichever way that lands, and nineteen documents are mis-filed today.

Consequences

analysis-and-evaluation gets smaller and sharper, which is the point, and no document leaves it — every one of the nineteen keeps it, because the methodological reading is real and additional. Fifteen of them gained a tag; four were refiled.

The topic is now nineteen and the count is written in four places. This decision updates luria.yaml’s header comment, the vocabulary’s own blurb, and the two sentences in CLAUDE.md that say “eighteen”. The dated records — curation entries and changelog fragments — keep their number, because they were true when written.

A boundary this sharp will be tested by the next filing, and the test to apply is the one in CLAUDE.md: would someone browsing capability-thresholds be right to expect this document? A scale-conditioned recommendation is not automatically a threshold claim, and SOTA-150 is the worked example of the difference.