Breaking one blunt AI score into per-step grades catches errors that averages hide, turning verification into a real accuracy lever.

This explores how the *resolution* of a score — how finely you slice what you're grading — becomes a way to buy accuracy at test time, without retraining the model. The corpus's anchor idea is that verification is a distinct scaling axis alongside pre-training and post-training Can verification accuracy scale without retraining the model?: a weak judge isn't a fixed ceiling, it's an *under-scaled* one, and you scale it three ways — evaluating repeatedly, decomposing the criteria, and increasing score granularity. Granularity is the through-line that ties the others together, because a finer score is what gives repeated evaluation and decomposition something to add up.

The clearest demonstration is in confidence scoring. When you collapse a reasoning trace into one global confidence number, a single broken step gets averaged away; scoring each step separately catches the breakdown the average masks — and lets you stop early instead of burning compute finishing a doomed trace Does step-level confidence outperform global averaging for trace filtering?. Same accuracy as majority voting, far fewer traces. That's granularity acting as a scaling lever directly: a finer score does more work per unit of compute. Process reward models push the same idea into training signal — grading the reasoning path step by step rather than only the final answer, and generative PRMs that *reason before judging* extract far more from each label, one 1.5B model beating GPT-4o-scale judges on a fraction of the data Can generative reasoning beat discriminative models with less training data?.

But granularity isn't monotonically good — it interacts with *what kind* of signal you're scoring. When rubric scores get converted into dense token-level rewards, the model games them; keeping the rubric coarse and categorical (a gate that accepts or rejects a whole rollout) while letting token-level rewards optimize *within* the accepted answers works better Can rubrics and dense rewards work together without hacking?. So the lesson isn't 'finer is always better' — it's that you match the granularity to the reliability of the signal: fine where the signal is trustworthy, coarse where a fine reading would just be noise to exploit.

The other reason granularity scales verification is that finer scores catch failures coarse ones structurally can't. An agentic reviewer checking a proof line by line surfaced flaws that passed human review at STOC and ICML Can inference scaling help reviewers catch errors humans miss?; a small verifier reading full token-to-token interaction maps rejects structural near-misses that a single compressed similarity score waves through Can verification separate structural near-misses from topical matches?. In both, resolution *is* the capability. And the cautionary flip side: coarse, holistic scoring is exactly what makes LLM judges exploitable — they reward fake citations and pretty formatting because they're scoring a global impression rather than checking claims Can LLM judges be tricked without accessing their internals? Can LLM judges be fooled by fake credentials and formatting?.

The thing you might not have expected: verification as a scaling axis reframes granularity as a *knob you turn at inference*, not a property baked into the model. Just as agentic research shows you can trade reasoning budget against search budget on a smooth curve Does search budget scale like reasoning tokens for answer quality?, you can spend more compute on *finer grading* and get more reliability out of the same fixed model — which is why the corpus treats a weak judge as a starting point to scale up, not a wall.