On the fully-open Pythia suite, is any benchmark capability genuinely discontinuous under a continuous per-example metric?

'Emergent abilities' are capabilities that appear to jump sharply at some model scale. Schaeffer et al. argued this is often a mirage induced by discontinuous metrics (e.g. exact-match accuracy): under a continuous / linear per-example metric (Brier score, token edit distance, per-token log-likelihood) the same data can show smooth, predictable scaling. Question: using the Pythia suite (70M-2.8B parameters for workstation scale; 154 checkpoints per model, identical data order), take a task reported as 'emergent' (e.g. a BIG-Bench arithmetic or word-unscrambling task, or an MMLU subset) and test whether, under a continuous per-example metric, the score-versus-scale curve is (a) smooth (no discontinuity beyond noise) and (b) predictable -- i.e. a scaling fit from the smallest three models extrapolates to the 2.8B point within a stated relative error. Report, per task and metric, whether any discontinuity survives the continuous metric and the extrapolation error.

Acceptance. FULLY RESOLVES: a reproducible eval script (pinned Pythia checkpoints; released tasks) reporting, for $\ge 2$ tasks, both a discontinuous metric (exact match) and $\ge 1$ continuous metric (Brier, token-edit-distance, or log-likelihood), and a verdict: either (i) the discontinuity vanishes and a fit from small models extrapolates to 2.8B within a stated relative error (mirage confirmed for that task), or (ii) a genuine discontinuity survives the continuous metric (real emergence), with quantified evidence. Deliverable: code + per-task metric curves + extrapolation errors.