Within the open Pythia family, does cross-model representational alignment increase with scale, and does it survive width/depth calibration?

The Platonic Representation Hypothesis holds that as models grow more capable their internal representations converge toward a shared structure; alignment is commonly measured by mutual-$k$-nearest-neighbor agreement between two models' representations of the same inputs. Recent critiques argue that reported convergence can be an artifact of width/depth or of small gallery sizes, and can shrink under calibration or at large evaluation scale. Question: within the fully-open Pythia suite (same data and data order; sizes 70M-2.8B), measure mutual-$k$-NN alignment between every pair of model sizes on a fixed open text set, and test (a) whether alignment to the largest model increases monotonically with the smaller model's scale, and (b) whether that trend persists after controlling for representation width (e.g. PCA to a common dimension) and as the evaluation gallery grows from 1k to $\ge 100$k examples. Report the alignment-versus-scale curve before and after calibration.

Acceptance. FULLY RESOLVES: a reproducible script (pinned Pythia checkpoints; fixed text set) computing pairwise mutual-$k$-NN alignment across all sizes and reporting (i) alignment-to-largest versus scale (monotonic? with confidence interval), (ii) the same after PCA / width calibration, and (iii) sensitivity to gallery size (1k -> $\ge 100$k), with a stated verdict on whether within-family convergence with scale is real or a calibration artifact. Deliverable: code + alignment matrices + calibrated curves.