Beyond Character Indices: Explicit Geometry for Proportional Text Art

A spatial quantity can be fully determined by a model's inputs yet remain useful to supply explicitly. We test this distinction in proportional-font text art, where horizontal position is the cumulative sum of known glyph widths. Pixel-preserving whitespace rewrites change character indices while holding the rendered artwork fixed. Paired Transformers share characters, true widths, target inputs and complete source access, differing only in an extra source scalar: matched index or cumulative position. Canonicalizing every source run in the specified whitespace family during training and evaluation makes each model exactly invariant to those rewrites. Cumulative positions still improve conditional nonspace prediction by 0.0365 bits/target. Three additional paired initializations at a fixed endpoint retain a 0.0410-bit gain. Width-only, calibrated row-scale and pseudo cumulative controls also favor cumulative positions. Frozen models retain a gain on 19 newly acquired, screened event artworks, and larger predictors retain gains with both normalized and raw/augmented inputs. In this controlled natural setting, explicit cumulative position remains useful after the specified encoding invariance is enforced.