We study how text serialization affects table lookup in instruction-tuned language models.
Our diagnostic asks the model to find the row containing a specified value under one named column, then return the value under another named column in that same row.
We render the same synthetic 256-cell tables in row-major form and in column-major form with each header placed beside its values, while varying the table aspect ratio across five shapes.
Across three models, the better format changes with table shape: row-major performs better on tall tables, whereas column-major performs better on wide tables.
At 64 x 4, row-major leads by 42.3-54.0 percentage points; at 4 x 64, column-major leads by 35.0-59.0 points.
Mapping wrong answers back to their source cells reveals a complementary error pattern: row-major tends to preserve the correct row but lose the target column, while column-major tends to preserve the correct column but lose the row.
We use the term relational locality to describe this pattern: serialization keeps one relation locally available while making the other depend on positional alignment.
A separate non-tabular ordering experiment supports this interpretation.
Thus, apparent width-related failures in text-serialized tables depend on linearization, not table shape alone.