Low-rank adapters are inserted into the query and value projections of every attention layer. That is the field's default and it comes from an ablation in the original LoRA paper rather than from anything measured about the tasks at hand. TIM (Task Interference Mapping) chooses the placement instead of inheriting it. Before any training, it passes a few batches of each task through the model, takes principal angles between the two gradient subspaces per module, and adapts the modules where the tasks overlap least. On Llama-3-8B fine-tuned from code to prose, this retains 36.8% more of the model's original capability than the default placement with the same number of adapted modules (9 of 10 seeds, Wilcoxon p=0.006), with plain LoRA in both arms and no regulariser. The measurement takes minutes and trains nothing. Its ordering places o_proj first and q_proj second across three model families and three task pairs, while the last two positions do not transfer, which is why it is presented as a measurement to run rather than a rule to adopt. USPTO Patent Pending, Application No. 64/121,656 (filed 29 July 2026). Changes in this version (v1.2): adds a pre-registered control arm. Against a placement built from the published type composition with layers chosen at random, which is parameter-matched by construction, the measured placement retains 0.329 more in paired terms, winning in 10 of 10 seeds. Both arms were re-run in a single session. Adds a table of trainable parameter budgets, which the module-count control does not equalise. Adds a note on per-seed reproducibility across hardware.