Relation Order Reproducibly Shifts Entry into Multi-Hop Composition: Within-input relation order, prospectively defined acquisition entry, and independent-seed reproduction in a recurrent-depth reasoner

Preprint. This manuscript has not been peer reviewed.We ask a narrow developmental question: holding a latent relational task and learner fixed, does changing the order in which relations appear within each input change when compositional capability first crosses a fixed held-out competence criterion? We train a recurrent Transformer from scratch on a synthetic relational world under two renderings of the same 587,000 items. The renderings share grammar, sequence length, vocabulary and token multiset - the input token multiset is identical across arms - and differ only in the order of the relation tokens. Acquisition entry is defined prospectively as the first crossing of a strict held-out accuracy criterion. Under this isolation the application-order arm entered two-hop competence at epoch 273, while the canonical-order arm did not enter by its registered horizon of 1872 and is right-censored. We then repeated the comparison in a second, independently initialized realization against outcome branches frozen before that training existed. Both entries were observed: A=287 and C=1349, satisfying the prospectively frozen inequality C >= 4A (4A=1148); only after adjudication, R=4.70 with an absolute separation of 1062 epochs. We make no claim about subsequent depth acquisition: the two available application-order realizations diverge sharply after entry, and we report that as a scope boundary rather than a second result. Epoch-denominated coordinates are not translated into compute, sample efficiency or cost.