Shared Experiences for Collective World Models: Exact Team and Tree Synchronization Laws after Unpaired Learning

Robot teams can learn useful predictive representations from separate trajectories while still using different latent coordinate systems. We isolate the remaining synchronization problem after unpaired learning has reduced this ambiguity to a known compact linear group $G\le O(d)$. The exact generic number of globally shared experiences that identifies all relative frames, up to one unavoidable common gauge, is the generic base size of $G$ and is independent of team size. If pair-free operators generate a simple block $M_n(\mathbb R)\otimes I_m$, the threshold is exactly $\lceil m/n\rceil$. When simultaneous team-wide events are unavailable, a tree of pairwise calibration links is sufficient exactly when every edge carries at least the base-size number of paired experiences, so the exact total pairwise budget is $(N-1)b_{\rm gen}(G)$. A deterministic noisy block bound further shows that orthogonal-frame error is at most twice the anchor noise divided by the anchor stack's smallest singular value, with edge errors accumulating additively along tree paths. These results are exact inside the stated residual-group model; they do not assume that arbitrary neural world-model latents satisfy that model. The main implication for robot learning is architectural: abundant unpaired data can reduce the residual symmetry before scarce synchronized physical experience is spent.