Move First, Commit Later: Selective LiDAR-to-BIM Global Initialization via Sequential Consensus with Symmetry-Aware Abstention

Global LiDAR-to-BIM initialization must place a robot within an as-designed building model without a prior pose. In repetitive interiors, the principal failure mode is not low-confidence registration but confident aliasing: a submap can match several BIM regions with comparable scores, producing a high-scoring pose displaced by symmetry. We present Move First, Commit Later, a selective layer that treats a registration front-end as an evidence source and decides whether to commit. Candidates from multiple submaps are mapped to a common $\mathrm{SE}(2)$ anchor; a top-1 consensus $B_m$, invariant to non-champion multiplicity, aggregates cross-submap evidence; and topology serves only as a binary feasibility gate. The decision is typed--COMMIT, DEFER, or AMBIGUOUS($\tau$), reporting the detected symmetry period--and reversible: symmetry-breaking motion upgrades AMBIGUOUS to COMMIT. On a real multi-room building and a controlled symmetric simulation, the layer commits correctly in every tested trajectory-scale configuration and otherwise abstains with a typed state, whereas forced-choice policies on the same front-end select wrong rooms in most cases. Committed anchors are within 0.02--0.36 m of an independent laser-tracker position reference and within $1.9^\circ$ of a BIM-registration orientation proxy. The evaluation covers one building and one front-end; the layer is designed to be front-end modular.