A multi-differential constraint map for quarkonium suppression mechanisms in high-multiplicity pp and pPb collisions

The multiplicity-dependent suppression of $\Upsilon(nS)$ excited states in high-multiplicity $pp$ and $p$Pb collisions is analysed using publicly available CMS and LHCb data; preliminary CMS Physics Analysis Summary results in $p$Pb and light-ion collisions are used only as supporting cross-system evidence. Six complementary differential constraints are considered: cone isolation, azimuthal-sector equivalence, transverse sphericity, transverse-momentum ordering, forward-$E_T$ long-range correlation, and the pPb/Pbp forward-backward asymmetry. Taken together, these constraints disfavour mechanisms controlled solely by local track density or by total multiplicity, and are consistent with an early, globally correlated, topology-sensitive suppression pattern. The characteristic multiplicity scale at which suppression sets in is independently consistent with the onset of a qualitative change in soft-sector behaviour identified by Campanini and Ferri \cite{CampaniniFerri2011} from inclusive charged-particle observables. The result is a data-driven constraint map consistent with an early, coloured pre-hadronic environment, possibly involving a deconfined stage.