Infrared Spectral Gap in a Gluonic Dark Sector and the Galactic Acceleration Scale

We further develop a trace-anomaly-motivated gluonic scenario in which cold dark matter (CDM) is modeled as a long-lived color-singlet Bose-Einstein condensate seeded at the QCD confinement transition. Specifically, guided by the near-universality of the galactic acceleration scale $g^{}_\dagger \simeq (1\text{--}2)\times10^{-10}\,\mathrm{m\,s^{-2}}$ inferred from the RAR, we hypothesize that this relic gluonic condensate organizes, at galactic distances, into a spectrally rigid lowest-weight structure characterized by a protected infrared gap. Within an effective representation-theoretic framework, Lorentz covariance together with positive-energy lowest-weight unitarity naturally favors the AdS algebra $\mathfrak{so}(2,3)$ as the minimal algebraic structure supporting such a discrete tower of states. The resulting condensate produces, by construction, a cored halo profile with finite total mass $M_h$. Normalizing this profile by the observed approximate universality of the central DM surface density, $\Sigma_0\simeq141\,M_\odot\,\mathrm{pc}^{-2}$, yields a universal characteristic acceleration $g^{}_\star ={G\, M_h}/{r_{\rm c}^2} \simeq \pi^2 G\,\Sigma_0 \simeq 1.9\times10^{-10}\,\mathrm{m\,s^{-2}}$, independent of the particular halo scale; since $\Sigma_0$ fixes the final expression, the dependence on the collective correlation length $r_{\rm c}$ drops out. Notably, its predicted value lies well within the empirical range of the acceleration scale inferred from the RAR. We also provide an illustrative comparison with representative rotation curves from the SPARC database, indicating phenomenological compatibility of the finite-mass profile with realistic baryonic decompositions. This comparison is not a precision fit to the full SPARC sample, and the agreement with the RAR scale should not be interpreted as a first-principles derivation of the RAR itself.