A Standard Ultraviolet Continuum Can Hide Supercritical Accretion in GN-z11

The ultraviolet continuum from a high-redshift accreting black hole is routinely used to infer its mass. GN-z11 offers a sharp test of whether that inference is secure. A thin-disk fit to its continuum gives an Eddington mass of $M_{\mathrm{E}}=1.12\times {10}^7\text{Msun}$, an order of magnitude above the $\log (\text{Mbh}\mathrm{/}\text{Msun})=6.2\pm 0.3$ inferred from broad N~$\text{textsc}iv$. We show that this apparent tension is not imposed by the ultraviolet slope alone. We derive a closed-form criterion comparing the radius where observed photons are produced with the radius where a supercritical flow departs from efficient solution. For GN-z11, the criterion places the supercritical transition inside the ultraviolet-emitting region. Composite disks retaining the outer solution confirm this numerically, requiring ${\text{Mdot}}_{\mathrm{o}\mathrm{u}\mathrm{t}}=3.1$–$4.4\text{Msun}\mathrm{y}{\mathrm{r}}^{-1}$ and placing $\text{Rsph}=(1.2$–$1.8)\times {10}^3\text{rg}$ inside $\text{Ruv}=(2.6$–$2.9)\times {10}^3\text{rg}$. Replacing the inner $\sim {10}^3\text{rg}$ by a supercritical flow shifts the fitted slope by only $\mathrm{\Delta }\text{betaUV}=+0.08$ to $+0.11$, comparable to uncertainties from standard spectral modelling. Reversing the radial ordering requires the effective transition to move outward by a factor $1.7$–$2.1$. Within our composite models, the measured slope constrains black-hole mass only to around ${10}^6\text{Msun}$, an order of magnitude below the continuum Eddington mass. Continuum Eddington masses should therefore be treated as model-dependent bounds that assume global thin-disk efficiency. The same hierarchy appears in three additional JWST sources under the disk-dominated interpretation, where separation masses are only $4$–$6$% of continuum Eddington masses. This distinction can substantially weaken the seed-mass and early-growth demands inferred from ultraviolet continua at cosmic dawn for the first massive black holes.