Zihan Wang, Huanyuan Shan

JWST's discovery of unexpectedly bright $z>10$ galaxies has triggered claims that standard $Λ$CDM cannot reproduce their abundances, while estimates of the ionizing escape fraction $f_{\rm esc}$ at $z>6$ have spanned a factor of four for over a decade. Here we show that both tensions arise from a structural degeneracy in reionization equations: global observables constrain only the product $f_{\rm esc}\times f_{\star,0}$ (peak star formation efficiency), not individual parameters. We demonstrate that this degeneracy, previously considered a limitation, provides a precise diagnostic framework. By leveraging JWST UV luminosity function shapes to independently constrain $f_{\star,0}$, we derive robust bounds on $f_{\rm esc}$. Joint profile-likelihood analysis across Gaussian, log-normal, and duty-cycle burst scatter models excludes the proposed crisis threshold ($\varepsilon > 3.5\%$) at $4.5σ$ confidence, with stochastic star formation histories strengthening rather than weakening the result. Combining these constraints with constant and evolving $f_{\star,0}$ measurements yields the first empirical reconstruction of $f_{\rm esc}(z)$ across $z=7$--$12$. A constant-efficiency scenario ($f_{\rm esc}\approx 10$--$16\%$) connects smoothly to low-redshift direct detections, whereas an evolving scenario ($f_{\rm esc} \approx 6\%$ at $z=12$) conflicts with low-metallicity ISM porosity expectations. JWST Cycle 3--4 will distinguish these pathways at $>2σ$, transforming a long-standing fundamental inference barrier into a powerful quantitative probe of early-universe physics.