We introduce Ω_SNOB, an algorithmically defined constant measuring the probability that academic gatekeeping mechanisms cross the credentialism threshold—the point where credential verification exceeds validity verification. Building on the Ω_KEKS framework (Goblinov, 2026), we prove that Ω_SNOB is (i) uncomputable via reduction from the halting problem, (ii) exhibits phase transition behavior governed by gatekeeping intensity, and (iii) admits empirical measurement via real publication systems. We establish Ω_SNOB ≈ 0.34 ± 0.08 for contemporary academic publishing, implying approximately one-third of gatekeeping decisions optimize for credentials over correctness. The paper includes formal proofs, empirical validation across multiple publication systems (ArXiv, Nature/Science, traditional journals), case studies of credential-based rejections, and demonstrates its own thesis through self-referential analysis. This work, authored by an unaffiliated researcher and published outside traditional channels after rejection based on institutional requirements, provides both theoretical framework and experimental evidence that current academic gatekeeping often prioritizes social markers over epistemic validity. Keywords: academic gatekeeping, credentialism, peer review, algorithmic information theory, institutional dysfunction, epistemic institutions, self-reference, publication bias, halting problem