Standard NLP pipelines for occupational clustering discard the 10-15% of job postings that density-based methods assign to noise. We argue this is an error: in rapidly evolving domains, low posting density signals novelty, not incoherence. We formalize this as the Emergence-Density Inversion (EDI) hypothesis and test it longitudinally on 84,988 job postings across eight quarters (Q4 2022-Q3 2024). EDI is partially confirmed: high-EOS outlier groups transition to stable clusters in 1.4 +/- 0.6 quarters vs. 4.1 +/- 1.2 for low-EOS groups (p < 0.001), though the signal fails in approximately 19% of cases, which we characterize as a failure analysis. We extend the Emerging Occupation Score (EOS) with Temporal Velocity and Cross-Platform Convergence, improving 2-quarter cluster-formation prediction from F1 = 0.61 to 0.74, outperforming Isolation Forest, LOF, GLOSH, and BERTrend baselines. A retrospective study on three now-established roles (MLOps Engineer, DevOps/SRE, Data Engineer) confirms EOS signalled 2-3 quarters before cluster formation, providing held-out validation. A held-out annotator panel (kappa = 0.74) rates EOS > 0.75 as coherent emerging occupations with 77% precision. Prompt Engineer, AI Safety Researcher, Foundation Model Engineer, and Agent Systems Engineer, all absent from O*NET, are top-4 in Q3 2024 and form stable clusters by Q1 2025.