arXiv:2507.03043v1 Announce Type: cross Abstract: Early evaluation of children's language is frustrated by the high pitch, long phones, and sparse data that derail automatic speech recognisers. We introduce K-Function, a unified framework that combines accurate sub-word transcription, objective scoring, and actionable feedback. Its core, Kids-WFST, merges a Wav2Vec2 phoneme encoder with a phoneme-similarity Dysfluent-WFST to capture child-specific errors while remaining fully interpretable. Kids-WFST attains 1.39% phoneme error on MyST and 8.61% on Multitudes--absolute gains of 10.47 and 7.06 points over a greedy-search decoder. These high-fidelity transcripts power an LLM that grades verbal skills, milestones, reading, and comprehension, aligning with human proctors and supplying tongue-and-lip visualizations plus targeted advice. The results show that precise phoneme recognition cements a complete diagnostic-feedback loop, paving the way for scalable, clinician-ready language assessment.