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Theorems, Proofs, and Derivations for N'Ko Script-Native ASR

This document collects the formal mathematical results underlying the N'Ko Brain Scanner and ASR system. We present five main theorems with proofs, three derivations of key quantities, and two corollaries that connect the LLM diagnostic thread to the ASR construction thread. The results establish: (1) a phonetic transparency advantage for CTC decoding on bijective scripts, (2) bounds on the translation tax in under-represented scripts, (3) completeness and soundness of the FSM phonotactic validator, (4) a circuit d

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This document collects the formal mathematical results underlying the N'Ko Brain Scanner and ASR system. We present five main theorems with proofs, three derivations of key quantities, and two corollaries that connect the LLM diagnostic thread to the ASR construction thread. The results establish: (1) a phonetic transparency advantage for CTC decoding on bijective scripts, (2) bounds on the translation tax in under-represented scripts, (3) completeness and soundness of the FSM phonotactic validator, (4) a circuit death theorem for reasoning layers processing unseen scripts, and (5) rank-efficiency bounds for script adaptation via LoRA.

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