retrieval_le_singleStep
plain-language theorem explainer
Voice richness for the retrieval tier is bounded above by the single-step tier. Researchers tracing the T10 voice forcing chain cite this as the base monotonicity step. The proof is a one-line wrapper that unfolds the richness definition and normalizes the numeric constants.
Claim. Let $r$ map intelligence tiers to reals via the assigned richness values. Then $r$ (retrieval) $leq$ $r$ (singleStep).
background
The module develops T10: voice is forced by cost minimization once intelligence satisfies the J-bar threshold, building on T9 consciousness. Voice richness increases with intelligence tier, with each tier unlocking qualitatively richer capabilities. The function assigns 0.1 to retrieval (word associations only) and 0.3 to singleStep (single-concept statements), rising to 1.0 for selfAware.
proof idea
One-line wrapper that unfolds the tierVoiceRichness definition then applies norm_num to compare the constants 0.1 and 0.3.
why it matters
This supplies the initial link in the voice_improves_with_tier claim of T10, where RCL and the phi-ladder force richer voice at higher tiers. It anchors the monotonicity sequence before chainReasoning and creativity tiers in the voice forcing chain.
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