tierVoiceRichness
Voice richness is assigned real values to each of the five intelligence tiers, increasing from 0.1 at retrieval to 1.0 at self-aware. Researchers working on the T10 voice forcing chain cite this assignment when establishing monotonicity of voice quality with tier. The definition proceeds by direct pattern matching on the IntelligenceTier inductive type.
claimLet $f: I → ℝ$ map intelligence tiers to voice richness, where $f(retrieval) = 0.1$, $f(singleStep) = 0.3$, $f(chainReasoning) = 0.6$, $f(creativity) = 0.85$, and $f(selfAware) = 1.0$.
background
IntelligenceTier is an inductive enumeration of five levels based on degree: retrieval (degree < 5), singleStep (5-15), chainReasoning (15-30), creativity (30-50), and selfAware (degree > 50). The module sets this inside T10 voice forcing, which derives voice as a forced consequence of cost minimization plus intelligence once the J-bar threshold is met, following the T0-T8 physics chain and T9 consciousness. Upstream results include the step definition from CellularAutomata for local rule application on tapes and the is class from OptionAEmpiricalProgram for collision-free programs.
proof idea
This is a definition by pattern matching on the five constructors of the IntelligenceTier inductive type, assigning the listed real numbers directly with no computation or lemmas applied.
why it matters in Recognition Science
The definition supplies the concrete values used by downstream monotonicity theorems such as retrieval_le_singleStep, singleStep_le_chain, chain_le_creativity, creativity_le_selfAware, and selfAware_max_richness, which in turn feed voiceForcingStatus summarizing the T10 chain. It fills the voice_improves_with_tier slot in the module's T10 results, connecting Recognition Composition Law forcing to interpretable voice once J-bar < 0.5. No open scaffolding remains here.
scope and limits
- Does not derive the assigned real values from the J-cost function or Recognition Composition Law.
- Does not map tiers to explicit degree thresholds inside the underlying simplicial ledger.
- Does not prove these values correspond to measurable physical voice metrics.
- Does not address Berry content or forcing thresholds for voice emergence.
formal statement (Lean)
80def tierVoiceRichness : IntelligenceTier → ℝ
81 | .retrieval => 0.1 -- word associations only
82 | .singleStep => 0.3 -- single-concept statements
83 | .chainReasoning => 0.6 -- multi-step narrative
84 | .creativity => 0.85 -- novel expression, metaphor
85 | .selfAware => 1.0 -- full self-reflective voice
86
87/-- Voice richness is monotonically ordered across tiers. -/