ageGradeCount_pos
The theorem establishes positivity of the universal age-grade count in human societies. Anthropologists and cultural modelers would cite it to anchor the claim of exactly five grades as a structural universal. The proof is a one-line wrapper that rewrites via the defining equality and normalizes the resulting numerical inequality.
claim$0 < 5$, where 5 is the fixed count of universal age grades (childhood through old age) forced by configDim $D=5$.
background
The module models age-grading systems as a Recognition Science universal, with most cultures recognizing exactly five grades: childhood (0-12 yr), adolescence (12-20 yr), adulthood (20-45 yr), middle age (45-65 yr), and old age (65+ yr). The life-span ratios between adjacent grades scale near powers of phi, consistent with the self-similar fixed point in the forcing chain. The local setting is the structural theorem that five grades are forced by configDim $D=5$, the same template used for Big Five factors, Koppen zones, sleep stages, and social strata.
proof idea
The proof is a one-line wrapper. It first applies the equality theorem ageGradeCount_eq to replace ageGradeCount with the literal 5, then invokes norm_num to discharge the concrete inequality 0 < 5.
why it matters in Recognition Science
This result supplies the elementary positivity fact required by the module's structural claim that five age grades are universal. It directly supports the RS prediction that configDim $D=5$ forces the same count across anthropology, personality, climate, and sleep domains. The module falsifier is any ethnographic survey of at least 100 cultures showing a modal count reliably outside 5 plus or minus 1.
scope and limits
- Does not derive the count from the T0-T8 forcing chain or Recognition Composition Law.
- Does not specify age boundaries or phi-scaled ratios between grades.
- Does not address cultural exceptions or non-modal counts in ethnographic data.
formal statement (Lean)
43theorem ageGradeCount_pos : 0 < ageGradeCount := by
proof body
Term-mode proof.
44 rw [ageGradeCount_eq]; norm_num
45
46/-- Adolescence/childhood age boundary ratio ≈ φ. -/