ageGradeCount_eq
The equality fixes the universal count of human age grades at exactly five. Anthropologists and cross-cultural researchers would cite it when matching Recognition Science predictions to ethnographic patterns such as those in Murphy 1971 and Bernardi 1985. The proof reduces directly by reflexivity to the constant definition of the age-grade count.
claimThe number of universal age grades recognized across human societies equals five: $5$.
background
The module develops age-grading systems from the configuration dimension in Recognition Science. Age grades (childhood, adolescence, adulthood, middle age, old age) appear universally, with most cultures recognizing exactly five. This matches other five-fold structures forced by configDim D = 5, including the Big Five personality factors, five Köppen climate zones, and five sleep stages. The upstream definition ageGradeCount simply sets this count to the constant five.
proof idea
The proof is a one-line reflexivity wrapper that reduces the theorem directly to the constant definition of ageGradeCount.
why it matters in Recognition Science
This equality supplies the base count for the positivity theorem ageGradeCount_pos and the certification def cert that packages the full AgeGradingCert. It fills the structural claim that five grades are forced by configDim D = 5, consistent with the phi-ladder and eight-tick octave landmarks. The module doc flags the open ethnographic question of whether surveys of at least 100 cultures confirm the modal count remains 5 ± 1.
scope and limits
- Does not derive the count from configDim without the module's structural assumptions.
- Does not supply quantitative ethnographic data or statistical tests.
- Does not compute the specific age-boundary ratios or phi-scaling.
- Does not address cultural exceptions or historical variation in grade systems.
Lean usage
theorem ageGradeCount_pos : 0 < ageGradeCount := by rw [ageGradeCount_eq]; norm_numformal statement (Lean)
41theorem ageGradeCount_eq : ageGradeCount = 5 := rfl
proof body
42