cert
cert assembles an explicit AgeGradingCert instance asserting exactly five age grades whose childhood-to-adolescence duration ratio is positive and lies within 0.1 of φ. Researchers testing Recognition Science predictions for cultural universals would cite this when mapping configDim D=5 onto ethnographic patterns of five grades. The definition is a direct record constructor that assigns the three fields from prior equality, positivity, and bound results.
claimThe certificate cert asserts that the number of age grades equals 5, that the ratio of adolescence duration to childhood duration is positive, and that this ratio satisfies $|r - φ| < 0.1$.
background
In the anthropology module, configDim D=5 forces five universal age grades (childhood, adolescence, adulthood, middle age, old age) whose adjacent durations scale near φ, matching the observed childhood-to-adolescence ratio 20/12 ≈ 1.667. AgeGradingCert is the structure that packages the three required properties: grade count equals 5, the ratio adolescenceChildhoodRatio exceeds zero, and its absolute deviation from φ stays below 0.1. Upstream results supply these facts directly: ageGradeCount_eq by reflexivity, adolescenceChildhoodRatio_pos by normalization, and adolescenceChildhoodRatio_near_phi by bounding φ between 1.61 and 1.62 then applying the absolute-value inequality.
proof idea
cert is defined by constructing the AgeGradingCert record with grade_count assigned to ageGradeCount_eq, ratio_pos assigned to adolescenceChildhoodRatio_pos, and ratio_near_phi assigned to adolescenceChildhoodRatio_near_phi. This is a direct one-line structure builder that invokes no further lemmas or tactics.
why it matters in Recognition Science
cert closes the structural theorem for age-grading systems by supplying the concrete certificate that realizes the configDim D=5 prediction of five grades with ratios near φ. It supplies the terminal object in the module that would feed any larger claim linking Recognition Science to cultural patterns such as the Big Five factors and Köppen zones. The construction rests on the phi fixed point from the forcing chain T5-T6 and the eight-tick octave that also governs physical constants.
scope and limits
- Does not prove that five grades appear in every culture.
- Does not derive specific year boundaries from first principles.
- Does not address societies whose modal grade count deviates from five.
- Does not connect directly to the T0-T8 forcing chain.
formal statement (Lean)
66noncomputable def cert : AgeGradingCert where
67 grade_count := ageGradeCount_eq
proof body
Definition body.
68 ratio_pos := adolescenceChildhoodRatio_pos
69 ratio_near_phi := adolescenceChildhoodRatio_near_phi
70