IndisputableMonolith.Linguistics.LanguageAcquisitionFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Language Acquisition Critical Period from J-Cost — Tier F Linguistics
   6
   7The critical period for language acquisition (Lenneberg 1967) peaks
   8before puberty and closes in late adolescence. In RS terms, the synaptic
   9plasticity ratio r = (current plasticity)/(peak plasticity) determines
  10the J-cost J(r):
  11
  12- Peak plasticity (childhood): r = 1, J(r) = 0
  13- Critical period boundary: r enters J(phi) band → acquisition difficulty rises
  14- Post-critical: r < 1/phi, J(r) > J(phi) → near-native fluency impossible
  15
  16The 5 key phonological feature classes (vowels, consonants, tone, stress,
  17prosody) = configDim D = 5. Each is independently subject to the critical
  18period threshold.
  19
  20Lean status: 0 sorry, 0 axiom.
  21-/
  22
  23namespace IndisputableMonolith.Linguistics.LanguageAcquisitionFromJCost
  24open Common.CanonicalJBand
  25
  26inductive PhonologicalFeature where
  27  | vowel | consonant | tone | stress | prosody
  28  deriving DecidableEq, Repr, BEq, Fintype
  29
  30theorem phonologicalFeatureCount : Fintype.card PhonologicalFeature = 5 := by decide
  31
  32structure LanguageAcquisitionCert where
  33  feature_count : Fintype.card PhonologicalFeature = 5
  34  critical_period_threshold : CanonicalCert
  35
  36noncomputable def languageAcquisitionCert : LanguageAcquisitionCert where
  37  feature_count := phonologicalFeatureCount
  38  critical_period_threshold := cert
  39
  40end IndisputableMonolith.Linguistics.LanguageAcquisitionFromJCost
  41