ITU Tier 1+ #36: Education + Learning (K_edu)

Tier 1+ Pass-1.5 paper 36 of 45. ITU-derived education + learning on curriculum + student + pedagogy + assessment + institution. Ebbinghaus + Bloom 2-sigma + Khanmigo + ChatGPT EDU 2024.5. Defines K_edu = -log ρ_edu as the operator-algebraic modular Hamiltonian on H_curriculum ⊗ H_student ⊗ H_pedagogy ⊗ H_assessment ⊗ H_institution. K_edu inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Ebbinghaus 1885 R(t)=exp(-t/tau) + SM-2 spaced repetition: 30-day K_edu savings = 304.7 nat-days, 3.7e11 retention advantage at t=30. Bloom 1984 2-sigma + AI tutor: P(score>80) - control 0.1%, AI tutor (+1.5sigma) 6.6%, 1:1 tutor (+2sigma) 16.0%. AI tutor closes 75% of Bloom 2-sigma gap. Topics covered. Plato 387 BCE Academy, Bologna 1088 / Oxford 1096 / Paris 1150, Humboldt 1810, Piaget + Vygotsky + Skinner + Bloom, Ebbinghaus 1885, Khan Academy 2008 150M users, Coursera 2012 100M+ + edX 2012, ChatGPT 2022.11.30 + NYC ban 2023.1 reversed 2023.5, Khanmigo 2023.3 GPT-4 + ChatGPT EDU 2024.5 + Claude Education 2024.11, NAEP 2022/2024 largest declines 30yr, Byju's $22B bankruptcy 2024, US student debt $1.77T 2024.10 + Biden v Nebraska 2023.6.30 + demographic cliff 2025, PISA 2022 Singapore 575 + Japan 536 + USA 465, UNESCO SDG 4 + 87% literacy + 260M out of school + Afghanistan girls banned 2021, SFFA v Harvard 2023.6.29 + House v NCAA $2.78B 2024.10.7. 45-vertex polytope #36 top couplings: #2 AI (0.95), #28 Neuro (0.92), #33 Lang (0.92), #35 Law (0.85), #37 History (0.85), #9 FreeWill (0.85). Ten falsifiable predictions: P_avg=0.66, S/M/W=2/6/2: AI tutors halve achievement gap 2030 (0.55), Generative AI in 80% K-12 2027 (0.75), University demographic cliff 2030 (0.85), EU AI Act education compliance 2026 (0.75). Pass-2 roadmap: ~$1.8M: Edu BKT/DKT analytics ($600K) + Lean Mathlib ($200K) + AI tutor RCT Khan+OpenAI+Anthropic+Stanford+UPenn ($1M).