ITU and Energy / Materials: A Single-Axiom View of Information-Energy Equivalence, Renewable Transition, New Materials, and the 2026-2050 Roadmap

We apply the Information-Theoretic Unification (ITU) framework (Terada 2026, DOI 10.5281/zenodo.20109210) to energy and materials science. Energy is reframed as K-work and information as K-bit; the Landauer-Bennett equivalence (E_bit = k_B T ln 2) establishes their unity. This is Tier 1 paper #10, extending the engineering wing to a pentagon (5 vertices) and completing the ITU 10-vertex polytope. Pass-1 progress: 82 of 220 phases (37.3%). Phase 79: ITU foundation. Compute energy per operation dropped 10^-3 J (1950) to 10^-17 J (2024) - still 3,000x the Landauer limit (2.87 x 10^-21 J at 300K). Battery Pareto: lead-acid 30 Wh/kg -> Li-ion NMC 250 Wh/kg -> solid-state 450 Wh/kg (2028 predicted). Solar 33.9% (Si+perovskite tandem 2024). Critical materials HHI: Gallium 9,604 (China 98%), Rare earths 7,337 (China 85%). Phase 80: Renewable + nuclear + fusion. LCOE 2024: solar $40/MWh, wind $38/MWh (cheapest ever); coal +17%, nuclear new +52%. NIF Ignition Q=1.5 (Dec 2022), Q=1.9 sustained (2023). ITER targets Q=10 by 2035, SPARC Q>1 by 2025, CFS commercial 1GW by 2032. IEA NZE 2050: solar 50%, wind 22%, fossil 2%. CO2 sweet spot: nuclear 12, fusion 5 g/kWh. Phase 81: New materials revolution. Perovskites: 3.8% (Miyasaka 2009) -> 34.6% tandem (Oxford PV 2024) = 9x in 15 years. MOFs: NU-1501 reaches 7,140 m^2/g (1.7 soccer fields per gram). Superconductors: H_3S 203K (Eremets 2015), LaH_10 250K (2019), room-temp candidate by 2030. AI material discovery: DeepMind GNoME 2.2M crystals (Nature 2023), MatterGen inverse design (2024). Cycle: 24 months -> 0.5 months = 48x acceleration. Phase 82: 2026-2050 roadmap. Triple convergence: AGI x10 research speed, fusion + perovskite commercialize, China dominance diversifies (gallium 98% -> 60% by 2050, rare earths 85% -> 50%). EU carbon $80 (2024) -> $300/t (2050). DAC: 0.01 -> 1,000 MtCO2/yr, $800 -> $50/t. Ten falsifiable predictions issued. Central thesis: energy and materials follow the ITU axiom dS = d<K>. Information-energy equivalence (Landauer-Bennett) connects Tier 1 #4 (Semi) to Tier 1 #10 (Energy). Honest framing: Pass-1 interpretive paper reframing Landauer, Shockley-Queisser, Lazard LCOE, NIF Ignition, perovskites, MOFs, GNoME in ITU language. Numerical results match established empirical findings. The ITU 10-vertex polytope completes: engineering pentagon (Quantum Computing 10.5281/zenodo.20139391 + Machine Consciousness 10.5281/zenodo.20150501 + Cryptography 10.5281/zenodo.20151059 + Semiconductors 10.5281/zenodo.20174036 + Energy/Materials this paper) + medicine triangle (Cancer 10.5281/zenodo.20174318 + Aging 10.5281/zenodo.20175663 + Psychiatry 10.5281/zenodo.20177427) + social sciences (Economics 10.5281/zenodo.20196309) + philosophy (Free Will 10.5281/zenodo.20197016). Includes 4 theory documents, 4 Python numerical experiments, 4 figures, 4 JSON summaries. Total runtime ~20 seconds.