C3: RAIDE Atom — Economic Viability of a Price-Responsive Hydroelectric Edge-Computing Node for Renewable Curtailment Mitigation

This paper demonstrates the economic viability of a single RAIDE Atom node: a price-responsive AI compute installation co-located with a hydroelectric facility, operating exclusively on renewable energy surplus (curtailed or near-zero-cost electricity). The primary validation site is Miranda do Douro (Trás-os-Montes, Portugal), analysed across two scaling classes: M0 (20 MW IT) and M4 (144 MW IT with full floating photovoltaic coverage). The canonical value multiplier ΦBᶜan = 16. 8× (Mₙet = 1, 221 €/MWh against p₀ = 72. 62 €/MWh, the OMIE PT 2023–2025 mean) and the operational multiplier ΦBᵒps = 14. 7× (γ = 0. 875, ηₒcc = 0. 85) are derived from ten audited constants and validated against 8, 759 real OMIE 2024 hourly price observations. A dual-reference framework confirms ΦB, real = 19. 3× against the actual 2024 Portugal mean (63. 19 €/MWh). Φ remains ≥ 10× under all simultaneous pessimistic conditions documented since 2020. The GPU rental breakeven price is 0. 032 €/GPU-h — 47× below the current market floor of 1. 50 €/GPU-h. Full-site payback is 3. 1–3. 7 years (IRR = 33. 4%), incorporating a calibrated occupancy ramp-up trajectory (20% → 85% over three years) consistent with industry data for new compute facilities. Canonical payback without ramp-up is 2. 1 years, confirmed identically at M0 and M4 — demonstrating linear scalability. A four-state Adaptive Finite Automaton (AFA) governs node behaviour with sub-50 ms transitions, monthly threshold recalibration from two publicly observable OMIE signals, and three structural invariants that hold unconditionally across all admissible market conditions. Two self-reinforcing extension mechanisms preserve all Φ invariants: an endogenous FPV expansion trigger and a self-optimising internal AI reserving κAI = 6% of compute capacity, self-funded at break-even +4. 7 pp occupancy improvement. Cross-validation at four Iberian hydroelectric nodes — Miranda do Douro (PT, Douro), Alqueva (PT, Guadiana), Belesar (ES, Miño), and Ricobayo (ES, Esla) — confirms consistent payback across reservoir areas 12–250 km² and IT capacities 14–636 MW. Drought sensitivity analysis confirms WACC-viable payback under 1σ drought conditions across all four basins. A triple impact table across four deployment phases (Nano Atom 0. 013 MW through M4 Rede Ibérica 635 MW) quantifies financial, environmental, and social returns: revenue from <1 M€/yr to 3, 779 M€/yr; CO₂ avoided from <1 kt/yr to 1, 448 kt/yr; jobs created from 4 to 2, 540. The opportunity momentum coefficient M⁻ (Δt) formalises the cost of inaction: under the base case scenario at Miranda M0, a one-year delay destroys 178. 9 M€ in forgone net revenue — a cost that grows super-linearly due to infrastructure appreciation at r̄ = 0. 072 yr⁻¹. Wright's Law GPU price calibration (R² = 0. 992, six verified data points Jan 2023–Oct 2025, implied halving time 1. 6 years) confirms sustained viability under hardware cost trajectories through at least mid-2027 for the Blackwell B200 generation. Structural comparison with China's East Data West Compute (EDWC) programme establishes a 10–40× carbon advantage and full-spectrum latency superiority for the Iberian deployment. This paper is C3 of the five-paper RAIDE series: C1: A Structural Invariant in Zero-Cost Co-Production Systems C2: A Four-Axiom Framework for Selecting High-Performance Zero-Cost Co-Production Systems C3: RAIDE Atom — Economic Viability of a Price-Responsive Hydroelectric Edge-Computing Node (this paper) — DOI: 10. 5281/zenodo. 19632890 C4: RAIDE Network — Hub-and-Spoke Architecture for Sovereign Distributed AI Compute C5: RAIDE National — Framework Application to All 82 Eligible Portuguese Hydroelectric Nodes