[{"role":"user","content":"Run a pass: suppressing edge-localized modes (ELMs) in a tokamak."},{"role":"assistant","content":"## 1. Operator\n```python\nimport math\ndef elm_rmp_gain(pedestal_gradient, rmp_current_ka):\n drive = math.tanh(0.8 * pedestal_gradient) - 0.3 * min(1.0, max(0.0, rmp_current_ka / 5.0))\n return round(max(0.0, min(1.0, 0.5 + 0.5 * drive)), 6)\n```\n\n## 2. Analogy\nVector: [0.70, 0.85, 0.40, 0.90, 0.75]. Analogue: sandpile avalanches (self-organized criticality). Transfers: a slowly driven gradient that relaxes in bursts, and the idea that small continuous perturbations (RMPs ~ steady trickling) replace large avalanches with many small ones. Does NOT transfer: sandpiles have no magnetic topology or kinetic damping, so stochastic-field transport has no sandpile counterpart.\n\n## 3. Debate\n- Formalist (62): the operator is bounded but has no physics basis for the 0.3 coefficient.\n- Morphogenic (71): pellet pacing is a structurally different route that the operator ignores.\n- Strategist (78): RMP coils already exist on major devices, so this is the cheapest lever.\n- Empirical (55): RMPs reduce confinement; any gain must be checked against H-factor loss.\nFusion: RMP-first, with pellet pacing as fallback. Cheapest falsification: scan RMP current on an existing shot database and check if ELM frequency rises while energy per ELM falls.\n\n## 4. Stability audit\nVerdict: PROVEN (bounded, Lipschitz). d/dg of output \u003c= 0.5 * 0.8 = 0.4; d/dI \u003c= 0.5 * 0.3 / 5 = 0.03. Output is clamped to [0, 1].\n\n## 5. Synthesis\n1. Start with n=3 RMP coil scans at fixed density.\n2. Track ELM energy loss and H98 together, not ELM frequency alone.\n3. Add pellet pacing only where RMP penetration fails.\n4. Calibrate the 0.3 coefficient from the scan before trusting the operator."}]