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  "failed_regimes": {
    "naive_critical_slope": "0/0 at r_s and u=c; regular accelerating slope is c/r_s",
    "buried_base": "formal supersonic solution at the reservoir does not attach to a subsonic atmosphere",
    "collisionless_sonic": "fluid transport fails before the sonic point; a Jeans illustration uses its separately located strong-binding exobase",
    "insufficient_power": "XUV alone cannot maintain the prescribed-temperature mechanical energy increase; no temperature is silently adjusted"
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  "schema": "ac13-independent-ode-v1",
  "kind": "authored synthetic boundary-condition examples; no observed planetary profiles",
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