{
  "status": "PASS",
  "scope": "Continuous conditional model domain, not an observational theta_Bn interval or covariance region.",
  "domain": {
    "r": [
      "22500/18769",
      "32400/16129"
    ],
    "b": [
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    ],
    "t=r*h": [
      "0",
      "1"
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    "ordinary_fast": "0<=t<1; t=0 separately checked perpendicular limit"
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    "induction": "PASS",
    "normal_momentum": "PASS",
    "total_energy": "PASS"
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      ],
      "minimum_lower_bound": 0.028231496238252444
    }
  },
  "entropy": "Reuse the R93 algebraic dp2/dh=2*M*(r-1)^3/W^2>0 and perpendicular gas-Hugoniot lower bound. M,W remain positive on the enlarged domain; therefore the same positive entropy bound applies.",
  "inherited_entropy_lower_outward": "0.0014871475049217420582322361124611737540351547578899",
  "angle_mapping": "A=2*M*(1-t)^2/(r*W); dA/dh=-4*M*(1-t)*(2*r+1-t*(4-r))/W^2<0 for t<1, because the last factor >=3*(r-1)>0. h increases and A decreases; theta=atan(sqrt(A/h)) decreases continuously from 90 to 0 degrees.",
  "actual_regular_fast_angle_domain": "0<theta<=90 degrees under this normalized input domain; 83.3 degrees is not a physical cutoff.",
  "endpoint": "theta=0,t=1 is a switch-on/characteristic degeneracy. It remains UNRESOLVED as an ordinary class. Numerical guard neighborhoods remain UNRESOLVED even where the exact open-domain proof applies.",
  "other_regular_families": "For M>0 and 1<r<2.5, physical non-fast quadratic completions have 1/r<h<h_pole<1 and reverse Bt. They cross the normal Alfven characteristic and fail the necessary unrestricted transverse evolutionary test. A slow state requires h>1 where A<0. This excludes regular slow only under the stated inputs/flow, not observationally."
}