{
  "checkpoint": "R132",
  "final_scientific_lock": "PASS",
  "scope": "Two tilt-only planning strips, full tested upstream field angle 1..89 degrees; fixed R131 construction",
  "proof": {
    "energy_polynomial": "H(z)=A*(1-X*c*z)^2+z*(1-c)*((5*X+1)-2*c*z*(4*X-1)); c=cos(theta)^2, X>1, z>0",
    "fast_necessary": "bn^2<1/X implies bracket>(X-1)*(5*X-2)/X>0, hence A<0",
    "slow_necessary": "bn^2>1 implies bracket<3*(1-X)<0, hence A>0",
    "theta_domain": "1..89 degrees lies strictly inside 0<theta<90, so 0<c<1 throughout",
    "guard_logic": "Necessary signs apply to any hypothetical ordinary competing root, including roots hidden by numerical or cell guard bands. A rational pole is not an ordinary finite-state root. Other degeneracies remain unresolved and are not promoted to either ordinary family.",
    "numerics": "60-digit outward-rounded Decimal interval arithmetic over contiguous 0.125-degree tilt intervals, with a rigorous Taylor remainder and Machin arctangent series enclosure of pi.",
    "roundoff_padding": "Input floats padded by relative 2e-14, vector components by absolute 2e-14. This is conservative numerical padding, not new observational uncertainty.",
    "no_new_MHD_root_sweep": true
  },
  "planning_region": "ASSUMED axis-aligned box; tilt-only strips use theta in its full tested [1,89] range; no measured covariance or confidence level.",
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  "conclusions_downgraded": false,
  "scientific_scope_unchanged": "No observed E05 fast shock, slow shock or two physical waves identified.",
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