{
  "summary": {
    "status": "PASS",
    "checkpoint": "R100",
    "source_R99_sha256": "34aa2f1d11bf10c6a5a5d9028486cdcf64737a1bed5129069241c84ae89f30c4",
    "protocol_sha256": "9cc889f066a9604bbee2126aac68f2b4a82fd9fe79e43095953f062282efa93f",
    "case_results": [
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      {
        "name": "C_dependent_strip",
        "status": "FAST_EXCLUDED_OVER_SET",
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    "same_marginal_bounds_B_C": true,
    "strip_Bernstein_certificate": "STRICTLY_POSITIVE",
    "wrong_Mach_squared_convention_rejected": true,
    "equality_not_excluded": true,
    "arithmetic": "exact rational endpoint, monotonicity and polynomial certificates; no sampling certificate",
    "error_semantics": "declared model hard bounds, not observational confidence intervals",
    "historical_audits_rerun": false,
    "fast_state_constructed_in_overlap": false,
    "unique_slow_identification": false,
    "solar_identification": false,
    "native_browser_tested": false
  },
  "reference_compression_enclosure": {
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  "reference_Mach_squared": "3",
  "x_definition": "M_n/sqrt(3)",
  "fast_bound": "4x²/(1+x²)",
  "signed_margin": "r - 4x²/(1+x²)",
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      "compression_absolute_error": {
        "exact": "1/20",
        "decimal": "0.05"
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      "Mach_relative_error": {
        "exact": "1/20",
        "decimal": "0.05"
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      "x_bounds": {
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          "exact": "19/20",
          "decimal": "0.95"
        },
        "upper": {
          "exact": "21/20",
          "decimal": "1.05"
        }
      },
      "Mach_squared_bounds": {
        "lower": {
          "exact": "1083/400",
          "decimal": "2.7075"
        },
        "upper": {
          "exact": "1323/400",
          "decimal": "3.3075"
        }
      },
      "fast_bound_at_upper_Mach": {
        "exact": "1764/841",
        "decimal": "2.0975029726516052318668252080856123662306777645659928656361474435196195005945303"
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      "minimum_location": {
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        "x": "21/20"
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      "maximum_location": {
        "r": "r0 + compression_error",
        "x": "19/20"
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      "monotonicity_certificate": {
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        "dG_dr": "1 > 0",
        "H_monotonicity": "dH/dr=1+x²>0; dH/dx=2x(r-4)<0 on these sets"
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      "polynomial_sign_route": {
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      "status": "FAST_EXCLUDED_OVER_SET",
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    {
      "name": "B_wider_box",
      "set_type": "Cartesian hard set; all marginal combinations allowed",
      "compression_absolute_error": {
        "exact": "1/20",
        "decimal": "0.05"
      },
      "Mach_relative_error": {
        "exact": "1/10",
        "decimal": "0.1"
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      "x_bounds": {
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          "exact": "9/10",
          "decimal": "0.9"
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        "upper": {
          "exact": "11/10",
          "decimal": "1.1"
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      },
      "Mach_squared_bounds": {
        "lower": {
          "exact": "243/100",
          "decimal": "2.43"
        },
        "upper": {
          "exact": "363/100",
          "decimal": "3.63"
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      },
      "fast_bound_at_upper_Mach": {
        "exact": "484/221",
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      "minimum_location": {
        "r": "r0 - compression_error",
        "x": "11/10"
      },
      "maximum_location": {
        "r": "r0 + compression_error",
        "x": "9/10"
      },
      "monotonicity_certificate": {
        "dF_dx": "8x/(1+x²)² > 0",
        "dG_dr": "1 > 0",
        "H_monotonicity": "dH/dr=1+x²>0; dH/dx=2x(r-4)<0 on these sets"
      },
      "polynomial_sign_route": {
        "minimum_H": {
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            "exact": "-525640186055590305583046244405697396033338835817329153928519514363947/3291009114642412084309938365114701009965471731267159726697218048000000",
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        "maximum_H": {
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        "agrees": true
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      "status": "BOUND_OVERLAP",
      "fast_existence_established": false
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    {
      "name": "C_dependent_strip",
      "set_type": "imposed hard relation; not an inferred covariance",
      "definition": "t in [-1,1], δ in [-0.01,0.01]; x=1+0.1t; r=r0+0.04t+δ",
      "r_outer_bounds": {
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          "exact": "9/10",
          "decimal": "0.9"
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        "upper": {
          "exact": "11/10",
          "decimal": "1.1"
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      },
      "Mach_squared_bounds": {
        "lower": {
          "exact": "243/100",
          "decimal": "2.43"
        },
        "upper": {
          "exact": "363/100",
          "decimal": "3.63"
        }
      },
      "slope": {
        "exact": "1/25",
        "decimal": "0.04"
      },
      "strip_half_width": {
        "exact": "1/100",
        "decimal": "0.01"
      },
      "Mach_relative_error": {
        "exact": "1/10",
        "decimal": "0.1"
      },
      "minimum_margin": {
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      "minimum_location": {
        "t": "1",
        "delta": "-1/100",
        "r": "r0+0.03",
        "x": "11/10"
      },
      "maximum_location": {
        "t": "-1",
        "delta": "1/100",
        "r": "r0-0.03",
        "x": "9/10"
      },
      "monotonicity_certificate": {
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          "exact": "7200/48841",
          "decimal": "0.14741712905141172375667983866014209373272455518928768862226408140701459839069634"
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        "dG_dt_upper": {
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        },
        "dG_ddelta": "1 > 0",
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      },
      "Bernstein_certificate": {
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            "decimal": "0.31554745349257142913692070578471994183831542317014265925054925827422509051222634"
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            "exact": "1/2500",
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        "power_s": [
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          {
            "exact": "2/625",
            "decimal": "0.0032"
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        "Bernstein_coefficients": [
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            "decimal": "0.22247312285316952439292319480123607332986207823719717679348331811957555171178018"
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          {
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            "decimal": "0.017079936109291429196297379892115535731338542603007638471856930393018725016010109"
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        "coefficient_reconstruction_exact": true,
        "strict_lower_H_bound": {
          "exact": "56210225413188150922950858546581742528556566270704685751548636522453/3291009114642412084309938365114701009965471731267159726697218048000000",
          "decimal": "0.017079936109291429196297379892115535731338542603007638471856930393018725016010109"
        },
        "conversion": "t=2s-1, s∈[0,1]; H=Σ b_j C(3,j)s^j(1-s)^(3-j)",
        "status": "STRICTLY_POSITIVE"
      },
      "status": "FAST_EXCLUDED_OVER_SET",
      "fast_existence_established": false
    }
  ],
  "controls": {
    "Mach_vs_Mach_squared": {
      "correct_Mach_squared_bounds": {
        "lower": {
          "exact": "243/100",
          "decimal": "2.43"
        },
        "upper": {
          "exact": "363/100",
          "decimal": "3.63"
        }
      },
      "incorrect_Mach_squared_bounds": {
        "lower": {
          "exact": "27/10",
          "decimal": "2.7"
        },
        "upper": {
          "exact": "33/10",
          "decimal": "3.3"
        }
      },
      "incorrect_bound_at_upper_Mach": {
        "exact": "44/21",
        "decimal": "2.0952380952380952380952380952380952380952380952380952380952380952380952380952381"
      },
      "incorrect_minimum_margin": {
        "lower": {
          "exact": "15574643426512293003256822054230946276687602105934798936510631717453/691111914074906537705087056674087212092749063566103542606415790080000",
          "decimal": "0.022535631508190476473222257654264732823919616346976091530036533899017307160875076"
        },
        "upper": {
          "exact": "62298573706049172013027288216923785106750408423739195746042526869833/2764447656299626150820348226696348848370996254264414170425663160320000",
          "decimal": "0.022535631508190476473222257654264732823919616346976091530036533899024903615071684"
        }
      },
      "incorrect_status": "FAST_EXCLUDED_OVER_SET",
      "correct_status": "BOUND_OVERLAP",
      "invalid_convention_rejected": true,
      "meaning": "Wrong screen is a rejected convention control, not an alternative scientific result"
    },
    "equality": {
      "r": "2",
      "x": "1",
      "margin": "0",
      "status": "NOT_EXCLUDED_BY_BOUND"
    },
    "invalid_domains_rejected": [
      [
        "1",
        "2",
        "1",
        "2"
      ],
      [
        "2",
        "3",
        "0",
        "1"
      ]
    ]
  },
  "reference_compatibility": "Saved R99/R98 slow witness belongs to all three sets; no new witness calculated",
  "scope": "Evolutionary fast within the R99 ideal-MHD theorem; other structures remain unexcluded"
}