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      "maximum": 2e-13,
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      "actual": 1.5988968537094746e-15,
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      "maximum": 1e-12,
      "pass": true
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    {
      "actual": 0.8000999267131019,
      "id": "smooth-positive-density-N400",
      "minimum": 0,
      "pass": true
    },
    {
      "actual": 0.9999999999999972,
      "id": "smooth-positive-pressure-N400",
      "minimum": 0,
      "pass": true
    },
    {
      "actual": 4.440892098500626e-16,
      "id": "smooth-conservation-N400",
      "maximum": 2e-11,
      "pass": true
    },
    {
      "actual": 0,
      "id": "smooth-reconstruction-fallbacks-N400",
      "maximum": 0,
      "pass": true
    },
    {
      "actual": 2.7755575615628914e-15,
      "id": "smooth-pressure-invariant-N400",
      "maximum": 5e-12,
      "pass": true
    },
    {
      "actual": 7.216449660063518e-16,
      "id": "smooth-velocity-invariant-N400",
      "maximum": 5e-12,
      "pass": true
    },
    {
      "actual": 5.879153056466441e-16,
      "id": "smooth-primitive-pressure-recovery-residual-N400",
      "maximum": 2e-13,
      "pass": true
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    {
      "actual": 1.490439963373945e-15,
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      "maximum": 1e-12,
      "pass": true
    },
    {
      "actual": true,
      "expected": true,
      "id": "failure-injection-negative-pressure-primitive",
      "pass": true
    },
    {
      "actual": true,
      "expected": true,
      "id": "failure-injection-superluminal-primitive",
      "pass": true
    },
    {
      "actual": true,
      "expected": true,
      "id": "failure-injection-non-dominant-conserved-state",
      "pass": true
    },
    {
      "actual": true,
      "expected": true,
      "id": "failure-injection-entropy-violating-expansion-shock-branch",
      "pass": true
    }
  ],
  "environment": {
    "architecture": "arm64",
    "arithmetic": "IEEE-754 binary64 Number operations",
    "dependencies": "Node.js standard library only",
    "network": false,
    "node": "v24.18.0",
    "platform": "darwin",
    "random_input": false,
    "wall_clock_input": false
  },
  "exact_problem_1": {
    "entropy": {
      "left_rarefaction_log_p_over_rho_gamma_change": 4.440892098500626e-16,
      "right_shock_log_p_over_rho_gamma_increase": 11.479832882116584
    },
    "initial_data": {
      "diaphragm": 0.5,
      "domain": [
        0,
        1
      ],
      "gamma": 1.6666666666666667,
      "left": {
        "p": 13.333333333333334,
        "rho": 10,
        "v": 0
      },
      "right": {
        "p": 0.000001,
        "rho": 1,
        "v": 0
      }
    },
    "lax_compressivity": {
      "lambda_plus_ahead": 0.0012909928349957706,
      "lambda_plus_behind": 0.9017039364077882,
      "pass": true,
      "shock_speed": 0.8283980341905277
    },
    "positions": {
      "contact_at_t_0_4": 0.7856082803730546,
      "left_head_at_t_0_4": 0.21355405038422687,
      "left_tail_at_t_0_4": 0.5668945175728419,
      "right_shock_at_t_0_4": 0.8313592136762111
    },
    "pressure_root": {
      "iterations": 49,
      "pressure_bracket_log_width": 1.318944953254599e-13,
      "star_velocity_mismatch_before_alignment": 2.220446049250313e-16,
      "star_velocity_mismatch_maximum": 2e-13,
      "star_velocity_root_tolerance": 2e-15,
      "status": "converged"
    },
    "published_reference": {
      "citation": "Marti and Muller, Living Reviews in Computational Astrophysics 1, 3 (2015), section 6.3, Table 3; exact construction in section 8.5",
      "doi": "10.1007/lrca-2015-3",
      "values": {
        "compression_ratio": 5.070776,
        "shell_velocity": 0.71402,
        "shell_width_per_time": 0.114378,
        "shock_velocity": 0.828398
      }
    },
    "rankine_hugoniot_normalized_residual": {
      "D": 0,
      "S": 0,
      "tau": -2.3722898688700883e-16
    },
    "star_left": {
      "p": 1.4479451559941345,
      "rho": 2.639295549545604,
      "v": 0.7140207009326364
    },
    "star_right": {
      "p": 1.4479451559941345,
      "rho": 5.070775964247518,
      "v": 0.7140207009326364
    },
    "wave_pattern": "left rarefaction / contact / right shock",
    "wave_speeds": {
      "contact": 0.7140207009326364,
      "left_head": -0.7161148740394329,
      "left_tail": 0.16723629393210487,
      "right_shock": 0.8283980341905277
    }
  },
  "failure_injections": [
    {
      "diagnostic": "primitive state pressure must be positive",
      "id": "negative-pressure-primitive",
      "rejected": true
    },
    {
      "diagnostic": "primitive state velocity must satisfy |v| < 1",
      "id": "superluminal-primitive",
      "rejected": true
    },
    {
      "diagnostic": "injected non-dominant state violates E > |S|",
      "id": "non-dominant-conserved-state",
      "rejected": true
    },
    {
      "diagnostic": "shock branch requires pressure behind the shock to exceed pressure ahead",
      "id": "entropy-violating-expansion-shock-branch",
      "rejected": true
    }
  ],
  "limitations": [
    "This is a one-dimensional special-relativistic hydrodynamics verification problem, not a production GRHD or multidimensional solver.",
    "HLLE does not resolve the contact wave exactly; its diffusion is measured rather than hidden.",
    "The one-dimensional bundle cannot diagnose multidimensional carbuncle or odd-even grid-alignment instabilities.",
    "No atmosphere or primitive-variable floor is used; an inadmissible state terminates the run.",
    "The exact-solution quadrature and finite-volume evolution share the gamma-law equation of state but use different wave constructions."
  ],
  "numerical_method": {
    "boundary_conditions": {
      "shock": "constant outflow",
      "smooth": "periodic"
    },
    "conserved_variables": [
      "D=rho W",
      "S=rho h W^2 v",
      "tau=rho h W^2-p-D"
    ],
    "equation_of_state": "p=(Gamma-1) rho epsilon, h=1+Gamma p/[(Gamma-1)rho]",
    "flux": [
      "D v",
      "S v+p",
      "S-D v"
    ],
    "primitive_recovery": "safeguarded Newton-bisection solve for positive pressure with normalized residual and conserved-variable round-trip postconditions; no floors",
    "reconstruction": "piecewise-linear primitive variables with monotonized-central limiter and local first-order fallback only if a face state is inadmissible",
    "riemann_flux": "HLLE with local relativistic acoustic signal speeds",
    "time_integrator": "second-order strong-stability-preserving Runge-Kutta"
  },
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