{
  "applicable": true,
  "function": "catenary",
  "fragment": "arithmetic (lit/const/var/+/\u2212/\u00d7/unary\u2212) + clamp/abs (1-Lipschitz) + transcendentals sin/cos/tanh/atan (globally-Lipschitz) and exp/sinh/cosh (symmetric-domain local), nested to any depth",
  "regime": "absolute (cancellation-tolerant; inputs are sign-unconstrained so sums may cancel, where a relative bound would be unbounded)",
  "assumption": "IEEE-754 binary64 round-to-nearest, unit roundoff u = 2^-53 \u2248 1.110e-16",
  "input_ranges": {
    "scale": 5.0,
    "curv": 0.5,
    "x": 4.0
  },
  "bound_abs": 8.353752558773201e-15,
  "bound_ulps_of_result": 75.24391382167263,
  "output_magnitude_bound": 20.0,
  "lean_theorem": "Certcom.pipeline_nested_std  (arithmetic + sin/cos/tanh/atan/exp/sinh/cosh)",
  "lean_status": "machine-checked, sorryAx-free; claim_audit gate 'pipeline-arith-general-changelog'",
  "meaning": "For every input in the declared ranges, the compiled kernel's float64 result is within 8.354e-15 (absolute) of the exact real value, given the assumption. The soundness of this bound is the Lean theorem; this harness computes its instantiation for the kernel. clamp is 1-Lipschitz, so the clamped output inherits the pre-clamp arithmetic bound (absenc_lip, L=1).",
  "tier": "LOCAL",
  "lean_proof_file": "certificate/catenary_forward_error.lean",
  "lean_proof_tier": "TOOLCHAIN"
}