{
  "controller": "soft_actuator",
  "name": "Soft (tanh) actuator \u2014 smooth saturation, band-guarded",
  "kind": "controller",
  "label": "A transcendental control kernel. tanh gives smooth saturation (no derivative kick at the edge); the clamp is the hard guard. The @verify contract PROVES the output stays in [-1,1]; the forward-error certificate BOUNDS how far the compiled float64 tanh drifts from exact (Certcom.pipeline_nested_std).",
  "source": {
    "eml": "examples/soft_actuator.eml",
    "sha256": "66d899cb3171f438"
  },
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      "file": "emit/soft_actuator.cpp",
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      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "csharp",
      "category": "software",
      "file": "emit/SoftActuator.cs",
      "lines": 44,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "gdscript",
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      "file": "emit/soft_actuator.gd",
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      "ok": true,
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    },
    {
      "target": "go",
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    {
      "target": "java",
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    },
    {
      "target": "javascript",
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      "ok": true,
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    },
    {
      "target": "kotlin",
      "category": "software",
      "file": "emit/soft_actuator.kt",
      "lines": 27,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "luau",
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      "file": "emit/soft_actuator.luau",
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      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "matlab",
      "category": "software",
      "file": "emit/soft_actuator.m",
      "lines": 22,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "python",
      "category": "software",
      "file": "emit/soft_actuator.py",
      "lines": 21,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "rust",
      "category": "software",
      "file": "emit/soft_actuator.rs",
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      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "swift",
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    },
    {
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    {
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      "ok": true,
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    {
      "target": "glsl-es",
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      "ok": true,
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    {
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      "ok": true,
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    {
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    {
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    {
      "target": "llvm",
      "category": "compiler IR",
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      "lines": 38,
      "ok": true,
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    },
    {
      "target": "coq",
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    },
    {
      "target": "isabelle",
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      "ok": true,
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    },
    {
      "target": "lean",
      "category": "proof",
      "file": "emit/soft_actuator.lean",
      "lines": 47,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "aadl",
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      "file": "emit/soft_actuator.aadl",
      "lines": 39,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "ada/spark",
      "category": "safety-critical",
      "file": "emit/soft_actuator.adb",
      "lines": 24,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "autosar",
      "category": "safety-critical",
      "file": "emit/soft_actuator.autosar.c",
      "lines": 57,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "ros2",
      "category": "safety-critical",
      "file": "emit/soft_actuator_pkg",
      "lines": 0,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "solidity",
      "category": "blockchain",
      "file": "emit/soft_actuator.sol",
      "lines": 42,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "zkproof",
      "category": "blockchain",
      "file": "emit/soft_actuator.zk.json",
      "lines": 14,
      "ok": true,
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    }
  ],
  "proof": {
    "theorem": "soft_actuator_within_band",
    "claim": "the soft-actuator output is always within the band [-1, 1], for any input",
    "trail_file": "proof/soft_actuator_within_band.axioms.txt",
    "clean": true,
    "forbidden_axioms_found": [],
    "rederived": "2026-07-10T08:02:45Z",
    "source_artifact": "examples/soft_actuator.eml  ->  eml-compile --target lean   (the artifact the zoo ships; NOT a probe)",
    "reverify": "make verify-proof",
    "tier": "REPLAY (re-derive: TOOLCHAIN \u2014 Lean)"
  },
  "sim": {
    "band": "[-1.0, 1.0]",
    "gain": 2.0,
    "samples": 400,
    "output_peak": 1.0,
    "trace_csv": "trace.csv",
    "plot_png": "soft_actuator.png",
    "check": {
      "quantity": "soft-actuator output samples outside the band [-1,1]",
      "value": 0,
      "relation": "=",
      "bound": 0,
      "holds": true,
      "context": "across a \u00b15 error sweep the tanh output saturates smoothly and stays in [-1.0,1.0] (peak |1.0|) \u2014 the band the theorem proves, the transcendental the forward-error certificate bounds"
    },
    "tier": "LOCAL"
  },
  "certificate": {
    "applicable": true,
    "function": "soft_actuator",
    "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": {
      "error": 100.0,
      "gain": 10.0
    },
    "bound_abs": 1.1113332476497817e-13,
    "bound_ulps_of_result": 1001.0,
    "output_magnitude_bound": 1.0,
    "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 1.111e-13 (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/soft_actuator_forward_error.lean",
    "lean_proof_tier": "TOOLCHAIN"
  },
  "hardware": {
    "tier": "n/a"
  }
}