{
  "controller": "vibration_rms",
  "name": "Vibration RMS \u2014 one-sided sqrt, range-guarded",
  "kind": "controller",
  "label": "A sqrt kernel \u2014 the one-sided-domain primitive. sqrt is only Lipschitz away from 0, so its forward-error certificate needs a positive lower bound on the argument; here ax\u00b2+ay\u00b2\u22650 plus an additive NOISE_FLOOR supplies it honestly. The @verify contract PROVES the RMS magnitude stays in the sensor range [0,50] via the clamp; the certificate BOUNDS the compiled float64 sqrt's drift (Certcom.pipeline_pos_over_arith \u2014 ln/sqrt over an arithmetic core, conditional on the noise-floor lower bound).",
  "source": {
    "eml": "examples/vibration_rms.eml",
    "sha256": "a3b7f9cd162f69b6"
  },
  "emitted": [
    {
      "target": "c",
      "category": "software",
      "file": "emit/vibration_rms.c",
      "lines": 30,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "cpp",
      "category": "software",
      "file": "emit/vibration_rms.cpp",
      "lines": 34,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "csharp",
      "category": "software",
      "file": "emit/VibrationRms.cs",
      "lines": 44,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "gdscript",
      "category": "software",
      "file": "emit/vibration_rms.gd",
      "lines": 23,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "go",
      "category": "software",
      "file": "emit/vibration_rms.go",
      "lines": 26,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "java",
      "category": "software",
      "file": "emit/VibrationRms.java",
      "lines": 32,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "javascript",
      "category": "software",
      "file": "emit/vibration_rms.mjs",
      "lines": 31,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "kotlin",
      "category": "software",
      "file": "emit/vibration_rms.kt",
      "lines": 27,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "luau",
      "category": "software",
      "file": "emit/vibration_rms.luau",
      "lines": 30,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "matlab",
      "category": "software",
      "file": "emit/vibration_rms.m",
      "lines": 22,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "python",
      "category": "software",
      "file": "emit/vibration_rms.py",
      "lines": 21,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "rust",
      "category": "software",
      "file": "emit/vibration_rms.rs",
      "lines": 24,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "swift",
      "category": "software",
      "file": "emit/vibration_rms.swift",
      "lines": 26,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "wasm",
      "category": "software",
      "file": "emit/vibration_rms.wasm.ll",
      "lines": 44,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "glsl",
      "category": "gpu shader",
      "file": "emit/vibration_rms.glsl",
      "lines": 37,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "glsl-es",
      "category": "gpu shader",
      "file": "emit/vibration_rms.glsles",
      "lines": 39,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "hlsl",
      "category": "gpu shader",
      "file": "emit/vibration_rms.hlsl",
      "lines": 45,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "metal",
      "category": "gpu shader",
      "file": "emit/vibration_rms.metal",
      "lines": 45,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "wgsl",
      "category": "gpu shader",
      "file": "emit/vibration_rms.wgsl",
      "lines": 35,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "llvm",
      "category": "compiler IR",
      "file": "emit/vibration_rms.ll",
      "lines": 43,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "coq",
      "category": "proof",
      "file": "emit/vibration_rms.v",
      "lines": 25,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "isabelle",
      "category": "proof",
      "file": "emit/vibration_rms.thy",
      "lines": 29,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "lean",
      "category": "proof",
      "file": "emit/vibration_rms.lean",
      "lines": 47,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "aadl",
      "category": "safety-critical",
      "file": "emit/vibration_rms.aadl",
      "lines": 39,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "ada/spark",
      "category": "safety-critical",
      "file": "emit/vibration_rms.adb",
      "lines": 24,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "autosar",
      "category": "safety-critical",
      "file": "emit/vibration_rms.autosar.c",
      "lines": 57,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "ros2",
      "category": "safety-critical",
      "file": "emit/vibration_rms_pkg",
      "lines": 0,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "solidity",
      "category": "blockchain",
      "file": "emit/vibration_rms.sol",
      "lines": 46,
      "ok": true,
      "tier": "LOCAL"
    },
    {
      "target": "zkproof",
      "category": "blockchain",
      "file": "emit/vibration_rms.zk.json",
      "lines": 14,
      "ok": true,
      "tier": "LOCAL"
    }
  ],
  "proof": {
    "theorem": "vibration_rms_within_range",
    "claim": "the reported RMS magnitude is always inside the sensor range [0, 50] m/s^2, for any input",
    "trail_file": "proof/vibration_rms_within_range.axioms.txt",
    "clean": true,
    "forbidden_axioms_found": [],
    "rederived": "2026-07-10T14:10:45Z",
    "source_artifact": "examples/vibration_rms.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": {
    "range": "[0, 50.0] m/s^2",
    "noise_floor": 0.25,
    "samples": 500,
    "peak_m_s2": 35.828,
    "trace_csv": "trace.csv",
    "plot_png": "vibration_rms.png",
    "check": {
      "quantity": "RMS magnitude samples outside the sensor range [0, 50] m/s^2",
      "value": 0,
      "relation": "=",
      "bound": 0,
      "holds": true,
      "context": "a swept-frequency 2-axis vibration with a burst peaking at 35.8 m/s^2 stays inside [0,50.0] throughout \u2014 the range the theorem proves, the sqrt the forward-error certificate bounds (conditional on the 0.25 noise floor keeping the argument > 0)"
    },
    "tier": "LOCAL"
  },
  "certificate": {
    "applicable": true,
    "function": "vibration_rms",
    "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": {
      "ax": 30.0,
      "ay": 30.0
    },
    "bound_abs": 6.042587933404901e-13,
    "bound_ulps_of_result": 5442.679353047153,
    "output_magnitude_bound": 50.0,
    "lean_theorem": "Certcom.pipeline_pos_over_arith  (ln/sqrt over an arithmetic core, conditional on a positive lower bound)",
    "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 6.043e-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/vibration_rms_forward_error.lean",
    "lean_proof_tier": "TOOLCHAIN"
  },
  "hardware": {
    "tier": "n/a"
  }
}