Source: https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/mechanism/

instrument mechanism / verified-clean

# Wien's Displacement Law Calculator mechanism

The inspectable method record for Wien's Displacement Law Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The numerical formula is standard and valid under its wavelength-domain and kelvin-unit assumptions. Resolve the exact band/color mapping, input validation policy, and constant precision before release.

- The formula λ_max = b/T is correct for the wavelength at which a blackbody's spectral radiance per unit wavelength peaks, assuming T is absolute temperature in kelvins and b = 2.898e-3 m·K.

- The requested spectral color/band output has no defined classification or conversion rule. A wavelength peak can be assigned to a band, but perceived color is not uniquely determined by peak wavelength alone.

- The stated b value is a rounded approximation; the calculator should document its precision or use a more precise CODATA value if matching reference calculations is required.

## Units and conventions

- T must be an absolute temperature in kelvins (K), not degrees Celsius or Fahrenheit.

- λ_max is returned in metres when b = 2.898e-3 m·K; equivalent unit conversions must be labeled explicitly.

- The formula applies to the wavelength-domain blackbody spectrum. The peak frequency and peak wavenumber use different Wien constants and do not equal c/λ_max in general.

- Temperature must be strictly greater than 0 K.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "T_K": 300
  },
  "expected_outputs": {
    "lambda_max_m": 0.00000966,
    "lambda_max_um": 9.66,
    "spectral_band": "infrared"
  },
  "working": "λ_max = b/T = (2.898e-3 m·K)/(300 K) = 0.00000966 m = 9.66e-6 m = 9.66 μm. This is infrared."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The plain arithmetic formula produces an undefined result at T=0 K, can overflow to Infinity for an extremely small positive temperature, and produces a negative nonphysical wavelength for negative temperatures unless explicit input validation is added. A bare temperature value also permits a K-versus-°C convention error.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`