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

instrument / verified-clean

# Wien's Displacement Law Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/wien-s-displacement-law-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-5

**Evidence ID**: t5-230

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "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."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

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

- `BOUNDARY_HAZARD_CATALOG.json`