Source: https://guthlabs.ai/docs/instruments/blackbody-spectral-radiance-plotter-planck-s-law/implementation/

instrument implementation / implementation-contract

# Blackbody Spectral Radiance Plotter (Planck's Law) implementation

A source-bound implementation contract for Blackbody Spectral Radiance Plotter (Planck's Law); deployment and executable qualification remain separate.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-with-binding-errata

**Evidence ID**: t6-113

**Effect**: Computation or source lookup only

## Input and validation requirements

Zero temperature and zero wavelength make the literal Planck expression undefined, while the plotted physical limits can be finite. A numerical branch near x=1 must also preserve continuity, and an unlabelled wavelength such as 500 is unit-ambiguous by orders of magnitude.

## Required corrections

````
[
  {
    "vector": 4,
    "field": "sampled_spectral_radiance",
    "wrong": 2.42439,
    "correct": 2.4243728,
    "cause": "micro: hand-computed exp(0.04795923)-1 = 0.0491276 vs true 0.0491283 (6th-sig-fig slip)"
  }
]
````

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "temperature_K": 300,
    "wavelength": "10 micrometres = 1.000000e-5 m"
  },
  "expected_outputs": {
    "sampled_spectral_radiance_W_m^-3_sr^-1": 9924033,
    "curve_features": {
      "wien_peak_wavelength_m": 0.00000965923985,
      "wien_peak_wavelength_micrometres": 9.65923985,
      "positive_wavelength_roots": "none",
      "limits": "B_lambda -> 0 as lambda -> 0+ and as lambda -> infinity"
    }
  },
  "working": "c2=hc/k_B=0.01438776877 m K. x=c2/(lambda*T)=0.01438776877/(1.000000e-5*300)=4.795922923. 2hc^2=1.191042972e-16. lambda^5=(1.000000e-5)^5=1.000000e-25 m^5. Numerator factor=(2hc^2)/lambda^5=1.191042972e9. exp(x)-1=exp(4.795922923)-1 approximately 120.01602. Therefore B_lambda=1.191042972e9/120.01602=9.924033e6 W m^-3 sr^-1. Wien peak: lambda_max=b_lambda/T=2.897771955e-3/300=9.65923985e-6 m."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/blackbody-spectral-radiance-plotter-planck-s-law/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/blackbody-spectral-radiance-plotter-planck-s-law/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/blackbody-spectral-radiance-plotter-planck-s-law/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-tranche6/tranche6-results.json`

- `tranche errata record`