Blackbody Color Temperature → RGB Approximation mechanism

Model scope

The honest-label statement is appropriate, but the exact published algorithm and citation are missing. Select and document one coefficient set, RGB color-space assumption, clamping rule, and rounding rule before implementation or claiming PASS.

• The specification names Tanner Helland / Mitchell Charity approximations but does not provide one exact formula, coefficient set, source citation, branch conditions, or output policy; these are not uniquely interchangeable algorithms.
• RGB rounding policy is unspecified: nearest integer, truncation, and clamping produce different swatches.
• The RGB color space, primaries, transfer function, and white-point assumptions are unspecified; the result should not be presented as colorimetrically defined RGB without those labels.

Units and conventions

• Input temperature is absolute temperature in kelvin (K), not degrees Celsius or mireds.
• The test calculations assume the commonly published Tanner Helland approximation with t=K/100: R=255 when t<=66, otherwise R=329.698727446*(t-60)^(-0.1332047592); G=99.4708025861*ln(t)-161.1195681661 when t<=66, otherwise G=288.1221695283*(t-60)^(-0.0755148492); B=0 when t<=19, B=138.5177312231*ln(t-10)-305.0447927307 when 19<t<66, and B=255 when t>=66.
• Expected outputs assume clamping each channel to 0..255 followed by nearest-integer rounding.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "temperature_K": 1000
  },
  "expected_outputs": {
    "R": 255,
    "G": 68,
    "B": 0
  },
  "working": "t=1000/100=10. R=255 because t<=66. G=99.4708025861*ln(10)-161.1195681661=99.4708025861*2.302585093-161.1195681661≈229.03999-161.11957=67.92042→68. B=0 because t<=19. Result=(255,68,0)."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The approximation has an observable discontinuity at the t = 66 branch boundary: 6600 K produces approximately (255,255,253), while 6601 K produces approximately (255,252,255). Inputs at or below 0 K also reach ln(0) or an invalid logarithm and must be rejected.

Other records

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