Radiocarbon (C-14) Age with Calibration Note mechanism

Model scope

The algebra and Libby convention are standard, but the instrument needs an explicit pMC-versus-ratio input mode, conversion rule, and domain behavior before release. The honest label must prominently state: uncalibrated conventional radiocarbon age only; real dates require an external calibration curve that is not bundled.

• The formula t = 8033·ln(1/f) is correct for conventional radiocarbon age when f is a dimensionless fraction modern ratio under the Libby 5568-year half-life convention.
• The input description is ambiguous: pMC means percent modern carbon and must be converted as f = pMC/100, whereas a ratio is already f. The panel must require an input mode or clearly define the conversion.
• The valid mathematical domain and interpretation are not specified: 0 < f <= 1 gives nonnegative conventional ages; f > 1 gives a negative conventional age, and f <= 0 is invalid or divergent.

Units and conventions

• 8033 years is the Libby mean-life constant, approximately 5568/ln(2), and the output is in years.
• f is dimensionless; ratio inputs are used directly, while pMC inputs are divided by 100.
• BP is conventional radiocarbon years before 1950 CE, not a calendar date.
• The result is uncalibrated; calendar-age conversion requires an appropriate calibration curve such as IntCal.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "input_mode": "pMC",
    "value": 100
  },
  "expected_outputs": {
    "fraction_modern": 1,
    "conventional_age_BP_years": 0
  },
  "working": "Convert pMC to fraction: f = 100/100 = 1. Compute 1/f = 1/1 = 1. ln(1) = 0. Therefore t = 8033 × 0 = 0 years BP."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The raw formula has an undefined input at f=0 and produces a mathematically finite but physically invalid negative age for f>1. A robust instrument must reject those inputs. The pMC-versus-ratio convention is also hazardous unless the representation is explicitly declared.

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