Source: https://guthlabs.ai/docs/instruments/radiocarbon-c-14-age-with-calibration-note/mechanism/

instrument mechanism / verified-clean

# Radiocarbon (C-14) Age with Calibration Note mechanism

The inspectable method record for Radiocarbon (C-14) Age with Calibration Note, kept separate from implementation and qualification.

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

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/radiocarbon-c-14-age-with-calibration-note/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/radiocarbon-c-14-age-with-calibration-note/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/radiocarbon-c-14-age-with-calibration-note/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`