Source: https://guthlabs.ai/docs/instruments/radiometric-dating-calculator/mechanism/

instrument mechanism / verified-clean

# Radiometric Dating Calculator mechanism

The inspectable method record for Radiometric Dating Calculator, kept separate from implementation and qualification.

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

## Model scope

The decay equation is valid under a narrow closed-system model with known or zero initial daughter. The specification is NEEDS_REVIEW because it simultaneously claims a known initial ratio without accepting it as an input and describes the ratio ambiguously as parent/daughter while the formula requires daughter/parent. The current formula can be retained only after explicitly restricting the instrument to radiogenic daughter/remaining parent ratios with initial daughter already subtracted, or after adding an initial-daughter correction and method-specific equations.

- The formula t = ln(1 + D/P)/lambda is correct only when D is radiogenic daughter, P is remaining parent, the initial daughter amount is zero or has already been subtracted, and the system has remained closed.

- The input description says "parent/daughter ratio," which conventionally means P/D, while the formula requires D/P. This ratio orientation must be made explicit.

- The stated assumption of a known initial ratio is not represented in the formula or inputs. With an initial daughter-to-parent ratio D0/P, the formula should be t = ln(1 + (D/P - D0/P))/lambda, assuming D/P is measured using the remaining parent.

- The preset systems are not interchangeable under one generic formula without method-specific corrections: K-Ar requires treatment of radiogenic versus atmospheric argon and the K-40 decay branching convention; U-Pb requires isotope-specific daughter products and common-lead correction; Rb-Sr generally requires an initial Sr ratio and is commonly solved by an isochron.

- The claimed method-specific range and limits are unspecified. The instrument needs explicit validity limits, such as nonnegative ratios, isotope-specific half-life conventions, and warnings for ratios outside the calibrated or geologically meaningful range.

## Units and conventions

- Parent and daughter must be expressed in compatible atom or mole units, so D/P is dimensionless.

- The half-life and reported age must use the same time unit; these vectors use years.

- The ratio used by the formula is radiogenic daughter divided by remaining parent, not parent divided by daughter.

- The logarithm is the natural logarithm.

- The C-14 value here uses the modern 5730-year conventional half-life, not the older Libby 5568-year half-life used in some conventional radiocarbon-age contexts.

- A zero initial daughter ratio is assumed in all vectors because the supplied formula has no initial-daughter input.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "isotope_system": "C-14 -> N-14",
    "parent_daughter_ratio_convention": "radiogenic_daughter/remaining_parent",
    "D_over_P": 1,
    "initial_D_over_P": 0,
    "half_life_unit": "years"
  },
  "expected_outputs": {
    "age_years": 5730
  },
  "reference_data": {
    "isotope": "C-14",
    "half_life_years": 5730,
    "source_convention": "IUGS-recommended/conventional radiocarbon half-life; widely tabulated standard value",
    "ln_2": 0.6931471805599453,
    "ln_2_source_convention": "mathematical constant"
  },
  "working": "lambda = ln(2)/half-life = 0.6931471805599453/5730 yr = 0.00012096809 yr^-1.\\n1 + D/P = 1 + 1.0 = 2.\\nt = ln(2)/lambda = 0.6931471805599453/0.00012096809 yr = 5730 yr.\\nEquivalently, D/P = 1 means one half-life has elapsed, so age = 5730 yr."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The exact zero-parent input makes the formula undefined and must be rejected. A separate specification hazard is the unclarified ratio direction: interpreting the stated parent/daughter ratio versus the formula's daughter/parent ratio produces substantially different ages.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/radiometric-dating-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/radiometric-dating-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/radiometric-dating-calculator/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-tranche7/tranche7-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`