Half-Life Calculator (multi-order) mechanism

Model scope

The algebraic formulas are standard for the stated idealized rate laws, but the specification is ambiguous about rate-law conventions, units, and how radioactive decay is selected and labeled. Define validation constraints, unit handling, and an explicit radioactive λ input or mode before release.

• The formulas are correct under specific rate-law assumptions: zero order requires -d[A]/dt = k, first order requires -d[A]/dt = k[A], and second order requires -d[A]/dt = k[A]^2 for a single reactant.
• The radioactive-decay claim is valid only when the supplied first-order k is explicitly the radioactive decay constant λ, with compatible time units. The specification does not define a separate radioactive mode or label k as λ.
• For reactions with stoichiometric coefficients or alternative second-order rate laws, the displayed formulas may require modification; the reaction/rate-law convention is not specified.

Units and conventions

• Zero-order k has concentration/time units, such as mol L^-1 s^-1; [A]0 is in the matching concentration unit; t½ is in the matching time unit.
• First-order k, including radioactive λ, has inverse-time units, such as s^-1 or yr^-1; t½ uses the corresponding time unit.
• Second-order k has concentration^-1 time^-1 units, such as L mol^-1 s^-1; k[A]0 therefore has inverse-time units.
• All numerical quantities must use mutually compatible concentration and time units before calculation.
• ln denotes the natural logarithm, with ln(2) approximately 0.69314718056.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "order": "zero",
    "k": 0.02,
    "k_unit": "mol L^-1 s^-1",
    "A0": 0.1,
    "A0_unit": "mol L^-1"
  },
  "expected_outputs": {
    "t_half": 2.5,
    "t_unit": "s"
  },
  "working": "t½ = [A]0/(2k) = 0.100 mol L^-1 / (2 × 0.020 mol L^-1 s^-1) = 0.100 / 0.040 s = 2.50 s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification admits inputs that produce division by zero or physically invalid negative half-lives, and it does not define validation behavior for zero or negative rate constants. It also does not explicitly define handling of an order value at or between formula branches.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json