Source: https://guthlabs.ai/docs/instruments/half-life-calculator-multi-order/

instrument / verified-clean

# Half-Life Calculator (multi-order)

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/half-life-calculator-multi-order/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/half-life-calculator-multi-order/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/half-life-calculator-multi-order/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/half-life-calculator-multi-order/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Chemistry & Materials

**Tranche**: tranche-4

**Evidence ID**: t4-287

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "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."
}
````

## Related workflows

[Reaction Energetics Benchtimescale](<https://guthlabs.ai/docs/instrument-workflows/reaction-energetics/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`