Drug Half-Life Accumulation / Elimination mechanism

Model scope

The existing educational, one-compartment, not-medical-advice label is appropriate but should also state the assumptions of instantaneous bolus dosing, first-order elimination, constant half-life, linear kinetics, and a specified concentration reference. Verdict is NEEDS_REVIEW because the decay and accumulation formulas are standard, but the claimed curve and time-to-steady-state/negligible outputs are under-specified without the repeated-dose equation, dose-to-concentration conversion, timing convention, and explicit thresholds.

• The elimination formula C(t)=C0·(1/2)^(t/t½) is standard for first-order, one-compartment exponential decay, provided t½>0 and t is measured from the reference concentration C0.
• The steady-state accumulation factor 1/(1−(1/2)^(τ/t½)) is standard for repeated instantaneous bolus doses, but only when C0 denotes the concentration increment caused by one dose. If the input is dose rather than concentration, volume of distribution and bioavailability are missing.
• The specification claims repeated-dose concentration curves but does not provide the full time-dependent repeated-dose equation or the timing convention (immediately after a dose versus immediately before a dose). For n bolus doses, the post-dose peak under the simple model is Cpeak,n=Cdose·[1−(1/2)^(nτ/t½)]/[1−(1/2)^(τ/t½)].
• Exact steady state is reached only asymptotically; a numerical threshold such as 90%, 95%, or 99% of steady state must be specified.
• Time to negligible level is undefined without a concentration threshold or residual fraction. The implementation should not silently choose one.
• The specification does not state constraints such as half-life>0, dosing interval>0, nonnegative dose/concentration, and nonnegative elapsed time.

Units and conventions

• t and t½ must use identical time units; τ and t½ must also use identical units before evaluating the exponent.
• C0 must be a concentration in the decay formula. For repeated dosing, a dose must be converted to a concentration increment using dose·bioavailability/volume of distribution if those quantities are intended.
• The accumulation factor is dimensionless; multiplying it by a per-dose concentration increment gives the post-dose steady-state peak concentration under the instantaneous-bolus convention.
• The test vectors explicitly state whether a concentration is measured immediately after a dose or immediately before a dose.
• Threshold-based times use a residual or accumulation fraction relative to the asymptotic steady state, not an exact finite time to steady state.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "model": "single-dose elimination",
    "C0_mg_per_L": 10,
    "half_life_h": 8,
    "time_h": 24
  },
  "expected_outputs": {
    "concentration_mg_per_L": 1.25,
    "curve_features": {
      "roots": "none at finite time for C0>0",
      "monotonicity": "strictly decreasing",
      "horizontal_asymptote_mg_per_L": 0
    }
  },
  "working": "t/t½=24/8=3. Therefore C(t)=10·(1/2)^3=10·1/8=1.25 mg/L. The exponential is positive for every finite t, decreases monotonically, and approaches 0 only as t approaches infinity."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The zero-half-life input creates undefined divisions in both the decay and accumulation formulas and should be rejected. The negative-concentration convention probe also exposes a validation hazard if the instrument accepts physically nonsensical signed concentrations without warning.

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-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json