Source: https://guthlabs.ai/docs/instruments/one-compartment-pk-simulator-first-order/mechanism/

instrument mechanism / verified-with-binding-errata

# One-Compartment PK Simulator (first-order) mechanism

The inspectable method record for One-Compartment PK Simulator (first-order), kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The honest-label text is appropriate and should remain visible on every panel. The core concentration equations are standard under the stated simplified assumptions, but the instrument is not complete or safe to mark PASS because C0, Cmax, Tmax, AUC, half-life conversion, parameter constraints, and the ka=ke limit are not fully specified. The fourth vector intentionally exposes the singularity; its corrected t=20 limiting concentration is 2.165364531 mg/L.

- The IV formula C=C0e^(-kt) is standard, but C0 is not defined from the listed inputs; for an IV bolus it should be C0=D/Vd, assuming dose D and volume Vd use compatible units.

- The oral concentration formula is standard for a one-compartment model with first-order absorption and elimination when ka != ke, but it is singular at ka=ke and needs the limiting formula C=(F·D/Vd)·ke·t·e^(-ke·t).

- The spec claims Cmax and Tmax outputs but does not provide their formulas. For oral dosing, Tmax=ln(ka/ke)/(ka-ke), followed by Cmax evaluated at Tmax; for IV bolus, Cmax=C0 and Tmax=0.

- The spec claims AUC output but does not provide its formula. For IV bolus, AUC(0-infinity)=C0/ke=D/(Vd·ke); for oral dosing, AUC(0-infinity)=F·D/(Vd·ke).

- The elimination-rate input is ambiguous when supplied as t½: the simulator must explicitly convert ke=ln(2)/t½ before using the formulas.

## Units and conventions

- Dose D is in mass units, Vd is in volume units, and concentrations are reported as mass/volume.

- ka and ke are positive rates in inverse time, and t is in the corresponding time unit; all time units must be consistent.

- Bioavailability F is dimensionless and should satisfy 0<=F<=1.

- AUC is assumed to mean AUC from time zero to infinity, with units concentration·time.

- The formulas assume an instantaneous IV bolus, no distribution phase, first-order absorption and elimination, and a linear, time-invariant one-compartment model.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "route": "IV bolus",
    "dose_mg": 500,
    "Vd_L": 50,
    "ke_per_h": 0.1,
    "times_h": [
      0,
      10,
      20
    ]
  },
  "expected_outputs": {
    "concentration_mg_per_L": {
      "0": 10,
      "10": 3.678794412,
      "20": 1.353352832
    },
    "Cmax_mg_per_L": 10,
    "Tmax_h": 0,
    "AUC_0_inf_mg_h_per_L": 100,
    "curve_features": {
      "root_or_zero_concentration": "No finite positive-time root; C approaches 0 as t approaches infinity",
      "asymptote_mg_per_L": 0
    }
  },
  "working": "C0=D/Vd=500/50=10 mg/L. C(t)=10e^(-0.1t). At t=0: C=10e^0=10 mg/L. At t=10: C=10e^(-1)=10(0.3678794412)=3.678794412 mg/L. At t=20: C=10e^(-2)=10(0.1353352832)=1.353352832 mg/L. Because IV bolus concentration decreases immediately, Cmax=C(0)=10 mg/L and Tmax=0 h. AUC=C0/ke=10/0.1=100 mg·h/L."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The oral formula is undefined when ka=ke unless a limiting-case branch is implemented. Negative rate constants also produce nonphysical growth and a divergent AUC, so the instrument should reject them.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/one-compartment-pk-simulator-first-order/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/one-compartment-pk-simulator-first-order/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/one-compartment-pk-simulator-first-order/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-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`