Source: https://guthlabs.ai/docs/instruments/cell-bacterial-doubling-time-calculator/mechanism/

instrument mechanism / verified-clean

# Cell/Bacterial Doubling Time Calculator mechanism

The inspectable method record for Cell/Bacterial Doubling Time Calculator, kept separate from implementation and qualification.

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

## Model scope

The existing educational/not-medical-advice and ideal-exponential-growth labels are appropriate but should be retained prominently. Verdict is NEEDS_REVIEW because the time unit and the doublings-count formula are unspecified, and domain behavior for equal or declining counts is not defined.

- The doubling-time and growth-rate formulas are standard for ideal exponential growth: td = t·ln(2)/ln(N/N0) and μ = ln(N/N0)/t.

- The claimed doublings-count output has no formula in the specification; it should be explicitly defined as log2(N/N0) = ln(N/N0)/ln(2).

- The formulas require N0 > 0, N > 0, and t != 0. A conventional positive doubling time additionally requires N > N0; otherwise declining populations produce a negative mathematical characteristic time, not an ordinary doubling time.

- The elapsed-time unit is unspecified, so the numerical unit of td and the reciprocal unit of μ are ambiguous.

## Units and conventions

- N0 and N are positive counts measured under comparable sampling conditions; their ratio is dimensionless.

- ln means the natural logarithm.

- The elapsed-time unit is carried consistently through t, td, and μ. For example, t in hours produces td in hours and μ in h^-1; t in minutes produces td in minutes and μ in min^-1.

- Doublings count is dimensionless and equals log2(N/N0).

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "N0": 100,
    "N": 800,
    "elapsed_time": 6,
    "time_unit": "hours"
  },
  "expected_outputs": {
    "doubling_time": 2,
    "growth_rate_mu": 0.34657359028,
    "doublings": 3
  },
  "working": "N/N0 = 800/100 = 8. ln(8) = 2.07944154168 and ln(2) = 0.69314718056. td = 6 × 0.69314718056 / 2.07944154168 = 2 hours. μ = 2.07944154168 / 6 = 0.34657359028 h^-1. Doublings = ln(8)/ln(2) = 2.07944154168/0.69314718056 = 3."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The formulas encounter undefined results for nonpositive or zero starting counts and at exactly zero net growth. A calculator that accepts N0=0 or emits a finite doubling time when N=N0 would fail this adversarial set.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/cell-bacterial-doubling-time-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/cell-bacterial-doubling-time-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/cell-bacterial-doubling-time-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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`