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

instrument / verified-clean

# Cell/Bacterial Doubling Time Calculator

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/cell-bacterial-doubling-time-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/cell-bacterial-doubling-time-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/cell-bacterial-doubling-time-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/cell-bacterial-doubling-time-calculator/qualification/>)

## Ledger state

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

**Area**: Biology, Medicine & Pharmacology (educational estimates only — every panel labeled not-medical-advice)

**Tranche**: tranche-4

**Evidence ID**: t4-122

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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).

## Boundary hardening

**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.

## 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": {
    "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."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## 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`