Source: https://guthlabs.ai/docs/instruments/population-growth-logistic-model/

instrument / verified-clean

# Population Growth: Logistic Model

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/population-growth-logistic-model/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/population-growth-logistic-model/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/population-growth-logistic-model/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/population-growth-logistic-model/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-6

**Evidence ID**: t6-039

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The growth formula itself is standard and correct for the constant-K logistic model. Verdict is NEEDS_REVIEW because the specification omits the inverse formula for 'time to reach %K', parameter/reachability constraints, and explicit time-unit and plotting-domain conventions. The existing 'idealized ecological model' label is appropriate, but the panel should also retain the stated educational/not-medical-advice disclaimer.

### Formula and scope findings

- The stated N(t)=K/(1+((K−N0)/N0)e^-rt) is the standard continuous logistic solution for constant carrying capacity K and intrinsic rate r, but its valid parameter constraints are not specified: N0 must be nonzero, and the usual population interpretation assumes K>0 and N0>0.

- The claimed 'time to reach %K' output has no explicit formula or definition of the target fraction. For target pK, the standard inverse is t=(1/r)ln((p/(1-p))((K−N0)/N0)), subject to domain and reachability constraints.

- The plotting specification does not define the time unit, population unit, allowed time domain, or whether cases with N0>K are supported. These choices affect interpretation of asymptotes and target-reaching times.

### Unit assumptions

- N0 and K use the same population-count or population-density units.

- r has reciprocal-time units, such as year^-1 or hour^-1.

- t must use the same time basis as 1/r; explicit conversion is required when t and r use different units.

- For 'reach %K', p is a dimensionless fraction between 0 and 1; percent values must be divided by 100 before substitution.

- The numerical examples treat t>=0 as the plotted ecological time domain unless otherwise stated.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The formula is undefined when N0=0 because it divides by N0. The instrument must reject that input; an implementation that relies on JavaScript Infinity could produce a misleading finite-looking result. A secondary hazard is ambiguity over whether negative r is allowed and how its sign is interpreted.

## 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,
    "K": 1000,
    "r": 0.1,
    "r_unit": "per year",
    "time": 0,
    "time_unit": "years",
    "target_fraction": 0.5
  },
  "expected_outputs": {
    "sampled_points": [
      {
        "time_years": 0,
        "N": 100
      }
    ],
    "time_to_target_years": 21.9722458,
    "key_curve_features": {
      "lower_horizontal_asymptote": 0,
      "upper_horizontal_asymptote": 1000,
      "inflection_time_years": 21.9722458,
      "inflection_population": 500,
      "maximum_growth_rate_population_per_year": 25,
      "finite_roots": []
    }
  },
  "working": "A=(K−N0)/N0=(1000−100)/100=9. At t=0, e^(−rt)=e^0=1. Denominator=1+9×1=10. Therefore N(0)=1000/10=100. For p=0.5, t=(1/0.1)ln((0.5/0.5)×9)=10ln(9)=10×2.197224577=21.9722458 years. The inflection occurs when N=K/2=500, at the same time. Its slope is rK/4=(0.1×1000)/4=25 population units/year. Since 0<N0<K and r>0, N(t) has no finite roots and approaches 0 backward in time and 1000 forward in time."
}
````

## 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-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`