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

instrument implementation / implementation-contract

# Population Growth: Logistic Model implementation

A source-bound implementation contract for Population Growth: Logistic Model; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-039

**Effect**: Computation or source lookup only

## Input and validation requirements

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.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/population-growth-logistic-model/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/population-growth-logistic-model/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/population-growth-logistic-model/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`