Population Growth: Logistic Model mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

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