Rule of 70 GDP Doubling Time mechanism

Model scope

The arithmetic formula is standard and the existing honest label of "Rough approximation" is appropriate. Review is required because the specification omits validation behavior for zero and negative rates and does not unambiguously define whether the UI accepts percentage points or decimal fractions.

• The formula years ≈ 70 / growth_rate_percent is the standard Rule of 70 approximation for a positive, constant, compounded annual growth rate. The spec does not state the required positive-rate constraint or behavior for zero and negative rates.
• The input representation is not fully explicit: growth_rate_percent must be entered as percentage points (for example, 7 for 7%), not as a decimal fraction (0.07).

Units and conventions

• The growth rate is an annual percentage expressed in percentage points, such as 2.5 for 2.5% per year.
• The calculation assumes constant annual compounding.
• GDP growth and the intended GDP measure must use matching units and definitions, such as both real GDP or both nominal GDP.
• The output is an approximate number of years.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "annual_gdp_growth_rate_percent": 2.5
  },
  "expected_outputs": {
    "years_to_double": 28
  },
  "working": "Apply Rule of 70: years ≈ 70 / growth rate %. Substitute 2.5: 70 / 2.5 = 28. Expected result: 28 years."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero growth rate causes division by zero and must be rejected or returned as undefined. Negative growth produces a raw negative quotient that is not a meaningful doubling time and therefore requires an implicit validity branch. The percent-versus-decimal convention can also produce a materially different result if the input unit is misunderstood.

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-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json