Source: https://guthlabs.ai/docs/instruments/gdp-growth-rate-calculator/mechanism/

instrument mechanism / verified-with-binding-errata

# GDP Growth Rate Calculator mechanism

The inspectable method record for GDP Growth Rate Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The formulas are conditionally standard, but the specification needs explicit frequency handling, percentage-scaling behavior, multi-period semantics, positive-denominator validation, unit normalization, and a precise definition of how the real-versus-nominal flag affects inputs and labels. The honest label should state whether results are nominal or real and should identify the periods and units supplied by the user.

- The period-over-period formula is standard as a fractional rate, but percentage outputs require multiplying the result by 100 or explicitly formatting the fraction as a percent.

- The annualized formula is correct only for consecutive quarterly observations: (GDP_t/GDP_t-1)^4 - 1. The specification does not define behavior for monthly, annual, irregular, or non-consecutive periods.

- The phrase 'GDP values for two+ periods' does not specify whether multiple periods produce separate adjacent-period rates, a cumulative growth rate, or a compound annual growth rate.

- The real-vs-nominal flag is underspecified: the formula compares whichever GDP series is entered, but does not convert nominal GDP to real GDP or apply a GDP deflator.

- GDP levels must be on a consistent basis, including currency, scale, price basis, and seasonal-adjustment basis, before applying the formula.

## Units and conventions

- GDP_t and GDP_t-1 are measured in the same currency, scale, price basis, and seasonal-adjustment basis; the units cancel in the ratio.

- For annualized growth, the two observations are consecutive quarters, so four compounding periods occur per year.

- The displayed percentage equals the fractional formula result multiplied by 100.

- A real GDP calculation requires real GDP inputs, typically at a stated reference-year price basis; the calculator does not itself perform inflation adjustment.

- GDP_t-1 is strictly greater than zero for both formulas to be defined.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "GDP_t": 20200,
    "GDP_t_minus_1": 20000,
    "units": "billions of currency units",
    "frequency": "quarterly",
    "basis": "real GDP",
    "periods": "consecutive quarters"
  },
  "expected_outputs": {
    "growth_pct": 1,
    "annualized_growth_pct": 4.060401
  },
  "working": "growth = (20,200 - 20,000) / 20,000 = 200 / 20,000 = 0.01; 0.01 × 100 = 1%. annualized = ((20,200 / 20,000)^4 - 1) × 100 = (1.01^4 - 1) × 100 = (1.04060401 - 1) × 100 = 4.060401%."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The calculator specification has an undefined-result failure when the prior GDP is zero and does not state a required validation response. It also leaves the annualization branch and sign-reporting conventions insufficiently explicit, creating risks of incorrect results or interpretation.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/gdp-growth-rate-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/gdp-growth-rate-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/gdp-growth-rate-calculator/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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`