Source: https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/mechanism/

instrument mechanism / verified-clean

# Geothermal Gradient / Depth-Temperature mechanism

The inspectable method record for Geothermal Gradient / Depth-Temperature, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The arithmetic formula is correct under a constant-gradient, downward-positive, unit-consistent model. Review is required because the default gradient value and input units are not explicitly defined. The honest label should state that 25–30 °C/km is only a broad reference range and that actual geothermal gradients vary substantially by region, tectonic setting, lithology, fluid flow, and depth.

- The linear formula T(depth) = T_surface + gradient × depth is standard as a first-order geothermal approximation when the gradient is constant and depth is measured downward.

- The specification does not state the numerical value of the default gradient, so behavior using the default is underspecified.

- The formula does not account for gradients that vary with depth, lithology, groundwater flow, or tectonic setting; this limitation must be explicit in the instrument labeling.

## Units and conventions

- Surface temperature and output temperature use the same temperature scale; Celsius is assumed for the test vectors.

- Gradient is in °C/km and depth is in km unless depth is explicitly converted to km first.

- Temperature differences in °C and K have the same numerical magnitude, so °C/km is numerically equivalent to K/km for the gradient.

- Depth is positive downward from the surface.

- A custom gradient must use units compatible with the supplied depth.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "surface_temperature_C": 12,
    "depth_km": 0,
    "gradient_C_per_km": 25
  },
  "expected_outputs": {
    "temperature_at_depth_C": 12
  },
  "working": "T = T_surface + gradient × depth\nT = 12 + 25 × 0\nT = 12 + 0\nT = 12 °C"
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

An extreme finite-looking input produces Infinity through numeric overflow, and the default-gradient branch cannot produce a unique expected value because the exact default is unspecified. Negative-depth interpretation also yields materially different results under plausible conventions.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/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`