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

instrument / verified-clean

# Geothermal Gradient / Depth-Temperature

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/geothermal-gradient-depth-temperature/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Earth & Space (astronomy, orbital mechanics, meteorology, geology, geodesy, oceanography)

**Tranche**: tranche-5

**Evidence ID**: t5-100

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

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

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`