Geothermal Gradient / Depth-Temperature mechanism

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

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