Source: https://guthlabs.ai/docs/instruments/materials-resistivity-conductivity-table/mechanism/
instrument mechanism / verified-clean
# Materials Resistivity/Conductivity Table mechanism
The inspectable method record for Materials Resistivity/Conductivity Table, kept separate from implementation and qualification.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Model scope
The lookup and geometric resistance formula are standard, but the temperature-adjustment algorithm, reference temperature, valid range, material grades, and table edition are unspecified. Define these items before release; therefore the verdict is NEEDS_REVIEW.
- The lookup formula ρ=table(material) is standard, and R=ρL/A is correct for a uniform conductor when ρ is in Ω·m, L is in meters, and A is in square meters.
- The specification claims an adjusted-for-temperature resistance output but does not define its formula, reference temperature, or temperature-coefficient convention. The standard assumed formula is R(T)=R(Tref)[1+αref(T−Tref)], with Tref=20 °C and αref in 1/°C.
- A linear temperature correction is only an approximation over a stated temperature range; resistivity and α vary with temperature, especially far from 20 °C.
- The specification does not state whether the table's resistivity and temperature coefficient are for annealed, pure, or a particular grade of each material.
## Units and conventions
- Table resistivity values are at 20 °C and are expressed in Ω·m.
- Length inputs are converted to meters and area inputs to square meters before applying R=ρL/A.
- Temperature inputs are in °C; temperature differences in °C and K are numerically identical.
- Temperature coefficient α is expressed in 1/°C and referenced to 20 °C.
- The conductor is uniform, has constant cross-sectional area, and uses a DC or sufficiently low-frequency resistance model with no skin-effect, contact, or lead resistance.
## Inspectable vector
One of 4 source-bound review vectors:
````
{
"inputs": {
"material": "copper",
"length": 10,
"length_unit": "m",
"area": 1,
"area_unit": "mm^2",
"temperature": 20,
"temperature_unit": "°C"
},
"expected_outputs": {
"resistivity_ohm_m": 1.68e-8,
"temperature_coefficient_per_C": 0.00393,
"resistance_at_20C_ohm": 0.168,
"adjusted_resistance_ohm": 0.168
},
"reference_data": {
"material": "copper",
"reference_temperature_C": 20,
"resistivity_ohm_m": 1.68e-8,
"temperature_coefficient_per_C": 0.00393,
"source_convention": "CRC Handbook / widely tabulated standard value"
},
"working": "A=1 mm^2=1×10^-6 m^2. R20=ρL/A=(1.68×10^-8 Ω·m×10 m)/(1×10^-6 m^2)=0.168 Ω. Temperature factor=1+0.00393×(20−20)=1. Therefore R(20 °C)=0.168×1=0.168 Ω."
}
````
## Failure boundary
- Area equal to zero causes division by zero; negative length or area must be rejected.
- Unknown material or missing table row must produce an explicit lookup error rather than a default value.
- The table must define valid temperature ranges; extrapolating the linear correction without bounds can produce inaccurate or even nonphysical results.
- The table convention and material grade must be retained with each value because copper and aluminum values vary by purity, alloy, annealing, and reference temperature.
- Unit ambiguity is hazardous: using mm^2 or cm^2 directly as m^2 produces errors of factors of 10^6 or 10^4.
- The blank honest_label is a concern: the instrument should state that temperature adjustment is an approximate linear model and that table values are nominal reference values, not universal material constants.
## Other records
[01**Overview**]()[03**Implementation**]()[04**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-tranche7/tranche7-results.json`