Materials Resistivity/Conductivity Table mechanism

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

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