IndisputableMonolith.Physics.ThermoelectricEffectFromJCost
This module applies the canonical J-cost band template to the thermoelectric effect. It defines regimes, counts, and certificates that embed thermoelectric phenomena inside the Recognition Science J-cost framework. Researchers deriving domain certs from the master chain would cite it. The module follows the reusable six-clause template imported from CanonicalJBand.
claimThermoelectricRegime and ThermoelectricCert are defined so that the J-cost on ratios satisfies $J(1)=0$ and $J(x)≥0$ for $x>0$, yielding a certified thermoelectric regime.
background
The module imports the Canonical J-Cost Band template, whose doc-comment states it supplies the reusable six-clause J-cost-on-ratio template for domain certs. Each such cert proves matched-zero J(1)=0 and nonnegativity J(x)≥0 for x>0. The module applies this template inside the physics domain to thermoelectric quantities.
proof idea
This is a definition module, no proofs. It introduces the four sibling objects ThermoelectricRegime, regimeCount, ThermoelectricCert, and thermoelectricCert by direct application of the imported CanonicalJBand template.
why it matters in Recognition Science
The module supplies one of the domain certs in the master cert chain for B-tier whole-science openings. It places the thermoelectric effect inside the J-cost framework that rests on the Recognition Composition Law and the forcing chain T0-T8.
scope and limits
- Does not derive numerical values for the Seebeck coefficient.
- Does not model explicit temperature gradients or currents.
- Does not address magnetic-field corrections to the effect.