heatTransferCert
plain-language theorem explainer
The declaration constructs a certificate asserting five heat transfer regimes whose adjacent Nusselt numbers stand in the ratio phi squared. A researcher working on RS-derived thermodynamics would cite it when verifying the phi-ladder scaling for conduction-to-radiation transitions. The construction is a direct structure instantiation that pulls the regime cardinality from a decide tactic and the ratio from an algebraic reduction on powers of phi.
Claim. The definition supplies an instance of the structure asserting that the cardinality of heat transfer regimes is five and that the ratio of successive Nusselt numbers on the phi-ladder equals $phi^2$ for every natural number $k$, by direct assignment of the pre-proved regime count and ratio lemmas.
background
In the Recognition Science treatment of thermodynamics, heat transfer proceeds through five canonical regimes: pure conduction, mixed convection, forced convection, natural convection, and radiation. These regimes are indexed on the phi-ladder, with the dimensionless Nusselt number advancing by two rungs at each regime transition. The upstream result regimeCount establishes that exactly five regimes exist by exhaustive enumeration, while nusseltRatio proves the scaling by direct expansion of the power-law definition of the rung values after a ring identity on the exponents.
proof idea
The definition is a one-line structure constructor that supplies the five_regimes field by invoking the decide-based regimeCount theorem and the phi_sq_ratio field by invoking the nusseltRatio theorem, which unfolds the rung definition and applies field simplification after a ring identity on the exponents.
why it matters
This definition closes the HeatTransferCert interface required for any downstream derivation of heat flux ratios in the RS framework. It directly implements the prediction that regime transitions occur at phi-squared steps on the Nusselt ladder, consistent with the phi-ladder and five-regime count. No immediate parent theorem is listed in the used_by graph, leaving open its integration into a full thermodynamic closure.
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