IndisputableMonolith.Materials.ThermalConductivityRegimesFromPhiLadder
This module defines thermal conductivity regimes derived from the phi ladder in Recognition Science materials modeling. It introduces the enumeration ThermalConductivityRegime together with functions kappa, kappa_ratio and the certification ThermalConductivityCert. Researchers working on RS-derived material properties would cite it when mapping conductivity to rung numbers on the phi ladder. The module is purely definitional, with no theorems or proofs.
claimDefine the type ThermalConductivityRegime as an enumeration of conductivity regimes indexed by phi-ladder rungs. Let $k$ be the thermal conductivity function $k(r) = k_0 phi^r$ for regime $r$, with ratio $k(r_1)/k(r_2)$ and positivity certificate ThermalConductivityCert.
background
Recognition Science derives material properties from the phi ladder, where lengths and masses scale as yardstick times phi to a power determined by rung and gap(Z). The module imports the RS time quantum tau_0 = 1 tick from Constants and builds conductivity definitions on top of that scaling. ThermalConductivityRegime classifies distinct regimes, kappa computes the conductivity value, kappa_ratio compares values across rungs, and ThermalConductivityCert certifies positivity and consistency with the ladder.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the core objects for thermal conductivity in the materials domain. It connects directly to the phi-ladder mass formula and the eight-tick octave structure of Recognition Science. No downstream theorems are recorded yet, so it currently serves as a leaf definition set for later material-property derivations.
scope and limits
- Does not compute numerical kappa values from first principles.
- Does not incorporate explicit temperature dependence.
- Does not address phonon scattering mechanisms beyond phi scaling.
- Does not extend to non-equilibrium or relativistic regimes.