IndisputableMonolith.Materials.HighTcSuperconductorFromPhiLadder
This module defines high-Tc superconductor families indexed by rung on the phi-ladder and shows that critical temperature increases with rung number. Condensed-matter physicists modeling unconventional superconductors would cite it for RS-native scaling predictions. The module supplies the core definitions HighTcFamily and criticalTemp together with their basic monotonicity properties.
claimLet $T_c(r)$ be the critical temperature for the family indexed by rung $r$ on the phi-ladder. Then $T_c(r+1) > T_c(r)$ for all $r$, with families constructed from the Recognition Composition Law and the time quantum $τ_0$.
background
Recognition Science places material spectra on the phi-ladder generated by the self-similar fixed point phi arising in the forcing chain. The module imports the fundamental RS time quantum $τ_0 = 1$ tick from Constants and the cost structures from Cost to parameterize high-Tc families. Higher rungs correspond to higher critical temperatures, consistent with the Recognition Composition Law.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the phi-ladder construction for high-Tc superconductors in the Recognition Science materials framework. It connects rung-dependent $T_c$ to the T5 J-uniqueness and T6 phi fixed point steps of the forcing chain, providing the scaling relation used in downstream material predictions.
scope and limits
- Does not derive microscopic pairing mechanism.
- Does not compute absolute numerical Tc values beyond ladder scaling.
- Does not address conventional low-Tc superconductors.
- Does not include doping, pressure, or magnetic-field effects.