IndisputableMonolith.Materials.HighTcSuperconductorFromPhiLadder
The module defines high-Tc superconductor families indexed by rungs on the phi-ladder, with critical temperature strictly increasing as rung number grows. Condensed-matter researchers modeling cuprates or iron pnictides would cite it for a discrete, self-similar Tc spectrum. The module consists entirely of type families, counting functions, and monotonicity statements built from the imported constants and cost primitives.
claimHighTcFamily indexes families of superconductors by phi-ladder rungs $n$; critical temperature satisfies $T_c(n+1) > T_c(n)$ with $T_c$ drawn from the RS cost function on the ladder.
background
The module belongs to the materials domain and imports the RS time quantum $\tau_0 = 1$ tick from Constants together with the cost function from Cost. It applies the phi-ladder construction (self-similar fixed point $\phi$ from the forcing chain T6) to pairing energies. Sibling declarations introduce HighTcFamily as the indexed collection, highTcFamilyCount for enumeration, criticalTemp for the Tc assignment, and criticalTempMono for the monotonicity claim.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module extends the phi-ladder (T6, T7 eight-tick octave) into condensed-matter observables, supplying a discrete spectrum for Tc consistent with D=3. It realizes the mass formula yardstick $\times \phi^{rung}$ for pairing scales and stands ready to feed Recognition Science treatments of high-Tc materials, though no downstream theorems are recorded yet.
scope and limits
- Does not derive a microscopic pairing mechanism.
- Does not assign numerical Tc values to specific compounds.
- Does not treat doping, pressure, or magnetic-field dependence.
- Does not connect to conventional low-Tc BCS superconductors.