IndisputableMonolith.Materials.SuperconductorVortexFromJCost
The module certifies that a superconductor vortex carries exactly one flux quantum by establishing J(1) = 0 as the minimal recognition cost. Condensed-matter theorists modeling type-II superconductors would cite it when deriving vortex lattices from the Recognition Science cost function. It consists of type definitions for vortex lattices together with a certification predicate that applies the imported J-cost directly to unit winding number.
claimA vortex lattice satisfies $J(1)=0$ where $J(x)= (x + x^{-1})/2 - 1$, certifying that each vortex carries the minimal flux quantum in RS-native units.
background
Recognition Science obtains all physics from the single functional equation whose solution is the J-cost $J(x) = (x + x^{-1})/2 - 1$, equivalently cosh(log x) - 1. The imported Constants module fixes the base time quantum τ₀ = 1 tick; the Cost module supplies the Recognition Composition Law and the associated defect measures. This module applies those definitions to superconducting vortices by introducing VortexLatticeType as an enumeration of lattice geometries and SuperconductorVortexCert as the predicate asserting that the cost is minimized precisely when the winding number equals one.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the J-cost certification that enables sibling declarations such as flux_quantum_minimal and vortexLatticeCount. It directly instantiates the T5 J-uniqueness step of the forcing chain for material systems, linking minimal recognition cost to the observed flux quantum without additional hypotheses.
scope and limits
- Does not derive the Ginzburg-Landau free energy.
- Does not compute critical magnetic fields or penetration depths.
- Does not address temperature dependence or type-I behavior.
- Does not connect the vortex cost to the fine-structure constant.