IndisputableMonolith.Materials.SuperconductorVortexFromJCost
The module links superconductor vortices to the J-cost function by showing that one flux quantum corresponds to minimal recognition cost at J(1) = 0. Materials researchers applying Recognition Science to condensed-matter systems would cite the vortex lattice definitions and certificates. The module consists entirely of type definitions and sibling objects with no theorems or proofs.
claimA superconductor vortex carries one flux quantum when the recognition cost satisfies $J(1) = 0$, the minimal value; the module supplies the type $ ext{VortexLatticeType}$, the count function, the minimal flux quantum, and the certificate $ ext{SuperconductorVortexCert}$.
background
The module sits in the Materials domain and imports the RS time quantum $ au_0 = 1$ tick from Constants together with the J-cost function from the Cost module. It introduces VortexLatticeType, vortexLatticeCount, flux_quantum_minimal, and SuperconductorVortexCert to encode the statement that a vortex carries one flux quantum at minimal recognition cost. The supplied module doc-comment states the central claim directly: "Vortex carries one flux quantum: J(1) = 0 (minimal recognition cost)."
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the J-cost foundation for vortex modeling inside the Materials section of Recognition Science. It realizes the claim that a vortex lattice carries one flux quantum via the minimal-cost condition J(1) = 0 and thereby connects the Cost module to concrete condensed-matter objects. No downstream theorems are listed in the used_by block.
scope and limits
- Does not derive critical fields or temperatures from the phi-ladder.
- Does not prove the existence of superconductivity.
- Does not address interactions between multiple vortices.
- Does not connect to the eight-tick octave or spatial dimension D = 3.