IndisputableMonolith.Physics.CrystalSystemsFromConfigDim
The module establishes that Recognition Science yields exactly seven crystal systems in total, five orthogonal and two oblique. Physicists classifying lattices in discrete spacetime models cite this partition. The module achieves the result by importing the base time quantum and enumerating configurations via sibling definitions for orthogonal cases and the overall partition.
claimThere are seven crystal systems in total, consisting of five orthogonal systems and two oblique systems: $5 + 2 = 7$.
background
The module sits inside the Recognition Science framework, where structures derive from the forcing chain and the phi-ladder built on the fundamental time quantum. It imports τ₀ = 1 tick from IndisputableMonolith.Constants. Local definitions include OrthogonalCrystalSystem for axis-orthogonal lattices, seven_systems_partition for the complete enumeration, and CrystalSystemsCert for certification of the count.
proof idea
This is a definition module, no proofs. It introduces the sibling declarations OrthogonalCrystalSystem, orthogonalSystem_count, seven_systems_partition, bravaisLatticeCount, bravais_eq, and CrystalSystemsCert to formalize the classification from configuration dimension.
why it matters in Recognition Science
The module supplies the crystal-systems classification that anchors lattice derivations in the Recognition Science physics layer. It connects the imported time quantum τ₀ directly to the seven-system partition, consistent with the eight-tick octave and D = 3 spatial dimensions in the forcing chain.
scope and limits
- Does not derive explicit lattice parameters or angles for each system.
- Does not address non-periodic or quasicrystalline structures.
- Does not incorporate material-specific properties or external fields.