Seam currents and the D6 charge lattice
A glowing integer lattice where even-sum sites are lit and odd sites stay dark, with a seam current hopping through it and always landing lit.
The relation on screen
Charge labels live on the dual of the seam lattice, so only commensurate values are admissible.
Symbols
- dual (reciprocal) lattice of admissible labels
- symmetry of the charge lattice
the selection rule
The single 2 in the Smith normal form is the whole story: it is the index-two sublattice, the even-sum condition, and the reason half the lattice is unreachable. In a crystal the same kind of arithmetic forbids certain Bragg peaks. Here it forbids certain load configurations, and it does so exactly, with no small parameter.
what to look for · The lattice is discrete before any quantisation postulate is made.
Consensus to physics
- 01port loads live in Z^12
- 02antipodal pairing quotients to Z^6 by the difference map
- 03conservative seam currents have image D6 = {z : sum z even}
- 04the Smith invariants (1,1,1,1,1,2) fix the lattice up to isomorphism
In standard physics
Reciprocal-lattice selection rules
A charge lattice with a conservation law. The even-sum condition is a selection rule: only configurations with even total load are reachable, exactly as a conserved quantum number restricts which states connect.
boundary · These integers are not yet electric charge. The identification with physical charge is open.