The ℤ₂ from Axiom S

Axiom S — two disjoint sectors ℒ and 𝒟, with an order-reversing involution σ mapping each to the other.

σ maps ℒ → 𝒟 and 𝒟 → ℒ. σ² = identity.

The group generated by σ is {id, σ} — which is ℤ₂.

The two-sector structure of the record algebra is a ℤ₂-graded structure.

This is not an interpretation.

It is the algebraic content of Axiom S — one non-trivial involution generating a two-element group.