Randomness in the NSk/ψ Programme: Branch Selection, Orientational Degeneracy and Selection Contract

In the PRE-PURE layer we introduce the admissible degeneracy pair (σ, −σ) inherited from NSk--Micro and the selection context as a local selection-neighbourhood relation on the lattice of regions. In the PURE layer we define the selection relation in full generality — as a partial function (deterministic selector) or a multi-valued relation (non-deterministic selector) — and prove local lemmas: the pair (σ, −σ) preserves the rung level Q and activation rank a(σ); well-definedness of selection is equivalent to context-induced branch discrimination. A no-go theorem shows that no canonical selection is possible from Z₂-symmetric data alone; an additional selection context is required. In track A (CORE-A) we introduce the stabilisation-entropic bias B_stab as a candidate family of selection contexts and prove an admissibility theorem: an antisymmetric bias induces an admissible partial selection relation. The q³D specialisation shows that the triplet selection gate is satisfied and non-trivial selection becomes admissible. The module exports the selection result σ*_u and the orientation marker χ^sel_u ∈ {−1, 0, +1} to NSk--Gravity and NSk--Mechanics. The full realisation mechanism of selection is not part of the current module core.