Physicality in the NSk/ψ Programme: Activation Gate, Ignition of Local P = 1 States, and the Cyclic Switching-On of the Physical World

In this paper, we introduce and formalise the mechanism of physicality activation in the NSk/ψ programme as a standalone logic gate, providing a bridge between the pure mathematical Anchor and the operational dynamics of the Universe. The activation of the physical world takes the form of a hard Physicality Gate (Φgate), defined as the conjunction of two independent conditions evaluated on a realisation lattice L for a local existence density P. The gate is expressed as Φgate=ArmCond∧IgnCond, where ArmCond is the arming of the gate (exceeding the threshold coarse-graining loss, Δ21S>θarm), and IgnCond is the ignition (the emergence of at least two localised P=1 states at a graph distance dL≤δign). The main results of the module include: a proof of the lack of mutual implication between the conditions: the entropic loss alone does not trigger ignition (it constitutes only the arming), and the localised P=1 states alone do not imply a sufficient information gradient; the derivation of a local saturation principle directly from the domain of the function P∈0, 1, which naturally protects the model from collapsing into a singularity (a topological analogue of the Pauli Exclusion Principle) ; the definition of a cyclic switching-on/off of physicality (PhysSect∈0, 1), where extinction deactivates the operational dynamics while preserving the intact background geometry; the establishment of a strict contract for the NSk--Micro module, delegating to it the task of the operational stabilisation of the thus initiated multi-scale error (T21).