Classical software model of entangled quantum states

Let’s consider a pair of particles with half-integer spin formed in a singlet state and moving freely in opposite directions. Let a be some unit vector and σ1 and σ2 are spin components of these particles. If the result A of the measurement (σ1, a) gives +1, then the result B of the measurement  (σ2, a) gives -1 and vice versa. Let’s add a random vector w to this description. Then the results of measurements A and B give A(a, w) = ±1, B(b, w) = ∓1. For the distribution probability ρ( w) the expectation amount is determined by the expression
P(a,b) = integral [ρ( w) A(a, w) B(b, w) dw]
The quantum mechanical expectation value is (a, b). Measurement result of the component (σ, a) gives sign(σ, a). Then
A(a, w) = sign(a, w)
B(b, w) = −sign(b, w)
or
A(a, w) = sign(cos(φ(t)) + θ1)
B(b, w) = −sign(cos(φ(t)) + θ2).
In other words a random process φ(t) obtained using a random number generator with ⟨φ(t)⟩ = 0 and the random phase θ in the range (0, 2π) is added.
The random semiqubit algorithm is a function of two variables
f(t, θ) = sign(cos(φ(t)) + θ))
where θ corresponds to the measurement angle set by the observer.e