The Conveyance Function

• Attempting the First Process It is not time per-se that we require a concept of, but rather more generally a notion of progression, shared from a single source. This notion of progression is indicative of the position within the Object Lifetime for which we are drawing an intrinsic binding. i.e. with the progression held to be fundamentally intrinsic to the process in question, indeed shared between all components in question, we can now finally construct our Identity Process.

At the heart of the Process is a represented notion of Progression. The definitive element of a process is its progress. At the very heart of the Transparent Process Language is this notion of Progress. Progress is necessarily localised to the Process in question.

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Let us now derive the Conveyance Function for the Identity Process.

Let $P$ be the Progression Space localised to the process $P$. The identical naming is indicative of the notion that the Process is interchangeable with the Progress. ${\Phi }_i$ and ${\Phi }_o$ are the Input Space and Output Space respectively. We define the Identity Process such that ${\Phi }_o={\Phi }_i=\Phi$ the Output Space is equivalent to the Input Space, in turn equivalent to the Total Explained Objective Space, also we define $\Theta :=\varnothing$ the Configuration Space as null. I am pretty sure that both expressing the Total Explained Objective Space as equal to the Input and Output Spaces and defining the Configuration Space as the empty set are superfluous to the definition.

Now ${\phi }_o(p)=f({\phi }_i(p),\theta (p),p)$ where $f$ is the Conveyance Function for $P$. By definition for the Identity Process. ${\phi }_o(p)={\phi }_i(p)\forall p$ with $p\in P$, therefore $f$ is simply the identity function on ${\phi }_i(p)$.

The crucial revelation of this definition is that $p$ is localised to $P$, that is we take a local reference $p$ to construct our objective representation.

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So generally our Conveyance Function $f$ on process $P$ is

Equation

${\phi }_o(p)=f({\phi }_i(p),\theta (p),p)$

It is important to note that $p$ is itself an operator of $f$, enabling the progression of the Conveyance Function itself.

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We need to remind ourselves that $\Phi$ does not provide a complete expression of our objective space, we must incorporate the unexplained objective space ${\Phi }^{\prime }$ to completely express the objective space $\Omega$.

Equation

$\Omega =\Phi ’\cup \Phi$ Noting that $\Phi ’\cap \Phi \equiv \varnothing$

With ${\omega }_o(p)\in {\Omega }_o$

\omega_o(p) &= \varphi_o’(p) \cup \varphi_o(p) \\ &= \varphi_o'(p) \cup f(\varphi_i(p), \theta(p), p) \end{aligned}$$ I am quite confident if we want to express the complete objective lifetime we can just say $$\omega_o = \varphi_o’ \cup f(\varphi_i, \theta)$$ but I think that is best left to next time...