## 3 MuReQua Decentralized Storage and Security Engine (MuReQua DeSSE)
### Some Details About the Oracle Covering Step 6 of the Uploading Section
Indeed, at different times, each fragment is in different positions from its initial allocation. This dynamic evolution occurs as follows: for each fragment and at every moment the oracle is free of tasks, it takes a fragment from position X, moves it to position Y, and updates the positioning of the pair of fragments connected to it, as described in point 4. The instant \(t1\) in which a given fragment \(FrA\) is located at position \(X^{FrA}(t1)\) is random; therefore, the variable \(X^{FrA}(t1)\) is a stochastic variable. The next instant \(t2\) in which the fragment \(FrA\) will be moved coincides with a time when the oracle is free of other processes and is thus also a random time, as is the new allocation \(X^{FrA}(t2)\), where the fragment will be placed. If \(K\) is the number of storage systems, this position will be chosen randomly among the \(K*\#(positions)\) that are empty. Ultimately, for a generic fragment, the stochastic equation of a stochastic variable in Equation (3) holds:  
\[|\,X(t2)\rangle=U(t1,t2)|X(t1)\rangle \tag{3}\]  
with \(U(t1,t2)\), the temporal evolution operator acts on the positional state of the fragment at time \(t\), denoted as \(|X(t1)\rangle\), and is defined as in Equation (4):  
\[U(t1,t2)=\exp(-iH(t2-t1)) \tag{4}\]  
where \(H\) is the Hamiltonian operator related to the computational system hosting the oracle. Thus, in analogy with Quantum Mechanics, \(H=T+V\), where \(T\) is the kinetic energy that the oracle imparts to fragment \(FrA\), proportional to its size and the square of the velocity with which it is moved from position \(X(t1)\) to position \(X(t2)\), and \(V\) is its potential, which is proportional to the size of the fragment, the acceleration with which it is moved, and the distance (understood as the distance between nodes) between the arrival position and the departure position. As is well known, therefore, the underlying equation for the motion of the fragments can be expressed in terms of Schrodinger equation in Equation (5), namely,  
\[i\frac{\partial}{\partial t}|X(t)\rangle=H\bigg{|}X(t)\bigg{\rangle} \tag{5}\]  
where we assumed the reduced [PERSON]'s constant \(\hbar=1\). Then, when the fragment is in a specific allocation \(X(t)\), we have:  
\[T=0\;\text{e}\;V=\delta(x-X(t))\]  
where \(\delta\) indicates the \(\delta\)-Dirac distribution, \(x\) is the position variable, and \(X(t)\) is the position of the fragment at time \(t\). Conversely, during a transition,  
\[T=\frac{1}{2}sv^{2}\;\text{e}\;V=0\]  
where \(s=size(FrA)\) and \(v\) is the transition velocity of the fragment from one allocation to another one. Now, let us focus on step 6.2 of conceptual architecture. To describe the process of entanglement and recombination in step 6.2, we also draw inspiration from Quantum Mechanics, specifically from Scattering Theory. Specifically, at time \(t-1\), corresponding to a moment before the interaction between two fragments, \(FrA\) and \(FrB\), the two fragments each carry two contents, denoted as \(C_{A}\) and \(C_{B}\). After the interaction between the two fragments, two new fragments, \(FrC\) and \(FrD\), will be generated, corresponding to contents \(C_{C}\) and \(C_{D}\), respectively. Graphically, Figure 3 shows the interaction. The interaction process is elastic, as represented in Equation (6):  
\[C_{A}+C_{B}\to C_{C}+C_{D} \tag{6}\]  
Therefore, the information contained in the two fragments is preserved, just as the total energy of two quantum particles is conserved before and after an interaction in an elastic collision. Furthermore, entanglement occurs between the two fragments as they interact and exchange (mix) informational contents.