# IoT Blockchain Data Vercity with Data Loss Tolerance
## 2 Materials and Methods
### Overview of IoT Blockchain Strength Monitoring
#### 2.3.1 IoT Blockchain Strength Monitoring Model  
In classical set theory, the membership of elements in a set is assessed in binary terms, it either belongs or does not belong to the set, as shown in Equation (1). The equation of a node \(X\) is a member of a set \(A\), can be defined as a function:  
\[ \begin{array}{l}1_{A}\ :\ X\rightarrow\{0,1\},\\ 1_{A}\ (X):=\left\{\begin{array}{l}1\,if\ x\in A\\ 0\,if\ x\ not\in A\end{array}\right\}\end{array}  \tag{1}\]  
By contrast, fuzzy set theory permits the gradual inclusion of membership in a set. A new node joining the blockchain starts with an initial value, as more nodes joini and the node performs more transactions, the value of membership increases accordingly. It is essential that the IoT blockchain be proven that its data veracity strength can be measured. The strength can be a mathematical analogy to a set ability as proposed by [PERSON] [22] and one of the potentials is accumulation of capacitance in the IoT blockchain. In this research, IoT blockchain data veracity strength is measured based on its capacitance value. Capacitance is the potential energy stored and it is measured by the value of energy it transformed into inductance. The relationship between IoT blockchain data veracity and its strength is an analogy to that of measurable capacitance and its inductance. In our approach to have data veracity strength measured by its capacitance, every IoT blockchain node is embedded with a capacitor (C). Total capacitance value increases with more nodes (members) and the number of transactions completed. Ultimately, the entire IoT blockchain has the sum of all the capacitance from all nodes. The capacitance is to be probed in the LC circuit. The LC circuit is configured to have an inductor (L) and a capacitor (C) in parallel. The change in electric potential around the whole circuit must be zero in the ideal no resistance environment, so we begin with [PERSON]'s circuit laws:  
\[ \begin{array}{l}\Delta\mathrm{V_{C}}+\Delta\mathrm{V_{L}}=0,\\ \frac{\mathrm{SQ}}{\mathrm{SC}}-\mathrm{L}\ \frac{\mathrm{SI}}{\mathrm{SI}}=0\end{array}  \tag{2}\]  
where Q is the charge, V is the voltage and C is the capacitance of the capacitor. The energy is in joules for a charge in coulombs, voltage in volts and capacitance in farads. By [PERSON]'s voltage law, the voltage \(\mathrm{V_{C}}\) across the capacitor plus the voltage \(\mathrm{V_{L}}\) across the inductor must equal zero. Energy stored in a capacitor is electrical potential energy and it is thus related to the charge Q and voltage V on the capacitor. The equation for electrical potential energy U\({}_{\text{C}}\) is  
\[\text{U}_{\text{C}}=\frac{1}{2}\;\text{C}\text{V}^{2} \tag{3}\]  
Whereas energy stored in an inductor is:  
\[\text{U}_{\text{L}}=\frac{1}{2}\;\text{LI}^{2} \tag{4}\]  
where in a LC circuit, U\({}_{\text{C}}\) energy will be transformed to U\({}_{\text{L}}\)  
\[\frac{1}{2}\;\text{C}\text{V}^{2}=\frac{1}{2}\;\text{LI}^{2} \tag{5}\]  
The capacitance conversion to inductance is a hyperbolic partial differential equation (PDE) in a wave form in one spatial dimension, where the equation is written as:  
\[\frac{\delta^{2}\mu}{\delta\text{t}^{2}}=\text{C}^{2}\;\frac{\delta^{2}\mu}{ \delta\text{x}^{2}} \tag{6}\]  
This capacitance conversion to inductance is proved with an observation of hyperbolic wave form during the LTSPICE schematic circuit simulation. It should be mentioned here that the LTSPICE schematic circuit software was used in this IoT blockchain's data veracity strength analysis. Each node contributes to the strength of the IoT blockchain data veracity as demonstrated by its capacitance value. Inductance on the inductor is used as the measurement of capacitance strength, which is equivalent to the strength of entire IoT blockchain. \[\sum_{i=1}^{\text{max cluster}}\;\sum_{j=1}^{\text{max transaction}}\text{C}_{i }+\text{C}_{j} \tag{7}\]  
LC circuit simulation starts with a charged capacitor and is connected to an inductor.