We want to formulate the data behind Bitcoin more scientifically since it got also attention from the science area. We start with some simple and basic defintions:

- \((B, <)\): Bounded lattice-ordered set of all blocks
- \((h, B_{h}, ts_{h}) \in B: h \in \mathbb{N}_0, ts_{h} \in \mathbb{N}_0\): \(h\)th element of all blocks where \(B_{h}\) is the (unordered) set of transactions in block with height \(h\) and \(ts_{h}\) the associated timestamp
- $latext t_{x} \in B_{h}$: Transaction \(t\) with id \(x\) in \(B_{h}\)
- \(A\): Set of all addresses
- \((S_{t_{x}}^{in}, <)\): Bounded lattice-ordered set of all inputs of \(t_{x}\)
- \((S_{t_{x}}^{out}, <)\): Bounded lattice-ordered set of all outputs of \(t_{x}\)
- \((i, a_{i}, v_{i}) \in S_{t_{x}}^{in}: i \in \mathbb{N}_0, a_{i} \in A, v_{i} \in \mathbb{N}_0^{+}\): \(i\)th element of the inputs
- \((j, a_{j}, v_{j}) \in S_{t_{x}}^{out}: j \in \mathbb{N}_0, a_{j} \in A, v_{j} \in \mathbb{N}_0^{+}\): \(j\)th element of the outputs with the condition: \((i, a_{i}, v_{i}) \in S_{t_{x}}^{in} . \exists! (j, a_{j}, v_{j}) \in S_{t_{y}}^{out} \land a_{i} = a_{j} \land v_{i} = v_{j}\)