Complete mathematical specification of Bitcoin consensus, extracted from Bitcoin Core. Read the Orange Paper.
Supply Convergence Proof
Theorem 6.2.3 (Supply Convergence): The total supply converges to exactly 21 million BTC.
Proof: The total supply can be expressed as a sum of geometric series. For each halving period \(k\) (where \( k = \lfloor h/H \rfloor \)), the subsidy is \(50 \times C \times 2^{-k}\) for \(H\) consecutive blocks.
\[ \lim_{h \to \infty} \text{TotalSupply}(h) = 21 \times 10^6 \times C \]The total supply is:
\[ \text{TotalSupply}(\infty) = \sum_{k=0}^{63} H \times 50 \times C \times 2^{-k} = H \times 50 \times C \times \sum_{k=0}^{63}2^{-k} \]Since \(\sum_{k=0}^{63} 2^{-k} = 2 - 2^{-63} \approx 2\) for large \(k\):
\[ \text{TotalSupply}(\infty) \approx H \times 50 \times C \times 2 = 210{,}000 \times 50 \times 10^{8} \times 2 = 21 \times 10^6 \times 10^{8} \]
Comparison of consensus coverage between Bitcoin Core (testing-based) and Bitcoin Commons (formal verification plus testing).