Bitcoin Infinity: A Perpetual Continuity Protocol for Long-Term Network Sustainability

The Bitcoin protocol Nakamoto, 2008 represents a landmark achievement in distributed systems and cryptographic engineering. However, its fixed-supply design embeds a critical long-term vulnerability: the mathematical inevitability of permanent supply contraction driven by generational private-key inheritance failure. This paper formalises the generational loss model through discrete probability theory and recurrence relations, demonstrating that conservative estimates predict 51% of total supply becoming permanently inaccessible within 264 years, while realistic models project 64% loss. We further establish that the cessation of block rewards at approximately block height 6, 930, 000 (2140 CE) eliminates the mining security budget, exposing the network to sustained 51% attack risk. We propose Bitcoin Infinity — the Perpetual Continuity Protocol — a minimal, mathematically grounded modification to Bitcoin Core's GetBlockSubsidy () function. The modification replaces a single hard-stop conditional with a modulo operation, restarting the original 50 BTC/block halving curve every 33 halvings (132 years) in perpetuity. We prove that under this scheme, circulating supply converges to a stable equilibrium C^* = S₀r/ (1 - r) (approximately 49 M BTC at 30% generational loss), mining incentives are preserved indefinitely, and all previously issued bitcoins remain fully valid. The implementation is verified against 113 boundary tests with zero failures, exhibits no undefined behaviour under C++17, and maintains complete backward compatibility with the existing network until the activation block. Link: https: //revistazen10. github. io/bitcoin-infinity/