Saving proof-of-work by hierarchical block structure
Valdemar Melicher
TL;DR
The paper tackles Bitcoin’s fundamental mismatch where security costs from proof-of-work are largely independent of the wealth moved, hindering micro-transactions and efficient on-chain payments. It introduces extended transactions with tunable security controls and a hierarchical, tree-like block structure (HBS) to scale throughput while tying fees and security to wealth transferred. A progression from a single virtual computer to sharded, multi-block structures is outlined, aided by a homotopy transition to ensure safe adoption and gradual integration with the existing chain. The proposed framework—comprising extended transactions, HBSs, MFNs, and distributed routing—promises thousands of on-chain transactions per second with wealth-proportional costs, though realizing this vision requires careful multi-stage deployment and robust network coordination.
Abstract
We argue that the current POW based consensus algorithm of the Bitcoin network suffers from a fundamental economic discrepancy between the real world transaction (txn) costs incurred by miners and the wealth that is being transacted. Put simply, whether one transacts 1 satoshi or 1 bitcoin, the same amount of electricity is needed when including this txn into a block. The notorious Bitcoin blockchain problems such as its high energy usage per txn or its scalability issues are, either partially or fully, mere consequences of this fundamental economic inconsistency. We propose making the computational cost of securing the txns proportional to the wealth being transferred, at least temporarily. First, we present a simple incentive based model of Bitcoin's security. Then, guided by this model, we augment each txn by two parameters, one controlling the time spent securing this txn and the second determining the fraction of the network used to accomplish this. The current Bitcoin txns are naturally embedded into this parametrized space. Then we introduce a sequence of hierarchical block structures (HBSs) containing these parametrized txns. The first of those HBSs exploits only a single degree of freedom of the extended txn, namely the time investment, but it allows already for txns with a variable level of trust together with aligned network fees and energy usage. In principle, the last HBS should scale to tens of thousands timely txns per second while preserving what the previous HBSs achieved. We also propose a simple homotopy based transition mechanism which enables us to relatively safely and continuously introduce new HBSs into the existing blockchain. Our approach is constructive and as rigorous as possible and we attempt to analyze all aspects of these developments, al least at a conceptual level. The process is supported by evaluation on recent transaction data.