A Formal Refutation of the Blockchain Trilemma

TL;DR

This paper formally refutes the blockchain trilemma by demonstrating it as a category error and providing a concrete protocol example that achieves scalability, security, and decentralization simultaneously.

Contribution

It introduces a formal, multi-domain analysis showing the trilemma as a fallacy and presents a practical protocol counterexample.

Findings

The trilemma is a category error and not a fundamental law.

A protocol with unbounded throughput, security, and decentralization is constructed.

The trilemma relies on flawed assumptions and composition fallacies.

Abstract

The so-called blockchain trilemma asserts the impossibility of simultaneously achieving scalability, security, and decentralisation within a single blockchain protocol. In this paper, we formally refute that proposition. Employing predicate logic, formal automata theory, computational complexity analysis, and graph-theoretic measures of relay topology--specifically Baran's model of network path redundancy--we demonstrate that the trilemma constitutes a category error, conflates distinct analytical domains, and relies upon unproven causal assumptions. We further expose its reliance on composition fallacies drawn from flawed system implementations. A constructive counterexample is presented: a blockchain protocol exhibiting unbounded transaction throughput, cryptographic security under adversarial load, and multipath decentralised propagation. This example is not hypothetical but grounded in protocol design enabled by compact block relay, SPV verification, and IPv6 multicast. The trilemma is revealed not as a law of protocol architecture, but as a heuristic fallacy sustained by imprecision and design defeatism.