Behavioural Homomorphism in Speculative Markets: Evidence from Search Query Divergence and Price Convergence in Bitcoin Markets 2017-2024

When financial markets enter speculative conditions, prices escalate beyond what any completed production history can account for. Classical explanations of this phenomenon invoke either shared belief, as in herd behaviour theory, or narrative convergence, as in narrative economics. Both traditions assume that behavioural convergence follows from prior belief convergence. This assumption fails at the scale of large speculative markets, where motivational homogeneity across millions of participants is structurally impossible. This paper proposes Behavioural Homomorphism as the mechanism by which divergent beliefs converge on identical market behaviour in speculative markets. The concept was first formalised in Nguyen (2026) at the firm level; the present paper extends it to the population level by identifying the narrative initiation mechanism and providing cross-linguistic empirical evidence. The framework integrates four layers: an evolutionary foundation establishing speculative markets as isomorphic to ancestral survival environments; a narrative initiation mechanism explaining how open-ended narratives produce multiple co-existing belief populations; a convergence mechanism grounded in pre-cognitive evolutionary response to shared price signals; and a self-reinforcing loop in which market price, by recording behaviour rather than belief, reflects each population's narrative back in a form that confirms its own prior convictions. Empirical tests using Google Trends search query data for 70 Bitcoin-related keywords across 421 weeks (2017-2024) identify four statistically distinct belief clusters through a fully data-driven procedure with no researcher-imposed categorisation. The co-existence of high inter-cluster correlation (r = 0.79-0.89 among three leading clusters) with robust cluster separation (Silhouette = 0.61, Adjusted Rand Index = 0.92) constitutes the strongest empirical signature of Behavioural Homomorphism: different beliefs, same behaviour. Three of four clusters Granger-cause Bitcoin price at a common two-week lead, jointly significant (block exogeneity F = 2.025, p = 0.042), with results surviving orthogonalization for the reflexive loop and confirmed out-of-sample. A novel finding of cross-linguistic homomorphism provides researcher-unmediated evidence that convergence operates below the level of linguistic and cultural mediation. Multivariate non-independence of all clusters confirms the Keynesian Beauty Contest as the co-determination mechanism. The paper provides the first simultaneous empirical evidence for both the narrative population formation mechanism of Shiller (2019) and the co-determination mechanism of Keynes (1936) within a unified framework. Scope is limited to pure speculative markets without productive fundamentals, for which Bitcoin constitutes an appropriate empirical case.