EQBSL: Against Trust Scores — Evidence, Uncertainty, and Trust Flow in Dynamic Networks

Most deployed reputation systems share a structural flaw: they present confident scalar scores whose derivation is neither traceable nor disputable. A number emerges; no one can interrogate its ledger. Evidence-Based Subjective Logic (EBSL) is the most principled existing corrective, anchoring trust computation in auditable evidence flows rather than opaque aggregation. EQBSL — Evidence-Quantised Belief Subjective Logic — is a systems-oriented extension of EBSL designed for the realities of modern distributed systems, where interactions are temporal, multi-party, and context-dependent. Building on the Subjective Logic formalism of Jøsang (2016) and the evidence-flow reformulation of Škorić et al. (2016), this paper introduces five coordinated extensions. First, scalar positive/negative evidence pairs (r, s) are replaced by evidence tensors e_ij(t) ∈ ℝ^m, capturing distinct categories of interaction — trade outcomes, attestation patterns, governance votes, dispute records — in a form that preserves their heterogeneity rather than collapsing them prematurely into a single scalar. Second, an explicit lift mapping Ψ translates evidence tensors into standard Subjective Logic opinion tuples (b, d, u, a) via application-defined aggregation functionals, making every design choice visible and disputable. Third, trust propagation is recast as a well-defined global update operator F acting on the time-indexed evidence state, replacing ad-hoc iterative convergence routines with a formal state-transition semantics amenable to batch and streaming deployment. Fourth, hypergraph-aware evidence handling is introduced to support natively multi-party interactions — DAO decisions, multi-signature executions, group swaps — without forcing them into pairwise fictions that erase accountability structure. Fifth, stable node-level trust embeddings are derived from the EQBSL evidence state, providing fixed-dimensional vector representations per agent with clear chain-of-custody provenance suitable for downstream machine learning pipelines. EQBSL is not a replacement for EBSL but a structured engineering extension of it: where EBSL provides the correct epistemic foundations, EQBSL adds the architectural scaffolding needed to deploy those foundations in systems that are temporal, multidimensional, hyperedge-native, and ML-adjacent. The framework has direct application in decentralised identity protocols, reputation-gated smart contract systems, distributed governance mechanisms, and cryptographically verifiable trust networks.