There has been tremendous interest in the development of formal trust models and metrics through the use of analytics (e.g., Belief Theory and Bayesian models), logics (e.g., Epistemic and Subjective Logic) and other mathematical models. The choice of trust metric will depend on context, circumstance and user requirements and there is no single best metric for use in all circumstances. Where different users require different trust metrics to be employed the trust score calculations should still be based on all available trust evidence. Trust is normally computed using past experiences but, in practice (especially in centralised systems), the validity and accuracy of these experiences are taken for granted. In this paper, we provide a formal framework and practical blockchain-based implementation that allows independent trust providers to implement different trust metrics in a distributed manner while still allowing all trust providers to base their calculations on a common set of trust evidence. Further, our design allows experiences to be provably linked to interactions without the need for a central authority. This leads to the notion of evidence-based trust with provable interactions. Leveraging blockchain allows the trust providers to offer their services in a competitive manner, charging fees while users are provided with payments for recording experiences. Performance details of the blockchain implementation are provided.