Cluster-based operation has emerged as an effective approach to tap the controllable potential of distributed resources and support the flexible operation of rural distribution networks. However

accurate quantification of the regulation power capacity of individual cluster remains challenging

primarily due to the difficulty in obtaining precise mechanistic parameters of rural distribution networks and the lack of trustworthy data interaction mechanisms among multiple agents within distributed resource clusters. To address these issues

this paper proposes a quantification and trustworthy verification method for the adjustable capacity of distributed resource clusters integrating inverse optimization and zero-knowledge proof. First

to tackle the problem of missing model parameters

an inverse optimization-based capacity quantification model is constructed

wherein the distribution system operator infers the true regulation power boundaries of a cluster by mining its historical price-response data. Second

the succinct non-interactive zero-knowledge proof under the Groth16 protocol is adopted to rapidly generate lightweight validity proofs

enabling each cluster to self-certify the authenticity of its claimed regulation capability without disclosing any underlying sensitive information. Finally

case studies based on practical rural distribution networks demonstrate that the proposed method can accurately quantify the regulation potential of distributed resource clusters while rigorously preserving the privacy of multiple agents

thereby offering a viable technical pathway for establishing a secure and trustworthy mutual-aid mechanism for clusters in rural distribution networks.