<p>Almost all crises or disasters have vast consequences in both spatial and temporal scale which are difficult to manage because of the size of hazards and their complexities. To conquer the vast size of consequences, it is possible to deploy potential of crowds but there are few developed tools to come over the complexity of required emergency processes. Dividing complex process into atomic crowdsourcing services would be a proper solution to use potential of crowds. We have innovated these services as atomic reply to spatial urgent requests including an informative, activity and confirmative segment. Proper composition of such atomic services in both spatial and temporal components would be able to manage sophisticated crisis fields. Administration of such services require a robust and operational framework. In this paper we have designed a crisis crowdsourcing mathematical framework which is constructed upon vector space elements and some meaningful eligible operations among them. The framework inherits tensor and differential geometry specifications. Vectors simulate crisis environment main objects in a multidimensional space. Likewise operations coincide possible actions among crisis objects.</p> <p>Proposed Framework introduces tools to compose and arrange atomic crowdsourcing services in optimum mode to conquer complex aiding process. Framework offers a mathematical intelligible documentation method too which is able to record process details as well as objects' status in space. To evaluate our framework we simulate different scenarios in a commercial simulation software and in our proposed framework. Defined scenarios included real field crisis reports, multi-agents interactive challenges for aiding and inquiry research forms for overall evaluation. Comparing results revealed considerable coincidence that could be evaluated as framework assurance.</p>