Dr. Cadavious Jones
Rust College, USA
Talk is at 11:00 AM Central Time (calculating your local time…)
Abstract
Pyramid schemes, Ponzi schemes, multi-level marketing (MLM) programs, and blessing looms are often described in financial or legal terms, but each also has an underlying mathematical structure. In this talk, we consider these recruitment-based systems primarily as directed graphs. We distinguish between a sponsorship graph, which records who recruited whom and determines compensation-relevant relationships, and a social or marketing graph, which represents broader influence, communication, and trust relationships and may contain cycles or multiple paths. This two-layer distinction allows us to give pyramid schemes, Ponzi schemes, MLMs, and blessing looms precise graph-structural descriptions.
We then examine regular sponsorship trees and self-similar branching patterns that arise in recruitment-dependent systems. These structures yield closed-form participant-count identities connecting recruitment depth, branching requirements, and finite population limits. Financial obligations are placed on the sponsorship graph using discrete participant-level quantities such as contributions, promised payouts, and available resources. This gives a resource-conservation framework for solvency: when total promised payouts exceed total available resources, some participant must remain unpaid. Under an explicit cohort-funding rule, this imbalance forces geometric growth in the sponsorship graph, linking payout promises directly to unsustainable recruitment expansion.