Rydberg Atoms as a Quantitative Probe of a Proposed Nested Space Medium: Fine-Structure Constraints, Resonant Boundaries, and Falsifiable SP3 Candidate Structures

Rydberg atoms provide a stringent testing ground for hypotheses that atomic structure has aphysically extended substrate. Their characteristic size grows approximately as n², adjacentlevel transition frequencies fall approximately as n⁻³, and fine-structure splittings involve thedimensionless electromagnetic coupling α. This paper formulates a proposed SP3 spacemedium “wrap” as a candidate physical structure, distinguishes observed atomic propertiesfrom unverified medium interpretations, and constructs numerical benchmarks for hydrogenicn = 10, 20, 50 and 100. A minimal medium model must reproduce the same α dependencewithout treating α as an arbitrary fitted geometric number. An explicit residual-basedspectroscopy protocol, state-dependence controls, and null criteria are proposed. The resultingproposal is a falsifiable research program, not experimental evidence for a medium.