Emergent Atomic Shell Structure from Response Degeneracy in the ECSM Framework

This work extends the Emergent Condensate Superfluid Medium (ECSM) framework to investigate the origin of atomic shell structure. Starting from localized excitation dynamics governed by a finite-response transport equation, we analyse the degeneracy structure of angular response modes. We show that the number of available excitation states within a localized response centre is determined by the multiplicity of angular modes, yielding a shell-capacity relation of the form Nₑffₛhell = 2 (ℓₘax + 1) ². This produces the sequence 2, 8, 18, 32,. . . consistent with characteristic atomic shell capacities. These results demonstrate that shell structure arises naturally from ECSM response degeneracy and occupancy constraints, without requiring orbital quantisation as a fundamental postulate. The framework provides a minimal route from finite-response medium dynamics to atomic-like organisation.