Correspondence between the Concentric Shell Theory Asymptotic Profile and Free-Particle Schrodinger Solutions: Toward a de Broglie-Type Double-Solution Interpretation

The Concentric Shell Theory (CST) models elementary particles as deterministic, spatiallyextended structures generated by a nonlinear complex scalar field, where inertial massemerges from the global mechanical resistance of the shell structure. Recent analytical solutionsof the CST radial field equation have demonstrated that the far-field profile exhibitsan asymptotic oscillatory structure with a 1/r^2 envelope. In this Brief Report, we show thatthis asymptotic, effectively massless regime is formally identical to the spherically symmetric,free-particle spatial solution of the linear Schrodinger equation. By equating the CSTspatial frequency with the quantum wave number (ω ↔ k), we suggest a possible deterministictopological interpretation for a restricted class of quantum wave profiles. This resultmay be viewed as a partial mathematical realization, at the asymptotic radial level, of deBroglie’s ”Double Solution” program, suggesting that the statistical probability density ofstandard Quantum Mechanics could be proportional to the actual physical density of theunderlying extended shell structure.