ICMM-FW-04 : FGF: Closed Fundamental Geometries and Stability Criteria

ICMM-FW-04 – This study provides the complete formalization of Closed Fundamental Geometries (FGF) within the ICMM (Complex Multi-Magnetic Information) framework. It introduces a rigorous definition of FGFs, clearly distinguishing topological identity from secondary stability, and develops a structured hierarchy of topological, morphological, and dynamical stabilities. Operational morphological signatures are defined, enabling the classification of secondary FGFs into qualitative families and the analysis of their fragility, rigidity, and rupture regimes. The study proposes falsifiable stability criteria, transition and rupture scenarios, and an autonomous conceptual framework, without embedded simulations. Numerical implementations, scripts, and associated data are available upon request within a formalized scientific collaboration framework. This preprint is part of the ICMM-FW corpus and directly extends ICMM-FW-01 to ICMM-FW-03, constituting a central theoretical component of the L’Alcahest Quantique Ver 2 project. Email: cordierfr@wanadoo.fr or frederic.cordier@alcahest-quantique.frORCID: 0009-0001-8661-3275Project page: https://www.alcahest-quantique.fr