Structural Non-Reconstructibility in Quantum Systems: Operational Formulation of OFID-G

This work proposes an operational framework, denoted OFID-G, to investigate whether quantum coherence remains fully reconstructible from locally accessible information, even when global unitary evolution is preserved. The framework is formulated within the Ontological Framework of Imbricated Degrees (OFID), in which physical states may involve degrees of freedom that are not fully accessible within a given local observational regime. Within this perspective, OFID-G defines a possible structural limitation on the local accessibility of coherence, without introducing any modification to quantum dynamics. The central concept is regime-dependent reconstructibility: coherence is said to be reconstructible if a single recovery operation, fixed by calibration alone, can operationally recover it across a tomographically informative family of preparations, and non-reconstructible if a persistent limitation remains despite such procedures. This state-independent formulation anchors the criterion in the theory of approximate recoverability of quantum channels. Rather than predicting a specific mechanism, the framework defines a falsifiable structural criterion distinguishing reconstructible and non-reconstructible regimes, based on controlled variation of physically relevant parameters. The approach remains fully compatible with standard quantum mechanics and does not invoke collapse models or deviations from unitarity. Its empirical content lies in testing whether all observed decoherence effects can be fully accounted for by known environmental mechanisms. This provides a minimal and operational test of the completeness of standard decoherence modeling, shifting the focus from dynamical mechanisms to structural limitations of information accessibility. The framework is developed within the OFID research program (DOI: 10.5281/zenodo.18868538); its concrete experimental realization is developed in a companion operational paper (DOI: 10.5281/zenodo.19351945). Project page :https://alexsasfrance.github.io/OFID-framework/