Reconstruction Limits and Structural Constants: A Metaformal Program for c, h, and G via Dimensionless Universality and Critical Scaling

This preprint presents the completed structural core of a metaformal reconstruction program aimed at interpreting the fundamental constants ccc, hhh, and GGG as necessary reconstruction limits rather than empirically fixed numbers. The work introduces a dimensionless universal invariant I∗I_\astI∗, obtained from critical reconstruction cascades and numerically demonstrated through period-doubling universality across different dynamical maps. Based on this invariant, a falsifiable scaling constraint is derived for the effective gravitational stiffness Geff(L)G_{\mathrm{eff}}(L)Geff(L) near a critical reconstruction scale. The preprint also introduces the concept of arithmetic confinement, providing a consistency filter that distinguishes admissible numerical structures from accidental or unstable ones. This work establishes the theoretical foundation (Phases I–III) and formulates a testable Phase IV protocol, to be developed further in follow-up studies.