Emergent Gravitational Coupling from Structural Coherence in the Modified Interwoven Non-linear Temporality (MINT) Framework

This is a self-contained theoretical research report—intended for open dissemination, citation, and future integration into a broader publication series—rather than a journal submission. It consolidates and extends the Modified Interwoven Non-linear. Temporality (MINT) framework, building upon three foundational preprints deposited in Zenodo: • A Dual-Foliation Model of Spacetime. . . [?], which introduced the geometric structure of two intertwined temporal foliations and the coherence-weighted effective metric geff = χg(1) + (1−χ) g(2); • Coherence, not coincidence. . . [?], which established the elliptic structural equation ∇2χ=−κR(χ−χ0) and first derived the coherence-dependent coupling Geff; • A No-Go Theorem on the Emergence of Temporal Duality. . . [?], which proved that scalar-mediated metric interpolation inevitably reduces to a bimetric form under natural symmetry and regularity assumptions. Here, we provide a complete, covariant derivation of the emergent gravitational coupling Geff = G 1 + G2c4 (∇χ)2, clarify its regime of validity as an effective-field-theory identification, and systematically explore its phenomenological consequences across cosmology, gravitational-wave physics, Big Bang nucleosynthesis, and dark-matter halo structure. Within MINT, spacetime admits two intertwined temporal foliations; their local alignment is quantified by a dimensionless coherence parameter χ(x) ∈[0,1]. Crucially, χ is not a fundamental propagating field, but a structurally constrained order parameter. The Newtonian constant G remains universal and fixed; the gravitational interaction measured by matter emerges as a state-dependent effective coupling, controlled solely by spatial gradients of coherence. This yields a modification of gravity that is scale-dependent, automatically screened in high-curvature regimes, and free of ghost or gradient instabilities.