A Dual-Foliation Model of Spacetime and Its Consequences for Energy Conservation

We present the consolidated foundational core (v6.2) of the Modified Interwoven Non-linear Temporality (MINT) framework. Spacetime is modelled as a single temporal structure T decomposed operationally into two foliations: a present-continuous foliation t₁ (domain of causal locality and General Relativity) and a historical-coexistent foliation t₂ (support of structural memory). Five coherence channels χᵢ(x) ∈ (0, 1) quantify the synchronisation between foliations across mass-energy, electromagnetic radiation, entropy/thermodynamics, gauge charge, and spin. Structural memory fields ξₑₛ꜀,ᵢ accumulate historical information in t₂, generating a causal tension φ = t₂ − t₁ that is algebraic by construction and governs the effective metric gᵉᶠᶠ_μν = χ̄ g⁽¹⁾_μν + (1 − χ̄) g⁽²⁾_μν Quantum information I(x) is introduced strictly as an inter-channel variable, mediating non-local correlations without entering the structural elliptic sector. The framework yields an exact geometric emergence of the Schrödinger equation on integrable submanifolds Σ, a unified definition of the quantum potential Q_MINT via horizontal curvature projection, and a variational closure for ξₑₛ꜀,ᵢ without Lagrange multipliers. Newtonian gravity and standard GR emerge as limits of vanishing memory (φ → 0, ξₑₛ꜀,ᵢ → 0), while effective couplings G_eff and quantum behaviour arise naturally from coherence strain. The model is mathematically elementary, spectrally stable, and falsifiable via redshift drift, atom interferometry, and galactic outskirts diagnostics. Physical laws are not imposed; they are negotiated through structural coherence.