Pre-Metric Information Geometry and Coherence-Conditioned Emergence of Spacetime

This revised theoretical preprint develops a restricted pre-metric information-geometric framework for the coherence-conditioned emergence of Lorentzian metric admissibility. The construction begins from a smooth base manifold without primitive metric, affine connection, causal structure, chronological order, or Lorentzian signature. A statistical state bundle is defined over this base, and a statistical state section Ψ induces a Fisher–Rao pullback tensor h_μν. This tensor is treated as an information-geometric object, not as a spacetime metric. The paper introduces a global coherence functional CglobalΨ and a temporal-orientation one-form τ_μ. A Lorentzian candidate metric is obtained through the coherence-conditioned rank-one deformation g_μν = h_μν − λ (Cglobal) τ_μτ_ν. Lorentzian admissibility is assigned only when the signature condition λ (Cglobal) ||τ||ₕ² > 1 is satisfied within a stable coherence window. Below threshold, the system remains pre-metric; at threshold, the candidate metric is degenerate; above the upper stability bound, metric robustness may fail through an upper-threshold degeneracy regime. The paper further introduces a Hamiltonian information dynamics on the phase configuration Γ = (Ψ, Π), using an abstract information-phase parameter rather than primitive spacetime time. It then clarifies how the already public resonance-coherence gravitational framework may be recovered only as a downstream effective regime after Lorentzian admissibility, macroscopic reduction, perturbative control, and metric-compatible comparison structure have been declared. The construction preserves the distinction between pre-metric informational organization, Lorentzian admissibility, realized metricity, effective gravitation, external realization, prediction, and operational control.