Log-Harmonic Field Theory (LHFT) - Compact Scientific Form

Abstract This manuscript presents the complete normal-form representation of the one-layer structural action S₁L in Log-Harmonic Field Theory (LHFT). The central claim is that observable spacetime physics is not introduced as primitive input, but arises as a projective recovery regime of a deeper structural domain X_str = ℝ_s × ℝ_u × S²_Ω with logarithmic scale coordinate u = ln(r/r₀). Starting from the structural fields D_f and Ψ, the quadratic sector of S₁L defines a structural Hessian K_str, whose normal-form target is a Dirac-type square D_str². Through a Lichnerowicz-type decomposition, this square contains the natural slots for curvature, gauge curvature, mass terms, and projection impedance. S₁L → S₁L² → K_str → D_str² → Π_O → GR + QFT/SM The observer map Π_O = P_O R_O C_O is treated as a contractive projection selecting a stable, non-suppressed visible remainder of the full structural state. Hidden sectors are not discarded; when coupled, they contribute through suppressed Schur/Feshbach backaction: D_O = D_vv − D_vh D_hh⁻¹ D_hv In this reading, general relativity, gauge theory, matter states, coupling constants, masses, and renormalization flow appear as observer-readable recovery sectors of one structural operator. The manuscript establishes the complete S₁L normal-form architecture and identifies the remaining coefficient-level proof obligations. It does not claim full microscopic derivation of all Standard-Model constants, masses, flavor matrices, anomaly constraints, projection maps, or beta functions. The present status is therefore: S₁L normal-form representation complete; full microscopic coefficient closure from S₁L open.