Log-Harmonic Field Theory (LHFT)

Log-Harmonic Field Theory (LHFT), developed by Christian Baganz in Potsdam, Germany, is an axiomatic projective recovery framework. It does not begin with a pre-given four-dimensional spacetime filled with particles and fields. Instead, it starts from a deeper structural layer described by structural order, state, coupling, and projection. structure → state → coupling → projection → observable recovery The basic structural objects are the structural evolution parameter s, the logarithmic scale coordinate u = ln r, the fractal-dimension field Df, and the structural state Ψ. Observable spacetime, effective metric structure, physical fields, matter sectors, and clock time are not assumed as fundamental primitives. They arise as observer-readable recovery objects inside an admissible projection window. ΠO^Ψ: (Df, Ψ, ΘO) → (MO, g_μνO, ΨₑffO) The mathematical proof architecture of LHFT is organized around the one-layer structural action S₁L, its quadratic Hessian Kₛtruct, a Dirac-type recovery normal form, and an observer-dependent projection-compression map. The central theorem-level statement is conditional: if the global recovery defect vanishes, the observer-readable projected sector recovers Standard-Model and General-Relativity structures. DLHFT→rec = 0 ⇒ observer-readable recovery of SM + GR The framework distinguishes strictly between definition, derivation, recovery, normal-form closure, candidate status, and open proof obligations. Selected sectors, especially the Alpha sector, are normal-form closed at the projected level. Matter, gravity, cosmological, and DARK-sector structures are treated according to their stated recovery or candidate status, without replacing open microscopic derivations by numerical agreement. LHFT therefore does not claim absolute microscopic closure of the total structural universe. Its claim is projective: finite observer-readable recovery sectors can be closed inside admissible projection windows, while the underlying structural layer is not exhausted by any single observable representation. projective closure ≠ absolute microscopic closure LHFT closes observer-readable recovery sectors projectively, not Sₛtruct absolutely. Under LHFT, Alpha becomes ontologically explainable because α is not treated as an isolated numerical constant, but as the dimensionless accessibility of the visible electromagnetic diagonal channel U (1) diagO inside an observer projection ΠO^Ψ; see the Alpha definition here: Alpha definition link. Correspondingly, α⁻¹ = K_αO = ΘO / ΓU (1) diagO is the projection impedance of this channel. In the stable low-energy recovery regime, Df → 3, this readout appears as the familiar constant α, but at high energies or small scales the recovery state changes, so Df (E), ΠO^Ψ (E), ΘO (E), and ΓU (1) diagO (E) change together. Therefore α (E) changes not because a detached constant arbitrarily “runs”, but because the electromagnetic visibility quotient of the projected recovery sector changes with energy. In standard language this is the running of α; in LHFT language it is the energy-dependent readout of electromagnetic projection accessibility.