OVERVIEW This record contains the strong-field QED paper of the Unified Substrate Theory (UST), deriving the behaviour of the substrate field φ(x) when hard electromagnetic quanta drive the deformation scalar z toward its Planck-scale saturation bound z_max = 1. No free parameters beyond the five Lagrangian constants are used. The five constants: C₁ = 1.000 | C₂ = 0.470 | C₃ = 0.018 | β = 0.650 | Γ = 0.920 KEY PHYSICS DISTINCTION The electromagnetic deformation scalar is: z_em = (ħω/m_ec²)² × (E/E_c)² where E_c = m_e²c³/(eħ) = 1.3233 × 10¹⁸ V/m is the Schwinger critical field. For low-frequency (classical) electromagnetic fields, ħω → 0 and z_em → 0 regardless of field magnitude. This resolves the apparent tension with observed magnetar surface fields B ~ 10¹¹ T > B_c — these are quasi-static fields and do not saturate the substrate. The bound z_em ≤ 1 applies specifically to hard electromagnetic quanta. MAIN RESULTS • UST modification to QED (E < E_c): δ_UST = κ(m_e/M_φ)² = 4.67 × 10⁻¹⁴ — same substrate loop correction as QED Rung 6 for the electron g-2. UST = QED to 13 significant figures for all accessible field strengths. LUXE, E-320, and ELI-NP cannot distinguish UST from QED. • Maximum Hard-Field Theorem: no hard electromagnetic quantum (ħω ≥ m_ec²) can propagate stably in a field exceeding E_c. At E = E_c the instanton action S_inst = π and the semiclassical approximation breaks down — the substrate enters full saturation. • Maximum black hole charge: Q_max = √(4πε₀ E_c r_s²). For M = M_☉: Q_max = 3.58 × 10⁷ C, compared to the GR extremal charge Q_ext = M√(4πε₀G) = 1.71 × 10²⁰ C. Ratio Q_max/Q_ext = 2.1 × 10⁻¹³. UST predicts astrophysical black holes are essentially electrically neutral — derived from first principles. • Vacuum birefringence ceiling: Δn_max = 2α²/(45π) = 7.53 × 10⁻⁷ for hard probe photons as E → E_c. In QED the birefringence formally grows without bound; in UST the z_max saturation provides a physical ceiling. • Cross-sector consistency: the same saturation exponent γ = 3.500 governs gravitational singularity resolution (Astrophysics Paper 4), UV closure of quantum loops (QFT Paper 21), and electromagnetic vacuum saturation (this paper). Consistency of γ across all three regimes is itself a falsifiable prediction. FALSIFIABLE PREDICTIONS • Hard photon (ħω ≥ m_ec²) detected at E > E_c → UST falsified • Black hole with Q > Q_max(M) observed → UST falsified • Birefringence Δn > Δn_max for hard probe photons → UST falsified • Electromagnetic saturation exponent ≠ gravitational exponent γ = 3.500 → UST requires revision A complete Python replication script (UST_StrongField_QED_Final.py) is included. All results are reproduced in < 1 second. Dependencies: numpy, scipy only. RELATIONSHIP TO PRIOR UST PUBLICATIONS Layer 1 — Foundations: 10.5281/zenodo.18855105Layer 2 — SM Sector: 10.5281/zenodo.19055534Layer 3 — QFT Closure: 10.5281/zenodo.19076205Layer 7 — Astrophysics: 10.5281/zenodo.19580619Layer 8 — Gap Closure: 10.5281/zenodo.19227984This record — Strong-Field QED The QED Rung 6 substrate loop correction used here is established in the SM Sector (Layer 2). The UV saturation factor (1 − z/z_max)^γ and its gravitational application are in Astrophysics Paper 4 (Layer 7). The QFT propagator structure comes from Layer 3. SUGGESTED CITATION Donnelly, D. (2026). Unified Substrate Theory: Strong-Field QED — Electromagnetic Saturation, the Schwinger Field, and Vacuum Structure at the Critical Threshold [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.19616660 Keywords Unified Substrate Theorystrong-field QEDSchwinger critical fieldEuler-Heisenbergvacuum birefringencepair productionelectromagnetic saturationReissner-Nordstromblack hole chargesubstrate saturationLUXEELI-NPmagnetarz_maxUV saturationfive constants Correspondence: unifiedsubstrate@gmail.com For inquiries, collaboration, or technical questions related to the Unified Substrate Theory (UST).