DFIM Companion Note 3: Addressing the Equivalence Principle at the Horizon—Consistency with General Relativity (Version 1.0)

This companion note clarifies the treatment of the Equivalence Principle (EP) within the Dual-Field Interface Model (DFIM). We address the potential conflict between the model's description of the horizon as a "Stiffness Weld" (High-Pass Filter) and the General Relativistic requirement for a smooth local spacetime. Key theoretical insights: The "Soft Breach" Mechanism: We demonstrate that the DFIM horizon acts as a frequency-dependent filter. Using the non-adiabatic Landau-Zener probability derived in DFIM v3.3 (P≈exp(−πκ2/2∣ρ˙m∣)), we show that the transmission probability depends on the interaction rate. Adiabatic Defense (EP Preservation): For massive, infalling observers (high momentum/high strain rate ∣ρ˙m∣), the transmission probability approaches unity (P→1). The "weld" cannot stiffen fast enough to resist the crossing, ensuring that the horizon remains locally transparent and preserving the Equivalence Principle for macroscopic matter. Echo Defense (Information Recovery): For low-energy perturbations like Hawking radiation or Gravitational Wave ringdowns (low strain rate), the transmission drops (P→0), causing reflection. This allows for the generation of Gravitational Wave Echoes without requiring a destructive "Firewall". Keywords DFIM, Equivalence Principle, AMPS Firewall, Gravitational Wave Echoes, Event Horizon, Landau-Zener Transitions, Quantum Gravity Phenomenology, Viscoelastic Spacetime. Related Identifiers Is Supplement To: [DOI of DFIM v3.3] References: Almheiri et al. (2013). JHEP, 2013(2), 62; Cardoso et al. (2016). Phys. Rev. Lett., 116.