Geometry-Determined Habitat Dosimetry and Radiation Transport Scaling for Sub-Relativistic Interstellar Flight: Independent GEANT4 Measurement of ηʰᵃᵇᵉᵗᵃᵗ and Analytic Derivation of the Survivability Ceiling

A central question in astrobiology is whether biological life can be distributed across interstellar distances (Bussard, 1960; Crawford, 1990; Chyba and Hand, 2005; Lingam and Loeb, 2020). Relativistic time dilation is experimentally confirmed by muon lifetime measurements (Rossi and Hall, 1941), atomic clocks (Hafele and Keating, 1972), and GPS corrections. In the spacecraft frame, ISM hydrogen becomes a forward-directed beam of kinetic energy E_k = (γ − 1)m_pc² per nucleon at flux Φ₀ = nₕβc (Semyonov, 2009; Hoang et al., 2017). The primary biological hazards are direct proton dose, secondary neutron buildup in shielding, hypervelocity dust erosion, and beam-deposited heat.

Prior analyses treated these hazards individually (Semyonov, 2009; Hoang et al., 2017; Atri, 2020; Durante and Cucinotta, 2011; Slaba et al., 2017). A key missing quantity has been the fraction of beam energy deposited in the crew habitat ηₕₐᵇᵉᵗₐᵗ, distinct from total material heating ηᵗᵒᵗₐˡ. This paper measures ηₕₐᵇᵉᵗₐᵗ directly using GEANT4, shows it is geometry-determined and shield-independent, and derives the structural radiation scaling inequality from verified transport physics