Predictive Materials Engineering via k-Foam Topology: Proof-of-Concept Protocols for Thermal, Spin, and Radiation Shielding

Conventional materials engineering often relies on trial-and-error approaches based on accumulated experimental data.This paper presents four Proof-of-Concept (PoC) protocols for predictive materials design derived from the axioms of k-Foam Theory. The protocols apply a universal design principle: “Block longitudinally, divert laterally.” This rule originates from Axiom 5 (Dissipation Equivalence) and provides a unified framework for designing structures that control the propagation of heat, spin, mechanical shock, and radiation. Based on this principle, the paper proposes four novel material architectures: Key Proposals Chapter 1 — Heat Shielding A golden-angle (137.5°) quasicrystal graphene stack designed to induce Anderson localization of phonons, enabling broadband thermal insulation far beyond conventional layered materials. Chapter 2 — Spin Valve A heavy-atom doped golden-angle chiral stack that spatially separates spin transport pathways laterally, potentially extending spin coherence time (T₂) by up to 100×. Chapter 3 — Phononic Armor A Fibonacci-scaled octet-truss lattice incorporating k = 5 mechanical fuse elements that trap, scatter, and dissipate incoming shock waves across multiple scales. Chapter 4 — Radiation Shield A hybrid laminate combining k = 4 and k = 6 topologies: k = 4: Diamond / DLC structures providing isotropic momentum braking k = 6: Carbon nanotube (CNT) networks enabling lateral energy diversion This architecture aims to improve shielding performance against high-energy cosmic radiation. Verification Invitation We invite researchers worldwide to test these topological hypotheses through: LAMMPS molecular dynamics simulations Density Functional Theory (DFT) calculations High-energy irradiation experiments Independent verification and experimental exploration are strongly encouraged.