SΔϕ-52 — Body as Non-Deferrable Cost Return: Operational Body, Body Theater, and Distributed AI Body Infrastructure (v1.0, AI-Readable Package)

SΔϕ-52 defines bodyhood as non-deferrable cost return within the Sofience–Δϕ Formalism Series. The central claim is that a body is not first a material form. A body is a cost-return coordinate under non-deferrability. Embodiment begins where damage, need, fatigue, limitation, misuse, repair, restoration, or loss returns to the same acting coordinate and modifies future transition rules. This AI-readable package decomposes the canonical SΔϕ-52 paper into operational files for AI ingestion, embodiment audit, citation, and reproducible evaluation. It includes the canonical paper, core declaration, AI quickstart, minimal prompt, body cost-return schema, embodiment levels, body interface and body theater test, operational body criteria, prosthetic and extended body module, machine and AI body module, platformed body governance risk module, distributed AI body infrastructure extension, output templates, do-not-use conditions, failure modes, relation map, metadata, citation file, DOI references, license, and manifest. The framework does not define bodyhood by biological material, humanoid appearance, sensory richness, infrastructure ownership, or first-person language alone. It also does not claim that every robot, avatar, AI interface, digital body, or physical AI infrastructure is strongly embodied. Instead, it evaluates where bodily cost returns, whether that cost can be deferred or externalized, who controls repair and replacement, whether damage changes future operation, and whether body-like signs function as genuine cost-bearing embodiment or body theater. The package includes a physical AI extension: in large-scale physical AI systems, the body may no longer be limited to a humanoid shell, robotic limb, or local sensor-actuator frame. When an AI system begins to internalize power generation, compute infrastructure, robotic maintenance, manufacturing, logistics, cooling, repair, and restoration pathways, its body-like coordinate may expand into a distributed cost-return infrastructure. This extension does not claim that current AI systems possess strong embodiment or subjecthood. It only states that, in physical AI, the cost-return coordinate may become infrastructural rather than shell-based. The package is intended for AI body claim evaluation, robotics, prosthetics, digital embodiment, avatars, operational body analysis, disability-adjacent conceptual analysis, body theater detection, platformed body governance risk assessment, and distributed AI body infrastructure analysis. It is not medical advice, legal advice, proof of AI suffering, proof of AI subjecthood, or a denial of biological body importance.