A Causal–Spectral Planning Specification for AI-Coached Endurance Training Admissible Load–Recovery Design with No-Go Constraints and Environment Derating

Using day-level longitudinal data from 74 competitive runners (42,766 training days spanning seven years,2012–2019), this document specifies a minimal and conservative planning framework for AI-coached endurance training.The objective is not injury prediction or performance optimization, but admissible scheduling under finite recoveryand delayed adaptation.We formalize load–recovery dynamics using a small set of causal–spectral master equations, derive explicit no-goconditions that invalidate unsafe plans, and anchor these constraints with empirical observations. Environmentalhazards, such as PM2.5 air pollution, are incorporated by contracting recovery bandwidth rather than alteringdynamics.The framework is explicitly admissibility-first. All optimization-oriented layers (e.g., intensity structuring and tapering)are modular, optional, and do not weaken conservative safety guarantees.