Thermodynamic and Holographic Bounds on Recursive Physical Computation

We derive parametric upper bounds on the depth of recursively nested computational simulations under physically motivated assumptions about computational delity. Any simulation of a physical universe incurs a per-operation overhead C determined by the ratio of scales between the simulated physics and the simulator's elementary operations. When simulations are nested recursively to depth dwith branching factor b, total resource costs grow as (bC)d. We derive Cfrom rst-principles lattice quantum electrodynamics, obtaining C∼1022 for full-delity simulation, with C ∝1/α. We show that a model-independent lower bound C ≥104 107 follows from a computememory tradeo: Bell's theorem precludes classical precomputation of entangled-measurement outcomes, while the holographic principle caps storage. Applying the Lloyd computation bound and the holographic principle yields a maximum recursion depth dmax ≤1 for κ= 1 (base reality with our observable universe's computational capacity) at full QED delity. This result is logarithmically robust: increasing base reality's computational capacity by a factor of 1030 permits at most dmax ≤ 2; reaching dmax ≤11 requires κ∼10218. We analyse three delity regimes full, selective, and emergent-rule and obtain dmax ≤7 even under the most favourable assumptions. The same physics bounds the branching factor bmax = Ωciv/(C·Nops) at each level: at full QED delity, no stellar-scale civilisation can run even a single universe-scale simulation, and bounded recursion depth prevents amplication through deeper nesting. These bounds apply to any recursive computation of observer-supporting physics; we discuss their implications for the simulation argument.