A perturbation budget for brain models: silencing interactions decay with order in connectome-constrained models, proved for linear networks and measured through order 5

A finite battery of perturbation experiments cannot certify how a brain model behaves under combinations it was not tested on unless the interactions among perturbations are bounded. Here the bound is proved for one model class and measured for another. In a linear network the interaction of a silenced set is a signed sum over the walks through every one of its nodes, so interactions of order d decay at least as fast as the per-step gain; for any set function with geometrically decaying interactions a battery closed under order d certifies all higher orders to a computable tolerance (machine-checked in Lean 4), which turns "how many perturbation tests" into a budget; for rectified units no such decay follows from the unit type, since a one-gate network has the same interaction at every order. In 50 connectome-constrained models of the fly visual system (flyvis), every silenced set up to order 5 was simulated under a preregistered protocol whose orders-4-and-5 predictions were extrapolated from exposed orders 1-3. Interaction energy fell about 70-fold from single types to quintuples and the share of interactions above a 0.2 tolerance halved with each order, but the decay slowed (per-order ratio 0.27 to 0.55) and the quintuple energy was twice the preregistered extrapolation, so the geometric hypothesis was not supported at order 5. Exploratory checks locate the deviation: nearly all high-order interaction sits in the growing minority of sets that contain a type whose own silencing saturates the readout, while other sets are close to additive. Synapse-count anatomy ranked where interactions were at every order (Spearman 0.75-0.79) but predicted their sign at or below chance, and the decay constants were model-specific. The resulting budget certifies 5-type combinations from triples at the mean-error level for this ensemble, shows what the published fly-emulation batteries do and do not license, and gives Eon's stated standard — validation on interventions the model was not tuned on — a measurable form. Paper 13 by Thomas Ryan. Preprint; not peer reviewed. The complete PDF includes the 13-page manuscript and 5-page supplement. The accompanying reproducibility package contains the frozen protocol and exposure record, new simulation outputs, analysis code, figures, theorem and checking records, Lean 4 source, and independent numerical re-derivation. Orders-1-to-3 simulation outputs are supplied by the published Paper 12 package (doi:10.5281/zenodo.23200104), as explained in the package documentation. Protocol, code, condition files, the surrogate values and the theory draft were hashed locally before confirmatory order-4 or order-5 simulation; this is an audit record, not third-party preregistration. AI assistance is disclosed in the manuscript; Thomas Ryan is the sole author. Original manuscript, figures, documentation and original research material are licensed under CC BY 4.0. Third-party software, pretrained models and cited works retain their respective rights and licenses.