The Price of a Lesson: Damage Laws for Sequential Weight Edits

Teaching a model a new fact by editing its weights damages other facts. This paper measures the physics of that damage on a small open-weight model under a sealed, pre-registered audit loop. Damage is trajectory-governed, not update-governed: dose, allocation, rehearsal, and a frozen protected-subspace fence all failed pre-registered bars, and although edit deltas lie >=99.9% off the protected gradient span in energy, the in-span sliver is ~4,000x more casualty-potent per unit energy — final-delta overlap is the wrong control surface. Placement works where allocation does not (last-window: a matched lesson's casualties 23 -> 6; the last-window loop kept 5/5 lessons). Understanding costs ~2x memorization (template-grade 1.429 vs knowledge-grade 0.688 facts per casualty, both carrying a single-template casualty denominator). Edited states sensitize (substrate-dominant 2x2; response dispersion, not mean shift) and generic training heals them monotonically at a lawful norm-price with a binding self-damage budget; casualty risk and dispersion health dissociate. The protected-gradient spine is characterized against calibrated nulls (top-1 share 0.5064 vs scramble floor 0.0958 on Qwen-3B; 0.056-0.137 elsewhere — a Qwen-3B outlier), with an unexplained sub-null cosine anomaly and an all-PopQA composition confound disclosed. Retractions and indeterminate gate verdicts are reported at full weight. Companion to "Auditable Continual Learning." Research conducted in close collaboration with an AI assistant (Claude, Anthropic) under a sealed pre-registration discipline; disclosure in the paper.