One ruler for every selector: a zero-parameter margin budget across selector species, and a product law for the stability of a generated trajectory

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Every decision a transformer makes at inference is a thresholded selection over a dictionary of directions with a top-k cut: a mixture-of-experts router, the vocabulary head that picks the next token, and a nearest-neighbour document retriever are the same object at three scales. The companion paper showed a routing decision's fragility -- its probability of flipping under representation noise -- is a closed-form margin budget with no parameters fitted to data, transferring across four laboratories' models. This paper carries that one closed form to the other selectors a production model runs, prices the computation between them, and composes it into a law for the stability of a whole generated sequence. The same budget prices the vocabulary decision (more than 97% of granite-3.0 next-token decisions immovable under 2% noise) and document retrieval, zero-refit. The central result, a product law registered in advance by the human author, prices generated-trajectory survival within 10% from one clean forward pass: confirmed at 24 tokens, it tightens at 96 tokens, is front-loaded in fragility, and survives the greedy-to-sampling swap via the Gumbel-max identity. Applications price the model's remaining layers, read effective context, and audit quantization and attention-drop damage from the same meter. Boundaries are reported at full price: the budget calibrates decision-flip probability, not correctness; the speed products are thin; the ceiling is a 1.4-3B model. Author contribution and use of AI: the research program and claims are the author's; experiments and drafting were done in collaboration with Claude, an AI system by Anthropic, under the author's direction, who verified the results and is responsible for the work. See the corresponding section in the PDF.