How You Build Superintelligence: From Scaling Laws to Construction Laws

A capability target does not specify the system that should be built to attain it. Scaling laws predict performance along a chosen development path, yet even exact knowledge of a scaling trajectory can leave the optimal resource allocation unidentified. We formulate construction laws: target-conditioned maps from identified mechanisms and physical resource constraints to a complete executable recipe, a forecast, and an auditable qualification test. We formalize superintelligence as an expert-relative capability specification that fixes the task population, within-task reliability, across-task breadth, and common information conditions. Our main inverse theorem converts uncertainty in forward predictions, resource costs, and task breadth into a guarantee on a qualifying construction; the controlling quantity is the price of target tightening, not prediction error alone. We then derive explicit construction laws for resource allocation, numerical precision and training data, reusable information, and conditional specialization, including an exact rule for jointly choosing sharing strength and specialist data. Prospectively frozen neural constructions reduce packed-weight storage by 1.33–1.59× while satisfying a predeclared 0.010-nat noninferiority criterion in all six target–seed comparisons. In a controlled hidden-support neural task, reusable structure reaches the same 80% reliability target with 32 rather than 256 task queries, while task-private structure removes the advantage. In external multi-hop retrieval, inherited transition structure consistently improves low-budget recovery, but a preregistered 2× budget-crossing forecast misses validation by 0.66 percentage points, illustrating the instability of discrete construction decisions near a target boundary. Construction laws turn capability scaling from a forward forecast into an inverse question: which system reaches the target, at what resource cost, and with what evidence?