Constitutive Normativity from Recognition Cost A Physical Grounding of the Is–Ought Bridge, with a Machine-Checked Core

I argue that the moral law is the constitutive law of agency, and I make the argument with a machine-checked core. The claim is not that a categorical "ought" can be derived from an arbitrary "is"; Hume's gap is real and I concede it. The claim is narrower and stronger: for any system that is a recognition agent (it persists across discrete update windows, carries a finite renewable cost budget, and deliberates among admissible options), sustained extraction, meaning holding the recognition skew σ away from balance, is not merely expensive but fatal, because its maintenance cost 2(cosh σ − 1) exhausts any finite budget in finite time. Not extracting is therefore a necessary condition of remaining an agent, and under positive coupling the same pressure drives equilibration with others. The bridge from this necessity to a genuine "ought" rests on one explicit posit, a transcendental kernel: a being that deliberates is rationally committed to its own continuation. Given the standard instrumental principle of practical reason and that single kernel, the moral law is rationally required of every deliberator. The load-bearing necessity step is a physical theorem, not a stipulation, and the formal development introduces no axioms beyond the three standard classical axioms of the proof assistant. This is, I claim, the strongest grounding a metaethics can have: constitutivism in which the constitutive aim is a conservation law rather than a philosophical posit.