Laws Without a Global Legislator: Lawlike Stability, Invariance Across Admissible Differences, and Constitutive Constraint in a Consistency-Constrained Information History

The companion paper on causation typed an individual difference-making or productive relation relative to a declared specification and made it adjudicable, but a typed relation is not a law: that a relation holds in a case does not settle that it holds stably across the differences under which it might have varied. This paper supplies the law-specification layer the series synthesis left open, and asks, for an embedded observer with no standpoint outside the history, under what conditions a relation earns lawlike standing. The discipline is to separate things routinely conflated: a world-side regularity from an empirical regularity in records; the world-side modal structure from its model-side law statement, from its place in an economical systematization, from an observer’s record-mediated estimate, from the attribution of lawhood, and from the entitlement to attribute. The signature commitment is that no law is legislated from outside the history: neither an extra-historical necessitator that enforces the regularities, nor a privileged external standard that fixes the simplicity and vocabulary of the “best system,” is presupposed. The central technical object is nomological invariance, the preservation of a declared relational structure across a covered subfamily of an admissible difference family, formalized as structure-preservation under transport rather than literal sameness, and sharply separated from objectivity-invariance. Lawlike support is read on two distinct, separately typed grounds—an invariance ground and a systematization ground—declared per claim and kept apart so that economy is never counted as a world-side property. The constitutive-versus-contingent status of a relation is displayed beside the support rather than folded into it. The verdict is a typed package comprising order eligibility, the support statuses of the declared grounds, constitutive status, specification admissibility, an observer-side epistemic profile, and, where declared, aggregated support and entitlement. No regularity, data fit, compressibility, or counterfactual coherence certifies its own lawhood. The paper supplies a specification-relative discipline for adjudicating lawlike claims, not a derivation of the actual laws, a unique law-set, or a metaphysics of necessity.