Nathaniel Wells

This paper defines a typed classification of intelligibility grounded in constraint structure. A claim is intelligible relative to an agent only if it occupies a position in constraint space that supports modal evaluation. A claim receives a type judgment when three conditions are satisfied: it is situated within a nontrivial, consistent norm set that partially determines a law space; this norm set admits a unique, well-posed MaxEnt projection under the symmetry-fixed base measure it entails; and the KL residual to the generating law can be reduced below a task threshold within the shell space constructible by the agent—or else a residual floor persists. This yields three ceilings: first, finite agents construct only finitely many shells, and thus have finite intelligibility images; second, even within intelligibility, finite norm sets generically imply nonzero residuals unless the generating law lies within the family, imposing a structural limit on knowability; third, fragmentation is destructive to constraint closure and can strictly downgrade a claim’s type, eliminating residual control and collapsing knowability under the same epistemic threshold.

I show that intelligible possibility requires constitutive norms — constraints that define a symmetry-compatible base measure and enforce bounded expectations. Under the Maximum Entropy principle, these norms uniquely select exponential-family laws. On multiplicative domains, scale invariance identifies the logarithm as the canonical information measure and produces Pareto-distributed tails that account for the observed 80:20 regularity. Renormalization stability isolates the Gaussian and power-law families as fixed points under transformation. A branching-process axiom system models gift-chain dynamics, allowing direct computation of survival and control from the associated probability-generating function. A projection theorem in Kullback-Leibler divergence formalizes the infinite–finite boundary as a positive information distance, under finite norm sets. Explanations are provided after formal claims. The Norms-First framework and vocabulary follow the V3 preprint (Wells, Nathaniel. A Quantum Ontology of Logos) to ensure alignment and citability.

Scope is metaphysical: it explains why order exists for physics to measure. This revision strengthens the ontological core by (i) retaining the Norms-First Possibility principle while tightening its measure-theoretic expression; (ii) sharpening the inferential bridge from ontology to physics via explicit exponential-family structure and a KL- projection theorem that formalizes the infinite–finite gap; and (iii) adding D5c (Gift- Chain Dynamics), a fully axiomatized result that derives contribution as the fitting mode of finite agents from a branching-process kernel under the gift grammar (receive → transmit → increase). D5c proves that gift-structured cascades are dynamically isomorphic (at the probability-generating-function level) to neutron-chain reactions and pay-it-forward processes, without category error, and shows how norms act as control policies on the offspring law to shift systems from subcritical to supercritical regimes under entropy-consistent control. The Christological hinge remains conditional and public-facing downstream of the metaphysical derivation.