The Invariant Core of Bounded Judgment: Meaning, Non-Arbitrariness, Non-Triviality, and the Partial Order of Reason

What structural form must an answerable world take for a bounded evaluator if judgments of persistence are to be meaningful, non-arbitrary, and non-trivial? This paper composes results from the Identity-Persistence Program into a Partial Order of Reason. It does not derive the constitution of reality simpliciter; it concerns reality insofar as it becomes answerable to a bounded method. Answerability under a co-declared standard grounds a verdict demand and sufficiently declared regime R with demand Q. Independently, conditions on meaningful and non-arbitrary identity judgment supply the relevant identity and admissibility structure. At their convergence, Q induces static answer-equivalence K0(R,Q), its greatest structure-compatible congruence Theta(R,Q), and the invariant quotient core N_Q(R). Safe evidence channels canonically forget down to this core, while declared verdicts factor out of it. Together with the static answer quotient A_Q(R), this gives a Kernel Sandwich separating retained evidence, operable structural identity, static answer-equivalence, and final judgment. Structural existence of the core is thereby distinguished from epistemic attainment of it. The core is demand-relative rather than a question-independent essence. Structural Transparency holds exactly when Theta(R,Q) equals K0(R,Q): static answer-equivalence is then already structurally transportable and the operable and static quotients coincide. The second edition shows that this architecture is governed by contextual saturation. Closing Q under the lawful translations generated by R defines a closure operator on extensional demands, whose variance-reversed image on answer kernels is the congruence interior. Hence operability is static answerability after contextual closure. The resulting Contextual Indiscernibility Characterization says that two states are operably identical exactly when no declared question distinguishes them after any lawful regime-generated context. This is interpreted as a Bounded Leibniz Principle: identity of indiscernibles made regime- and demand-relative, without assuming an exhaustive predicate universe or promoting relative identity to identity simpliciter. The same adjoint structure yields a general Demand-Meet Law under which joins of demands correspond to meets of their operable equivalences, while infinite inverse-limit realization remains a separate completeness question. The discrepancy between static and operable equivalence is isolated as a contextual defect whose witnessing contexts form a dependency-incidence structure. Residual symmetry, decomposition, governance, capacity, observables, probability, and verification are located downstream. Within the additive governance subclass, the representation-independent governance object is a positive projective ray, with PAS_h as a harmonic coordinate realization. Canonical weight ratios exist exactly when the admissible projective ray set is a singleton.