Validated Retrodiction: A Two-Coordinate Measure of Cumulative Complexity and a Method for Locating Obligatory Intermediate Nodes

Cross-substrate comparison of complexity requires a single measure that applies to elements, minerals, protein folds, and knowledge alike; the available measures fail for specific reasons. Building on the self-validation framework of the United Field Initiative Paper 0 series — in particular densification and mutual validation from Part 3 — we propose two things and one falsifiable hypothesis. First, a two-coordinate measure of complexity: a blueprint rank (nesting depth, derived for the lower substrate classes from the rule that the primitive of each level is a combination of the level below) and a count of mutually validated primitives within a level. Keeping the two separate — quality (which floor) apart from quantity (how saturated that floor is) — removes the apparent paradox by which a lower floor may hold more validated items than a higher one. Second, a retrodictive method that, given a validated construction M and a domain's instrument for detecting validity, disciplines reasoning about how M could have come to be. It separates the obligatory intermediate nodes — those every admissible history shares, written Ob (M) = ⋂ RV (M) — from the genuine forks where the route is undetermined, and it halts at forks rather than inventing a continuation. The method does not generate obligatory nodes; it organises and constrains an analysis whose admissible histories are supplied by domain knowledge. The sharpest falsifiable content is a growth hypothesis: if a new validated construction is a closed combination of k existing primitives, the number of new constructions should grow as dN/dt ∝ Nᵏ within a regime, with the exponent fixed by combination multiplicity — k = 1 is mere copying, k > 1 is the framework's prediction — testable against time-series once research effort is controlled for. We are explicit about status. We demonstrate the method on three known open problems (physics, chemistry, biology), where it reproduces — does not discover — what each field already regards as the obligatory node; these are illustrations of generality, not predictions, and no blind test was performed. The measure and the method we offer with confidence; the growth law, and the proposed unification of the downward (Ob) and upward (N (t) ) views, we offer as a research program, not a result.