novum: A Training-Free Structural Operator for Prediction and Generation

Abstract

We introduce novum, a training-free structural operator that reads and generatesdirectly from a table's structure. Worlds sit on typed axes and are related bycoincidence: agreement across a set of intrinsic gaps rather than closeness in ametric. Every act obeys a single invariant: an exact answer where the structureis exact, a bounded interval where the structure is partial, and a refusal wherethere is no structure to read. Nothing is ever fitted. The same operator predicts and generates. As a predictor it is competitivein-distribution with out-of-the-box RandomForest, gradient boosting, k-NN and aGaussian process on six public datasets, and it matches the retrained referenceunder covariate shift with no retraining, where the trained trees and the GPcollapse relative to their own retrained ceiling. As a generator it locatesdemanded entities and emits falsifiable intervals: Sc, Ga and Ge on the 1869periodic table as weight intervals containing the truth; the valley-of-stabilityenvelope on the chart of nuclides at containment 0.90; and a refusal of theisland of stability past the edge rather than a fabricated extrapolation. Every measured concession is reported: the decisive ablation margin is mostlyinterpolation between bracketing neighbours; the generative intervals arecompetitive with GP and conformal baselines, not dominant; composition gains area width artifact. What survives is architectural: one training-free,interval-valued, exact-or-refuse operator, self-configured from the data,carrying prediction and every generative act on one relation. Boundaries andnegatives are reported as loudly as the positives. The operator's internals are proprietary; every number is reproducible from thereleased compiled library together with the open benchmark code, and the paper'smechanistic claims are stated in behaviourally testable form, including ashipped behavioural test of self-configuration.