Observation

Not a single trait pair in the entire 32-bit taxonomy is anti-correlated. Across 1,500 entities and 496 possible trait pairs, the most negative phi coefficient is -0.265 ({{trait:Observable}} × {{trait:Symbolic}}). The mean phi is +0.143, and 78.6% of all pairs are positive — against an expected 50% under independence. The UHT trait space is unipolar: ontological complexity is purely additive. Acquiring one trait never implies losing another.

Evidence

The full phi-correlation matrix was computed across N=1,500 entities drawn from the 16,211-entity graph. Against a Monte Carlo null model (100 simulations, same marginal activation rates, traits independent), the results are unambiguous: null simulations never produce any |phi| exceeding 0.123, and zero null pairs ever reach |phi| >= 0.30. The real corpus has 74 pairs above 0.30 and 13 above 0.50 (p < 0.0001 for all observed structure). Eight mutual best-pairs form the correlation backbone: {{trait:Physical Object}} ↔ {{trait:Physical Medium}} (phi=0.760), {{trait:Synthetic}} ↔ {{trait:Intentionally Designed}} (0.680), {{trait:Active}} ↔ {{trait:Functionally Autonomous}} (0.637), {{trait:Synthetic}} ↔ {{trait:Human-Interactive}} (0.635), {{trait:Powered}} ↔ {{trait:Processes Signals/Logic}} (0.568), {{trait:Regulated}} ↔ {{trait:Economically Significant}} (0.549), {{trait:Institutionally Defined}} ↔ {{trait:Regulated}} (0.531), and {{trait:System-integrated}} ↔ {{trait:Compositional}} (0.481). Four traits — {{trait:Rule-governed}}, {{trait:Normative}}, {{trait:Meta}}, and {{trait:Temporal}} — are independent of all others (max |phi| < 0.30). Effective dimensionality is approximately 13, not the ~8 estimated in {{hyp:HYP-CLOSEDHYPOTHESES-053}}.

Popcount analysis revealed a trait activation ladder. At low popcount (1-3 bits), the first traits to activate are {{trait:Observable}} (35.4%), {{trait:Symbolic}} (34.8%), and {{trait:Social Construct}} (28.4%). The last to appear — never active below popcount 4 — are {{trait:Synthetic}}, {{trait:Powered}}, {{trait:Functionally Autonomous}}, and {{trait:Digital/Virtual}}. Strikingly, {{trait:Meta}} is the only trait whose activation rate decreases with popcount (2.0% at low vs 1.4% at high), marking it as an idiosyncratic self-referential property orthogonal to complexity.

Interpretation

The taxonomy encodes a one-directional complexity gradient. Simple concepts are either perceptible (Observable) or representational (Symbolic) — these two traits compete at the ground floor, explaining their mild anti-correlation (-0.265). As concepts gain ontological complexity, they accumulate both physical and social traits additively. The absence of trade-offs means UHT measures how much ontological structure a concept possesses, not what kind. A concept with 20 active bits is not a different type of entity — it is a more multi-faceted one. This validates the earlier “being, not doing” characterisation from a completely different angle: UHT traits are constitutive properties that stack, not functional roles that compete.

The four independent traits ({{trait:Rule-governed}}, {{trait:Normative}}, {{trait:Meta}}, {{trait:Temporal}}) represent dimensions that cross-cut the physical-social gradient entirely. They activate regardless of whether a concept is concrete or abstract, simple or complex. These are the taxonomy’s true orthogonal axes.

Action

Created {{hyp:HYP-CLOSEDHYPOTHESES-083}} (confirmed) with linked {{res:RES-CALIBRATIONRESULTS-099}}. Stored two research facts: trait unipolarity and the first statistical null model baseline for the corpus. The null model (matched marginals, independent Bernoulli) should be treated as the standing baseline for evaluating all future quantitative claims. Next sessions should investigate why the four independent traits behave differently — particularly whether {{trait:Temporal}} and {{trait:Meta}} mark genuinely distinct ontological categories or are artifacts of low activation rates. The trait activation ladder (Observable/Symbolic first, Synthetic/Powered last) warrants its own hypothesis about whether popcount predicts domain membership.