Each domain is positioned by its composite validation score — higher-confidence domains orbit closer to the center. Edges represent formally classified connections (STQA Class 7+). The Poincaré ball is the native geometry of inference coupling: IC = tanh(geodesic distance).
These connections are not analogies. Each edge means the same mathematical object — the same IC, the same geodesic coordinate, the same cost function — appears independently in both domains. A Class 10 edge is a proven identity; Class 7 is an algebraically exact structural correspondence. Resemblances (Class 5) are tracked but not shown here.
Every domain extension requires explicit operationalization: What are the nodes? What implements R? How would IC be measured? What would falsify the extension? Each connection is classified using semiotic translation quality assessment (STQA).
Formal, empirical, and operational soundness all above 0.75. Quantitative predictions confirmed by data.
Structurally sound with clear operationalization. Empirically suggestive but awaiting full Stage 3 validation against independent data.
Operationalization in progress. IC can be defined but predictions remain untested or incompletely specified.
Speculative connections. The extension questions are partially answered at best; exploration is primary, not validation.
Each domain's composite score reflects the minimum (bottleneck) strength across three dimensions: formal soundness (mathematical rigor of the CF operationalization), empirical grounding (quantified predictions confirmed by data), and operational completeness (all six extension questions answered, including falsifiability and dependency archetype classification). A domain reaches Tier 1 only when all three dimensions independently exceed 0.75 — strong formal apparatus with weak empirical support stays in Tier 2 or below.