How a Community indicator becomes a prefix of City, and City becomes a prefix of Region.
Pick a pillar below — one of the index's four measured dimensions — and trace it up the scales: the Community-tier indicators, the City-tier composite they feed, and the Region-tier indicator above that. Each scale's data is summarised as an embedding, a fixed-length list of numbers. The prefix relationship — Matryoshka Representation Learning — is drawn as three nested layers: the 64 numbers at Community are the first 64 of the 256 at City, which are the first 256 of the 512 at Region. Smaller scales are not aggregations of larger; they are prefixes of them. Status pills mark each indicator: live (wired source), partial, or mock (sample value).
Embedding telescope
64d → 256d → 512dThe rectangles are ordered by embedding size — larger scale, longer vector — but not drawn to scale. The Community rectangle is contained inside the City rectangle because — under MRL — its 64 dimensions are the first 64 of the 256-dimensional City vector. The Region rectangle (512d) contains both. Information is added at the boundaries (dimensions 65–256, 257–512), never lost on the way up. This is the technically-defensible aggregation argument: not weighted-mean, but prefix-consistency.
City ECI composite (256d)
The Generation-2 cell — the territory the index's earlier generations measured before the full matrix existed; what Boeing measured for Hamburg, what Utopies measured for Paris. The City ECI (Economic Complexity Index) composite has dimensionality 256. The first 64 dimensions come from Community-tier indicators (the prefix); dimensions 65–256 add the city-level industry and consumption signal (NACE / COICOP classifications, Metroverse).
Community indicators that prefix this cell (64d)
Region indicator this cell prefixes (512d)
The nested-rectangles diagram is a metaphor for the prefix-consistency property of Matryoshka Representation Learning. It is not a literal vector visualisation. Readers asking for the projection function (concatenation-then-PCA? learned projection? weighted-mean-then-pad?) are pointed to Aggregation Rules, where the gap is named openly: methodology v0 has not yet specified all four pillars' projection functions — an open item, in review toward v1.