External validation of census-derived spatial embeddings

Random cell-level splits leak spatial autocorrelation: a held-out cell's near-identical neighbors sit in the training set, and the probe interpolates rather than generalizes. All results here use contiguous-block holdout — 1,643 blocks of roughly 10 km², 19.9% of cells held out by block, so no held-out cell has a training neighbor inside its block. On this dataset, blocked-split and random-split results agree to within 0.01 R², which was verified rather than assumed.

The embedding was also probed against synthetic random fields generated to match the spatial autocorrelation of the real targets. If a representation "predicts" matched noise, its real-target scores are partly artifact. Result: |R²| ≤ 0.01 across all null configurations, on both blocked and random splits. The scores in Section 2 are signal, not spatial smoothness.

No quantity derived from the embedding's own training source is used as a validation target. Predicting one's training data through a held-out split measures shared-source agreement, not generalization. All targets below are external: satellite radiance, crowdsourced telecom infrastructure, place data, road networks, employment records, municipal service requests, and property assessment records.

Every reported number has a manifest entry recording the model artifact, evaluation query hash, split version, cell counts, and regularization. Certified results re-run under a regression guard: a shift greater than 0.05 R² between runs blocks publication.

Construction note for the daytime target: workforce counts were assigned to grid cells by census-block centroid, with block-level population from federal decennial counts as the comparison surface. Both sides reconcile exactly to published state totals (10 states, 63,413,961 population, 0.0000% error), and the assignment shares no geometry with the embedding's training pipeline.

Under-prediction increases monotonically with workplace dominance. The pattern holds individually in 9 of 10 states; the tenth has too few extreme-daytime cells for the stratum to be adequately powered. The same blindness is localized independently by a second physical source: cell-tower density is under-predicted in the same workplace-dominated strata.

A probe was trained on New York City 311 service-request density (2021–2022) and applied unchanged to Boston — no retraining, no Boston labels. Held-out rank correlation on Boston cells: Spearman 0.60. Raw-magnitude R² is negative under cold transfer, as expected: the two cities differ in base call volume, so levels shift while rank structure carries. The substantive claim is rank transfer — the property required to deploy a representation where no labels exist. Caveat: 311 volume reflects reporting propensity as well as underlying conditions; we treat this as a transfer demonstration, not a measure of municipal need.

Mean lift +0.12 R²; the embedding also outperforms the full uncompressed input set on average (+0.10), despite the latter having roughly twenty times the effective dimensionality. Road length is a loss and is reported as one: physical infrastructure is read better directly from raw variables, and it identifies a planned extension layer rather than a claim.

The evaluation sample (one full state: 27,837 cells, all 256 dimensions, plus the exact holdout fold assignments) supports independent replication of every result in this report, including the blocked-split construction. Validation targets used here are public datasets (VIIRS, OpenCellID, municipal 311, municipal assessment rolls). We invite re-scoring on the provided folds, on independent splits, and against reviewers' own targets — with the one methodological request that census-derived targets be treated as circular and scored accordingly.