Dimensional Folding, v2.1: Measured PCA Projection, Preservation Metrics, Deployment, and Discussion

Laboratory technical report (manuscript v2.1.0) that rewrites the Dimensional Folding Implementation Guide as an empirical study of PCA folding Rn→Rm with measured preservation and search metrics. This Zenodo deposit version 4.0.0 supersedes prior versions in this concept with measured laboratory results. Prior deposits framed dimensional folding with quadrillion-scale 2n−m state-space reduction, universal ρ≥0.99 information preservation, and multiplicative speedups combining 2n−m, n/m, and an O(n)→O(log n) indexing factor. This version implements folding as standard linear dimensionality reduction (PCA), reports wall-clock results on laboratory compute nodes, and adds deployment instructions plus discussion of when folding succeeds or fails. Key measured results (four multi-runs; 21 configurations × 4 seeds; N up to 3000): Strong spikes (mean of 6 configs): ρ=0.923, pairwise distance correlation ≈1.00, Recall@10=0.933, brute-force query speedups 2.6×–16.8× (mean 8.4×; order of n/m, not 2n−m). sklearn digits 64→16: ρ=0.728, distance correlation 0.970, Recall@10=0.714, speedup 2.80×. Isotropic Gaussians 256→32: ρ=0.193, Recall@10≈0.078 despite speedup 7.89× — runtime gain without neighbor fidelity. Spiked 2048→32: speedup 75.2× ≈ 1.18·(n/m); 22016 is not a runtime factor. Verdicts: 2n−m as continuous-PCA runtime speedup — rejected; ρ≥0.99 as a universal guarantee of aggressive folds — rejected; n/m distance speedup — partially confirmed at high n; folding alone implying O(log N) query complexity — rejected (ANN/HNSW conflation). What holds: PCA ρ is retained eigenvalue mass; pairwise geometry and Recall@k track spectral concentration; measured brute speedups scale roughly with n/m at high dimension. Deployment guidance covers prerequisites, multi-run aggregation, fold-transform persistence, m-selection, and a POC→pilot→production checklist grounded only in metrics actually measured. Files: PDF and HTML manuscript; scrubbed reproducibility package (dimensional_folding/ source + aggregate/run results; ops deploy script containing host IPs excluded). Note: This v4 supersedes the Implementation Guide narrative in earlier versions of this concept (including 10.5281/zenodo.18727937) with measured lab validation.