  We develop the theory and practical implementation of p-adic sparse coding of
data. Rather than the standard, sparsifying criterion that uses the $L_0$
pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be
node-ranked, as is standard practice in agglomerative and other hierarchical
clustering, but not necessarily with decision trees. In order to structure the
data, all computational processing operations are direct reading of the data,
or are bounded by a constant number of direct readings of the data, implying
linear computational time. Through p-adic sparse data coding, efficient storage
results, and for bounded p-adic norm stored data, search and retrieval are
constant time operations. Examples show the effectiveness of this new approach
to content-driven encoding and displaying of data.
