  In the last decades, the necessity to process massive amounts of textual data
fueled the development of compressed text indexes: data structures efficiently
answering queries on a given text while occupying space proportional to the
compressed representation of the text. A widespread phenomenon in compressed
indexing is that more powerful queries require larger indexes. For example,
random access, the most basic query, can be supported in
$O(\delta\log\frac{n\log\sigma}{\delta\log n})$ space (where $n$ is the text
length, $\sigma$ is the alphabet size, and $\delta$ is text's substring
complexity), which is the asymptotically smallest space to represent a string,
for all $n$, $\sigma$, and $\delta$ (Kociumaka, Navarro, Prezza; IEEE Trans.
Inf. Theory 2023). The other end of the hierarchy is occupied by indexes
supporting the powerful suffix array (SA) queries. The currently smallest one
takes $O(r\log\frac{n}{r})$ space, where $r\geq\delta$ is the number of runs in
the BWT of the text (Gagie, Navarro, Prezza; J. ACM 2020).
  We present a new compressed index that needs only
$O(\delta\log\frac{n\log\sigma}{\delta\log n})$ space to support SA
functionality in $O(\log^{4+\epsilon} n)$ time. This collapses the hierarchy of
compressed data structures into a single point: The space required to represent
the text is simultaneously sufficient for efficient SA queries. Our result
immediately improves the space complexity of dozens of algorithms, which can
now be executed in optimal compressed space.
  In addition, we show how to construct our index in $O(\delta\text{ polylog }
n)$ time from the LZ77 parsing of the text. For highly repetitive texts, this
is up to exponentially faster than the previously best algorithm. To obtain our
results, we develop numerous techniques of independent interest, including the
first $O(\delta\log\frac{n\log\sigma}{\delta\log n})$-size index for LCE
queries.
