Random access into compressed data is normally bought with density. We measure the exchange rate. Across four formats and nine axes on a common corpus, the cost of cutting a 254 MB archive into independently addressable 16 KiB units is 1.632% of the archive for an absolute-offset format against 6.57% for seekable zstd, and the gap widens as the unit shrinks: at 4 KiB, 5.33% against 10.06%. Because the cost is small, several properties follow that are usually unavailable: splitting an archive is free and occasionally profitable (-0.28% on tiled input), append needs no format change, seek latency does not depend on position, and one archive is read by both a CPU and a GPU decoder. We give three structural results with proofs and bit-perfect verification - that the repeat-distance chain of an LZ77 parse forms a substitution monoid and is therefore prefix-scannable without touching the bitstream, that self-overlapping matches are periodic rather than chained, and that dependency depth admits an encoder-enforced bound - and we report each measured limit together with the mechanism that sets it. Seventeen rejected directions are listed with their numbers, including one that improved density by 26% and was declined. Every claim carries a level: reproducible by command, measured with a stated reason, or estimated. The measurement tool is released separately (DOI 10.5281/zenodo.22713364) with 435 provenanced records.

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