Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Copy — where it appears

A phrase referring to an earlier occurrence rather than spelling itself out. Its source may overlap the phrase itself, which is what makes a long run of one character two phrases rather than hundreds — and what makes a run’s depths climb by one per character.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

02468101214mean 5.71depthshare of the collectionten revisionstwelve essays75,658 characters · 2,966 phrasesworst 14, mean 5.71

The shape of a real history's depth

Four essays here are about capping how far an extraction follows a chain of copies, and every number in them came from a generated collection. Here is the depth histogram of a real version history, which is a bell, and of twelve unrelated essays, which is nearly the same bell.

text · Parse 05101520510revisions in the collectiondepthone revision alone: 8worst depthmean depthfourteen revisions of another9 generations added exactly one

One revision, one level

The cap ladder assumed depth is generations of copying. On a real file it is exactly that — one more revision, one more level, nine times running — plus eight levels the first revision already had before any history existed.

structures · Parse 73 characters long24 runsto depth 7270 characters long24 runsto depth 69longest: 73 × "-" at position 11,0162,685 positions below depth 20, 2,685 of them inside a runeight source modules · worst depth 78100.0% in runs

The deepest text is punctuation

Eight source files reach depth 78 in a parse, on a collection with no version history in it at all. The positions between depth 20 and depth 72 are the same 48 characters at every level, and every one of them is a dash in a comment separator.

wrong · Parse

Named alongside it

The objects these essays reach for when they reach for this one.

CorpusDepthExtractionHistogramParsePhrase countControlRunVersion historyCapGenerated collectionGeneration

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