The Catalogue Is the Instrument: how the choice of sign inventory moves the statistics of an undeciphered script

Statistical arguments about undeciphered scripts — whether a sign system "behaves like language" — are computed on a transliteration, and a transliteration presupposes a catalogue of signs. For rongorongo the published catalogues disagree by an order of magnitude, from about fifty basic signs to about six hundred. Pozdniakov and Pozdniakov (2007) observed that the statistics "will differ markedly depending upon the inventory of glyphs chosen"; the point has not, to our knowledge, been quantified. Call the statistic itself the instrument — the ruler we read the corpus with — and the real structure it is trying to detect the signal. On the CEIPP corpus of twenty-five objects and 14,812 glyphs, using the normalised conditional entropy of Rao et al. (2010) — a standard measure of how predictable the next sign is, given the one just before it — as the instrument, we tried three published readings of the same inscriptions: three different, defensible decisions about what counts as one sign. Just relabelling the same glyphs moved the instrument by 0.318 of its [0,1] scale. The signal it is supposed to be measuring — how far the real corpus sits from a shuffled version of itself, all sequential order destroyed — is only 0.077. The catalogue moves the instrument four times further than it moves the signal: most of what changes when you switch readings is not the script, it is the ruler. A sweep over sizes from 25 to 633 shows this is mostly an effect of catalogue size, and that the field's own catalogue of about 125 signs sits where rising signal meets collapsing coverage. Composition matters less for entropy than for the scribes' own substitutions, where the published catalogue absorbs 40% of variants against 18% for the best mechanical rule of its size. Against real syllabaries at matched size and length, a fifty-sign rongorongo reproduces the syllabary's number while carrying 1.6 to 5.5 times less sequential structure, a gap that survives matching of run length, sample, genre and orthography. The identical code run on the Indus script returns the opposite verdict — close catalogues, large signal — so this is a property of one script's apparatus, not of undeciphered writing. The levels of these statistics belong to the catalogue and the sample; only differences travel.