How the choice of sign inventory moves the statistics of an undeciphered script: rongorongo under three published readings, with the Indus script as an outside check

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. 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 — 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 statistic by 0.318 of its [0,1] scale. The effect the statistic exists to detect — how far the real corpus sits from a shuffled version of itself, all sequential order destroyed — is at most 0.077, that being the largest of the three readings; the smallest is 0.046. Changing the catalogue therefore moves the statistic about four times further than the effect it is meant to measure: most of what changes when you switch readings is not the script but the coding of it. 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 a rising distance from the null 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 distance from the null—so this is a property of one script's transliteration problem, not of undeciphered writing in general. The levels of these statistics belong to the catalogue and the sample; only differences travel.