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

Abstract

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, beyond Korovina (2026), who runs one method on two transliterations of the same inscriptions and obtains different scores. 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 with 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, a 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. Version 12 (18 September 2026) closes the residue of the same check, on a second independent pass. The Acknowledgements credited only the second person to identify the *Staff sign correctly, where the appendix footnote had already been corrected to name Albert Davletshin first. A second quotation from Rao et al. dropped a symbol. The replacement ICIT sign counts, 694 and about 709, are now attributed to the publisher's listing and the project page they come from, since Wells (2015) itself is unread here - the same standard the figures they replaced failed. And the sign-class test now states that Davletshin's criterion is a bipartition of signs rather than a concentration of events, noting Linear B as the reference that behaves as his hypothesis predicts. No number changed. Version 11 (18 September 2026) changes no result, table or number. Every statement in the paper about someone else's work was checked line by line against the source text, and a dozen did not survive. The substantive ones: Davletshin (2017) calls two of Barthel's counts difficult to reconcile, where the paper had three that cannot be; Davletshin (2022) says the ABAB sequences resemble complete reduplication, used for intensity of action, reciprocals, frequentatives and derived adjectives, where the paper had him reading them as reduplication for intensives and plurals; the two-sign-class proposal is argued in Davletshin (2012) and restated in 2017, with hedges the paper had dropped; the rhetorical-repetition limit is already in print in Davletshin (2022) and not only in correspondence; the *Staff correction was named first by Albert Davletshin and supplied explicitly by Rafal Wieczorek the next day, where an earlier footnote credited only the second; a clause given as a quotation from Fischer (1995) was an encyclopaedia's paraphrase and is no longer quoted; Robinson's count of 63 of 113 sequences is cited to Robinson (2002); EBUDS is the filtered concordance used by Rao et al. rather than their dataset; the Wells and ICIT sign counts are 694 and about 709, not the unsourced 676 and 702; Sproat's page is dated to its own last modification in 2003; and a description of the field attributed to E. Korovina, which she did not make, is replaced by the constraint as our own choice, with her partial precedent now disclosed in the abstract. The AAA comparison now carries its non-reduplicating control. The figure is redrawn in pgfplots from the same numbers, so the paper builds from one file. All of it is listed in a new section, "Corrections in this version". Version 10 (2 September 2026) changes no result, table or figure. It adds a caveat from Albert Davletshin on the ABAB pattern: shown the alternations as lines rather than as counts, he replied that he holds every one of them in his own files and classes none of them as morphological reduplication, reading them instead as rhetorical repetition, on the evidence of parallel passages and of other rhetorical repetition nearby (personal communication, 1 September 2026). Doubling a word for emphasis and repeating a phrase for effect leave the same trace in a count of ABAB, and nothing measured here separates them; what the cross-language comparison establishes is the rate at which rongorongo alternates, not the mechanism behind it. It also repairs a cross-reference in the robustness section that had lost its markup and printed as source: the deposits of 29 August and 2 September (22158360, 22159262, 22252999) read "The ratio in Table~ ef{tab:ladder}" where the table number should be. The prose has been repunctuated throughout. Version 9 (2 September 2026) corrects one sign identification and adds a conclusion. Versions 1-8 identified Davletshin's "*Staff" sign as Barthel 200; it is Barthel 001 (R. Wieczorek, personal communication, 2 September 2026). The figures reported under that name were 200's, and correcting them reverses the finding: *Staff is the leading ABAB carrier of the 125 sign types at 2.4 times the ligature-corrected median, where it had been reported as a median sign ranking high only through its frequency. The error was itself an instance of the paper's subject, in that 200 appeared to be the corpus's commonest sign only because the Horley map folds eight Barthel codes into it. Nothing in the abstract above is affected. A plain-language conclusion (section 11) has been added.