The Indus Script Is Not an Emblem System Sequential dependency in 2,536 inscriptions, measured against matched linguistic and non-linguistic controls

IThe Corpus

Every figure on this page comes from excavated inscriptions in the published digitisation of the Corpus of Indus Seals and Inscriptions. No reconstructed, simulated or generated text enters the analysis at any point. This is worth stating plainly because the alternative is common in this field and hard to detect from outside.

IIThe Finding

At this corpus size every measure of structure is inflated. With 591 distinct signs and fewer than nine thousand tokens, the table of sign pairs is about two per cent occupied, and in that regime a corpus shuffled into complete meaninglessness still returns a large positive score. A raw figure therefore means nothing. What follows is in every case the margin over a matched control: the same corpus, its structure destroyed, measured the same way.

The second row is the one that rules out a weaker reading. Scrambling the order of signs within an inscription, while keeping exactly which signs co-occur, still destroys 0.900 bits. The information is in the sequence, not merely in the company.

The boundary result is the cleanest in the study. Whatever an inscription says, it finishes saying it: dependency across the join between two artifacts falls below chance. Each object carries one complete statement, and the corpus is not the scattered fragments of a longer running text.

IIIThe Controls

A structural result is uninterpretable until you know what other systems score. The identical analysis was therefore run on four control corpora, each matched to the Indus corpus on text count, length distribution, token count and vocabulary size. Without that matching one measures corpus size rather than writing system, which is the error that makes cross-corpus comparisons in this field unreliable.

A limitation we have not solved

The natural-language control is running prose cut into short segments, so it has no genuine text beginnings or endings. That makes it a poor comparator for directionality in particular, and it is why no claim is made that Indus directionality is language-like, only that it is real. A control built from genuinely short complete texts would settle it. We have not built one.

IVWhat Survived

The findings were attacked before they were published. The strongest objection was that duplicate seal impressions, the same seal pressed many times or mass-produced copies of one design, could manufacture all of these results from nothing. Collapsing every repeated inscription removes 634 texts. Each measure was then recomputed on the reduced corpus, and separately at each major site, so that no finding rests on pooling two traditions that might differ.

The effects persist after deduplication and hold independently at Mohenjo-daro and Harappa, two sites some six hundred kilometres apart, showing the same structure.

How many independent inscriptions are there really?

Collapsing only identical inscriptions is the weak version of this control. Indus seals were also copied, and near-identical texts are not independent observations either. Grouping inscriptions that differ by one or two sign edits reduces 1,902 distinct sequences to 1,141 and then to 558. Intervals computed on the raw count are therefore too narrow, which is a problem for most published statistics on this corpus, and was for ours.

The three main results hold on 558 inscriptions, under a quarter of what we started with. That is the number they should be judged on.

Is the headline number an artifact of the estimator?

This is the sharpest objection available and it has been made before, against earlier entropy work on this corpus. At 11,135 tokens across 591 sign types the table of sign pairs is 0.84 per cent occupied, 2,919 filled cells out of 349,281. In that regime the naive maximum-likelihood estimator overstates dependency badly, and a figure quoted without correction cannot be trusted.

Our figure is already a margin over a permutation control computed with the same estimator, which cancels most of that bias because the control shares the sample size, alphabet and marginal frequencies. It does not cancel it exactly. So the same quantity was recomputed under three published bias-corrected estimators, each applied to the observed data and to the control alike.

Correction moves the result upward, not downward. The excess rises from 1.033 to 1.677 bits as the correction gets stronger, because the correction reduces the control far more than it reduces the observed data. The shuffled corpus is dominated by sign pairs seen once, which is exactly the situation these estimators exist to fix. The uncorrected figure we publish is therefore the conservative one, and every estimator tested puts the interval clear of zero.

What was left when we looked again

Withdrawing a result is not the same as showing there is nothing there. The original test asked one broad question (do a dozen induced categories arrange themselves in order?) and spent all its evidence on it. Three narrower tests were run afterwards on the deduplicated corpus, each able to fail independently.

The categories are more stable under resampling than chance, but not by much. Compressing 591 signs into a dozen categories costs nothing measurable on unseen text. The interval crosses zero, so the honest reading is no detectable loss, not an improvement.

The third test held up at first. The signs that open inscriptions and those that close them differ in the company they keep, and not merely in where they sit: the comparison uses each sign's neighbours with position information removed. Twenty-one openers and forty-eight closers form two distributionally distinct groups at z = 6.02.

It does not survive the harder duplicate control. Collapsing near-identical inscriptions as well as exact ones takes it to z = 4.6 at edit distance one, and to z = 0.5 at edit distance two, which is nothing at all. We are leaving it here as a reported result rather than a claim: it may be real and merely under-powered once the corpus is cut to genuinely independent inscriptions, or it may be another artifact of repeated seals. On this corpus we cannot tell.

VWhat This Settles

VIThe Picture and the Object

Every Indus seal carries an image, most often a one-horned bull, sometimes an elephant, a rhinoceros, a tree or a human figure, set above the row of signs. The natural reading is that the signs caption the picture. If so, the two channels must share information, and the image would become a weak bilingual: a known concept standing beside an unknown word.

The caption reading is not supported. Before deduplication the motif appears to carry substantial information about the signs; after repeated seal impressions are collapsed, almost all of it disappears. What remains does not clear the bar once the three channels tested here are accounted for. The picture and the text are, as far as this measurement goes, independent channels. Whatever the signs record, it is not a description of the animal above them.

The object itself is a different story. What a piece is, whether seal, tablet, tag or potsherd, genuinely conditions which signs appear on it, and survives deduplication comfortably. Text length tracks it too: seals average 5.06 signs, tablets 3.70, pottery 2.78. The corpus is not one uniform practice, and analyses that pool it are averaging over at least two.

Whether it could be a list of names

A standing objection to the whole enterprise is that these are ownership marks, personal names, lineages and titles, rather than text. That hypothesis makes a sharp prediction. A corpus of one-off identifiers never settles down: every new object introduces new signs, and the vocabulary grows about as fast as the corpus itself. Reused language does the opposite, because a finite lexicon is being drawn on repeatedly.

Indus sits at 0.488, against 0.415 for matched English prose. Vocabulary growth is slightly faster, consistent with more one-off signs, but nowhere near the behaviour of a list of unique identifiers. The sign inventory is genuinely reused. Whatever the signs are, they are drawn from a working vocabulary rather than minted per object, and the pure name-list reading has to account for that.

VIIHow Close Is This To A Decipherment

Reading an unknown script is not one problem but a sequence of them, and the later ones are far harder than the earlier ones. Setting them out in order makes it possible to say where this work actually sits, and where the field sits, without either being flattered.

5 of 11 rungs cleared here, one partial, which is roughly 50% of the way up. That figure should be read with care. The rungs are not equal in size, and the remaining ones are much larger than the ones already climbed.

VIIIWhat Is New Here, And What Is Not

A structural analysis of this corpus published in 2026 by Ashish Nair, How Non-Linguistic Is the Indus Sign System? A Synthetic-Baseline Scorecard (arXiv:2604.17828), works from the same underlying digitisation and computes several of the same quantities. Anything here has to be read against it, so the overlap is set out first rather than left for a reader to find.

Independently replicated

These were computed here before that paper was read, from different sign identifiers and separate code. The agreement is close enough to be worth stating plainly.

Extends existing work

The duplicate-structure problem was identified in that paper at the level of exact repeats. Here it is carried further: inscriptions differing by one or two sign edits are also not independent observations, which takes 1,902 distinct sequences down to 1,141 and then 558, and every headline measure is reported at all three levels. Separately, the bias-correction result in section IV appears to run against expectation, since correcting a null-referenced statistic increases the margin rather than shrinking it.

Not previously attempted, as far as we can establish

No dispersion measure appears to have been applied to this corpus. We applied one, asking whether signs divide into a frequent evenly-spread class and a rare bursty class, which is how function words separate from content words in every natural language. They do not. The apparent split is 94 per cent explained by frequency alone, and once each sign is compared against a null matched to its own frequency, not one of 153 signs survives correction. This is a negative result and it is the clearest thing in this work that nobody had checked.

Withdrawn

Five results looked strong and did not survive their own controls: a twelve-category induced grammar, a claim that those categories recovered most of the script's predictability, a correlation between the picture on a seal and the signs above it, the closed-class split above, and a distinction between opening and closing sign classes. Each is described where it arose. None is claimed.

IXMethods

The implementation is not published. The protocol is, in enough detail to be attacked.

Corpus

2,536 inscriptions from the published digitisation of the Corpus of Indus Seals and Inscriptions: 11,135 sign tokens, 591 sign types, mean length 4.39, ten sites. Analysis runs on the deduplicated set unless stated. Object type, material and iconographic motif are carried as covariates. No reconstructed or generated text is used anywhere.

Statistics and controls

Every quantity is reported as a margin over a matched null, never as a raw value. Two nulls are used: a global shuffle preserving sign frequencies and length distribution, and a within-inscription shuffle preserving which signs co-occur while destroying their order. The difference between the two isolates ordering from co-occurrence. Nulls run at 1,000 to 5,000 iterations. Significance is a z-score against the null distribution.

Estimator bias

At 0.84 per cent occupancy of the sign-pair table, maximum-likelihood entropy is strongly upward-biased. Referencing every statistic to a null computed with the same estimator removes that bias to first order. Because it does not remove it exactly, the principal result is also reported under Miller-Madow, Chao-Shen and Chao-Wang-Jost corrections.

Independence

Seals were copied, so inscriptions are not independent draws. Results are recomputed after collapsing exact duplicates and then near-duplicates at edit distance one and two, and separately at Mohenjo-daro and Harappa. Intervals come from subsampling inscriptions without replacement; resampling with replacement reintroduces the duplicate structure the analysis exists to control for, and produces intervals that do not bracket their own estimate.

Comparison corpora

Controls are matched to the Indus corpus on text count, length distribution, token count and vocabulary size, then run through the identical procedure. Four arms are used: natural language, a modelled administrative-record system, a modelled ownership-mark system, and randomly ordered signs. The random arm returning approximately zero on every measure is the calibration check.

Discipline

Findings are put to an adversarial review instructed to refute rather than confirm them, and any result that fails deduplication, per-site replication or a matched null is withdrawn and recorded rather than removed. Where a hypothesis is generated and tested automatically, it is registered with its predicted direction before the test runs, and significance is judged against a false-discovery threshold recomputed over every test performed.

Availability

Corpus provenance is public and named above, so the inputs are independently obtainable. Researchers wishing to compare results against their own measurements, or to see the figures behind any table here, are welcome to make contact.