A method of identifying allographs in undeciphered scripts and its application to the Indus Valley Script

The study investigates how to systematically determine the true number of distinct signs in an undeciphered script by grouping together variants that represent the same grapheme (allographs). The context is the Indus Valley Script (IVS), for which prior sign lists range widely (417–694 signs) and exhibit substantial visual variation due to diverse media and techniques. A key research question is whether many visually distinct signs—especially asymmetric signs and their mirrored counterparts—are redundant allographs and whether mirroring denotes direction of writing rather than a semantic or phonetic difference. The purpose is to create a replicable, data-driven grouping framework, moving beyond purely visual, ad hoc judgments. Establishing accurate sign counts and reading direction is critical for future decipherment and linguistic analysis.

Prior compilations and analyses include Mahadevan (1977) with 417 signs, and Wells (2015) with 694 signs, with many singletons in each list. Scholars often assumed a consistent right-to-left reading direction and treated many visual variants as distinct. Daniels and Bright (1996) noted higher frequencies for symmetric signs compared to asymmetric ones. Wells (1998, 2011, 2015) distinguished mirrored sign variants and provided statistical analyses of certain symbols, sometimes arguing for grammatical roles of mirroring. Fuls (2013) conducted positional analyses. Broader computational and statistical approaches to the IVS include entropy and n-gram studies (Rao et al., 2009a,b; Yadav et al., 2010), while earlier epigraphic and archaeological syntheses were provided by Parpola (1986, 1994) and others. Despite numerous decipherment attempts, a systematic, explicit method for grouping allographs has been lacking.

Data sources comprised the Interactive Corpus of Indus Texts (ICIT) online database (Wells and Fuls, 2017) and the Corpus of Indus Seals and Inscriptions (CISI) volumes (Joshi and Parpola, 1987; Shah and Parpola, 1991; Parpola et al., 2010). The authors curated a dataset by cross-verifying ICIT entries with CISI and focusing only on signs attested in CISI. Each seal/tablet instance was documented in a MongoDB database with fields: CISI ID, sign number, sign location/position in sequence, co-occurring signs, inscription length, and a multi-line flag. MongoDB enabled flexible correlations and frequency tabulations via queries. The analysis emphasized asymmetric signs and their mirrored counterparts. Mirrored occurrences were categorized into deliberate (Type 1: reversed sequences; Type 2: multiple mirrored signs on the same artifact; Type 3: space-saving on crowded seals; Type 4: boustrophedon; Type 5: underlying grammatical meaning for a limited subset) and accidental (Type 6: database notation errors; Type 7: location anomalies; Type 8: carving errors or style changes over time). The team inspected artifacts case-by-case, cross-checking ICIT claims against CISI images or drawings, and assessed sign positions (initial/medial/final), paired sequences, and artifact context (e.g., material, crowdedness, damage). Probabilistic arguments were used to show the implausibility of coincident multiple mirrored signs on the same artifact if mirroring carried independent meaning (e.g., joint probabilities ~10^-8). Boustrophedonic layout was identified when alternate lines reversed direction. The authors then articulated six general reasons for grouping signs as allographs: (1) space-constrained deformation/squishing; (2) mirroring without meaning; (3) occurrence in the same short sequences with only tiny visual differences; (4) location anomalies suggesting directionality rather than distinct graphemes; (5) incorrect sign notations in databases or carving errors; and (6) high visual similarity with variants occurring only once. These reasons were applied to propose merges across 50 sign pairs (23 mirrored, 27 non-mirrored), reducing the sign list.

- Identified 23 pairs of mirrored asymmetric signs in the IVS. Across these, original signs occurred 1,659 times versus 110 occurrences for mirrored forms (~6.7%), indicating mirroring is rare and typically not semantically distinct. - Classified mirroring causes: most mirrored instances fall into non-grammatical categories (Types 1–4 deliberate direction/layout and 6–8 accidental/data or carving issues). Only a subset of a specific mirrored pair category (Type 5) may function as a grammatical marker (as previously suggested by Wells). - Demonstrated multi-directionality of the IVS: mirrored signs can indicate reversed reading direction, crowded layouts, or boustrophedon. Numerous case studies (e.g., K-6, M-599/600, H-278–H-284 sequences) support this. - Showed many supposed mirrors are database errors or carving anomalies upon CISI inspection; several are location anomalies where a form appears only at a distant site with very low frequency. - Using six explicit reasons for grouping, the authors propose merging 50 pairs of signs (23 mirrored and 27 non-mirrored) as allographs, substantially reducing the sign inventory compared to Wells (2015). This reduces singletons and the overall search space for phonetic assignment. - Provided sequence-based evidence that tiny visual variations often co-occur in the same short sequences and positions, making it unlikely they encode distinct grammatical categories. - Quantified improbabilities of multiple mirrored signs co-occurring by chance on the same artifact (examples on the order of 10^-8), arguing these reflect directionality/layout rather than new graphemes.

The findings address the central questions of sign count, allography, and directionality in the IVS. The rarity and contextual patterns of mirrored signs, combined with positional and sequence analyses, indicate that mirroring typically reflects direction of writing, layout constraints, or accidental factors, not distinct graphemes. This supports the conclusion that the IVS is multi-directional, including right-to-left, left-to-right, and boustrophedon arrangements. By offering explicit, checkable criteria for merging visually similar forms, the study provides a reproducible framework that reduces subjective judgments. The reduction of 50 redundant signs meaningfully shrinks the hypothesis space for phonetic assignment and statistical modeling. The authors also caution that mirrored instances arising from Types 1–4 and 6–8 should be excluded from grammatical/statistical analyses, whereas only limited Type 5 cases might bear grammatical significance. Overall, the approach advances a more coherent and parsimonious sign inventory, improving the foundations for future decipherment efforts.

The study introduces a systematic, data-driven methodology to detect allographs and reduce redundancies in undeciphered scripts, applied here to the Indus Valley Script. Through positional, frequency, and contextual analyses, 50 sign pairs (23 mirrored, 27 non-mirrored) are identified as redundant, substantially reducing the sign list derived from Wells (2015). The evidence indicates the IVS is multi-directional and that most mirroring denotes writing direction or layout, not different meanings. This reduction simplifies subsequent decipherment tasks by narrowing the space of phonetic assignments. Future work could extend the methodology to additional anomaly classes and incorporate richer metadata: artifact context and provenance, diachronic usage patterns, object types (e.g., seals vs. tablets), and cross-script comparisons. Integrating advanced image analysis and machine learning with curated epigraphic checks may further refine sign groupings and illuminate sign functions.

- The grouping framework, while explicit, is not fool-proof; additional valid reasons for grouping may exist, and some judgments rely on expert inspection of often damaged or crowded artifacts. - Dependence on ICIT and CISI introduces risks of cataloging or transcription errors; several corrections were necessary, and not all artifacts have high-quality images. - Some conclusions rest on small sample sizes or single occurrences (singletons), increasing uncertainty. - Analyses were limited to signs found in CISI; generalizability to material outside these volumes is untested. - Directionality assessments can be ambiguous on fragmentary sherds or atypical artifact forms (e.g., triangular tablets), and some probability estimates assume independence approximations.