Deciphering ancient scripts begins with identifying the unique signs. This process of grouping sign variations representing the same concept is often implicit in research, lacking systematic analysis. The Indus Valley Script presents a particularly challenging case, with estimates of its sign count ranging from 417 to 694. The script's diverse inscription methods (carving, chiseling, etc.) and materials (bone, ceramic, etc.) contribute to significant sign variations. Furthermore, the reading direction has been a point of contention, with most scholars assuming a right-to-left direction. This study aims to systematize the grouping of sign variations and investigate the writing direction of the Indus Valley Script by focusing on asymmetric signs and their mirrored counterparts. The large number of mirrored asymmetric signs is a unique feature of the Indus Valley Script, and their analysis is key to understanding the script's writing system and reducing the number of distinct signs.

Previous attempts to decipher the Indus Valley Script have numbered over 100, mostly assuming a consistent right-to-left reading direction and treating all sign variations as unique. Scholars like Mahadevan (1977) proposed a smaller sign list (417 signs), while others like Wells (2015) proposed a larger list (694 signs). The debate highlights the lack of a systematic approach to grouping similar signs. Wells (1998) acknowledged the existence of mirrored signs but treated them as distinct entities, differing from the approach of Mahadevan and other scholars. This work draws upon the large sign list compiled by Wells (2015) and leverages datasets such as the Interactive Corpus of Indus Text (ICIT) and the Corpus of Indus Seals and Inscriptions (CISI) to analyze sign frequencies and positions. Existing analyses by scholars like Fuls (2013) and Wells (2011, 2015) on positional analysis and statistical properties of specific symbols inform the current study.

The authors employed data mining techniques to analyze the positions of signs within inscriptions from various sources, including Mahadevan (1977), Parpola (1986, 1994), Wells (1998), and the CISI and ICIT datasets. A MongoDB database was created to store information about each seal, including its CISI ID, sign numbers, locations, other signs on the seal, seal length, and a multi-line flag. This database facilitated the analysis of sign frequencies and relationships. The analysis focused on asymmetric signs and their mirrored pairs. The study categorized mirrored signs into deliberate (types 1-5) and accidental (types 6-8) mirroring based on various factors, such as reversed sequences, space-saving measures, boustrophedonic writing (alternating writing directions), and potential underlying grammatical meaning. The authors carefully examined each instance of a mirrored sign to determine the underlying cause of mirroring. A detailed analysis was performed on 23 pairs of mirrored asymmetric signs, noting their frequencies, artifact IDs, and categorized types. The study then established six criteria for grouping similar signs: signs squished due to space constraints, mirrored signs without semantic meaning, signs found in identical sequences, location anomalies, incorrectly noted signs, and visually similar signs with infrequent variations. Applying these criteria led to the identification of 50 pairs of signs that could be merged. In addition to the criteria based on statistical properties, visual similarities of signs were considered alongside frequency analysis, including singletons and near singletons.

The study found at least 23 pairs of mirrored asymmetric signs in the Indus Valley Script. Analysis of these mirrored signs revealed that mirroring often indicates writing direction rather than a change in meaning. Five reasons for deliberate mirroring were identified, while accidental mirroring was attributed to factors such as data entry errors and carving inconsistencies. A statistical analysis, considering the positional information and context, revealed 50 pairs of signs that could be grouped together due to insignificant variations. These pairs included 23 mirrored and 27 non-mirrored pairs. This reduction significantly shrinks the number of unique signs. Several examples were presented illustrating how signs were modified due to space constraints or were incorrectly identified in the ICIT database. Location anomalies, where a particular sign variation was prevalent in a specific geographical area, were also considered in the grouping process. The analysis of sign sequences indicated that similar signs may have played grammatical roles. The researchers provided detailed explanations for each grouping, enhancing the robustness and verifiability of their findings. The study explicitly states the criteria used for grouping, thus making the results more objective than previous approaches.

The proposed method for identifying allographs contributes significantly to Indus script decipherment by reducing the number of unique signs. The reduction in the search space, from potentially 694 to a substantially smaller number, makes the task of assigning phonetic values more manageable. The findings of multi-directionality add a critical layer to our understanding of the Indus Valley Script, challenging previous assumptions about a solely right-to-left orientation. The detailed explanations provided for each sign grouping enhance transparency and reproducibility. While this study focused primarily on mirrored and visually similar signs, further analysis incorporating contextual information, temporal aspects, and cross-linguistic comparisons could yield additional insights into the script’s structure and meaning.

This research presents a novel, data-driven method for identifying allographs in undeciphered scripts, successfully reducing the number of candidate signs in the Indus Valley Script by grouping 50 sign pairs based on six defined criteria. This methodology enhances the prospects of future decipherment attempts. Future research could expand on this by integrating contextual information (location, time period, object type), and comparing Indus script with other contemporaneous writing systems.

The study relies heavily on the accuracy of existing datasets (ICIT, CISI). Errors or inconsistencies in these datasets could affect the analysis. While the authors provide detailed justifications for their groupings, some subjective judgments may be involved in classifying certain sign variations. The analysis focuses primarily on visual similarities and positional information, and further investigation incorporating semantic analysis and linguistic patterns would strengthen the findings.