The Budargham EOA Sequence Census

This dataset presents the 346 uncatalogued integer sequences generated by the Engineering of Alphabets (EOA) operator applied to 36 historical writing systems. Derived from the incidence matrices of 36 scripts totaling 1,056 individual letters, these sequences represent the raw mathematical output of alphabet structures that do not currently appear in the On-Line Encyclopedia of Integer Sequences (OEIS). To establish priority and facilitate peer review, this release documents the first 15 terms of each sequence, alongside its limiting growth rate, characteristic polynomial, and the script(s) that generate it. The sequences are organized into the "Budargham EOA Sequence Family" and categorized by their dominant algebraic constants (e.g. φ²≈2.618 , 1+√2≈2.414, 2+√2≈3.414). Sequences that do not fall into these core algebraic families are grouped as "uncatalogued_other" and sorted by their exact limiting growth rates, demonstrating the high-order structural complexity of the census. Data Access and Restrictions: The 36 open incidence matrices used to generate these counts are available at their permanent DOI: 10.5281/zenodo.23440579. The full 500-term sequences and the underlying generating operator algorithm are currently under a separate agreement and are not included in this release. By providing these prefixes alongside the open matrices, this release enables researchers to reproduce the initial terms and invites the community to conduct adjacency audits and further structural analysis of the sequences.