The Alphabet as a Sequence Engine: A Census of What Letter Names Generate, and What the OEIS Has Never Seen
Year: 2026
Type: article
Abstract: We evaluate integer sequences generated across 36 human writing systems under the Engineering of Alphabets (EOA) operator. By auditing all 1,056 letter-sequences against the On-Line Encyclopedia of Integer Sequences (OEIS), we establish a cross-script census of recursive growth. Our analysis identifies 402 distinct sequences: 14 match classical mathematical identities (verified term-for-term against the OEIS), while 388 appear in no current catalogue despite satisfying explicit integer linear recurrences. Random-baseline controls confirm these results are statistically significant: random alphabets of matched size never form the compact name-graph cores observed in natural scripts (0 of 250 simulations), and the unique spectral properties of the English E5 encoding do not occur by chance (0 of 100 simulations). The Crown Jewels: Exact Cross-Script Algebraic Invariants Our census reveals that natural letter-naming graphs systematically collapse into small, strongly connected cores (2 × 2 to 4 × 4 matrices), generating a set of stable algebraic constants that recur across historically independent writing lineages: The Golden Ratio Squared (φ² ≈ 2.618034): Defined by x² − 3x + 1. This constant emerges as a dominant growth factor across Ge’ez, Thai, Hebrew, Phoenician, and Japanese-pronounced Latin, generating Fibonacci bisections (A001906), odd Fibonacci numbers (A001519), and odd-index Lucas numbers (A002878). The Silver Ratio (1 + √2 ≈ 2.414214): Defined by x² − 2x − 1. Dominant in Arabic and Osmanya, generating Pell-family sequences (A048739 and A094723). Silver-Square Recurrence (2 + √2 ≈ 3.414214): Defined by x² − 4x + 2. Dominant in Burmese, Aramaic, and Syriac, generating the silver-square recurrence (A007070). Summary Census Breakdown Total Letter Rows: 1,056 Total Distinct Sequences: 402 OEIS-Catalogued Unique Sequences: 14 (verified identities, including the families above and basic sequences like powers of two). Uncatalogued Unique Sequences: 388 (satisfied by explicit linear recurrences but absent from all catalogs). These uncatalogued sequences concentrate in high-degree scripts (English E5, Greek, Gothic, Runic, Ogham, Glagolitic). Full census data, incidence matrices, and verification scripts are included in this release bundle.
Author: Budargham, Bahaa
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223894772