The study presents a system-level extension of the Equidistant Letter Sequence (ELS) protocol in the Torah [1], using a strict a priori framework that eliminates researcher degrees of freedom. The starting point is a prior finding, according to which the word “Torah” appears at a fixed skip of 49 letters from two central anchor points, with an extremely small random probability (~1 in 1.41 billion, before multiple testing corrections).
The current study examines whether this phenomenon is merely local or part of a broader structure. To this end, the exact same parameters are preserved (anchor positions, target word, and skip range), and a comprehensive count of ELS occurrences is performed across the entire Torah text (304,805 letters).
The results reveal four statistically notable, text-wide patterns, including exact counts (such as 50, 32, and 1,000 occurrences) that consistently emerge from the same constrained framework. This structure appears as a coherent system that recurs both at the local level and across the entire text.
To evaluate statistical significance, hundreds of millions of Monte Carlo simulations were conducted while preserving letter frequencies. The result: a probability of approximately 1 in 4.8 million for obtaining the observed system-level structure by chance. When combined with the base finding, the overall rarity reaches a scale of quadrillions (≈1 in 10¹⁵–10¹⁶).
The central conclusion is that the observed pattern does not behave as a localized phenomenon, but rather as evidence of a broader, consistent, constraint-driven structure operating across the entire text. Accordingly, the study proposes a fundamental shift—from analyzing isolated skip patterns to examining integrated structural systems—providing a new methodological framework for further exploration of complex textual patterns.
[1] https://www.thefirstverse.com/he/research/els-root-protocol-study