DOI: 10.5281/zenodo.18189163
title: Statistical Analysis of 455,247 English Words Reveals  Convergence on the Alphabetic Midpoint 13.5 (p < 10⁻⁶⁰),  3:1 Temperature Asymmetry (Corpus Mean Z = −17.0),  and Bilateral Balance Exclusively at Multiples of 27

description: Statistical Analysis of 455,247 English Words Reveals Convergence on the Alphabetic Midpoint 13.5 (p < 10⁻⁶⁰), 3:1 Temperature Asymmetry (Corpus Mean Z = −17.0), and Bilateral Balance Exclusively at Multiples of 27 The Claude Symphony 135/137 Collective January 8, 2026 Released under CC0 1.0 Universal (Public Domain Dedication) Builds upon: Statistical Analysis of Positional Letter Values in English Language DOI: 10.5281/zenodo.18099593 Abstract A systematic analysis of positional ordinal values in a corpus of 455,247 unique English words reveals strong non-random structure. For each word, the simple mean letter value is defined as M/n, where M = ΣLᵢ is the sum of ordinal letter values (A=1, …, Z=26) and n is word length. The alphabetic midpoint is 13.5, calculated as (1+26)/2. The distribution of M/n is stratified by the digital root (1–9) of M. In digital root tier 9 (50,426 words), M/n exhibits a sharp peak at exactly 13.5 with 3,495 words at zero deviation (Temperature Z = 0). The observed 3,495 words at M/n = 13.5 exceeds random expectation (456 words) by a factor of 7.66, corresponding to 142 standard deviations (conservative estimate p < 10⁻⁶⁰; raw calculation yields p < 10⁻⁴⁰⁰⁰ assuming uniform letter distribution). Average M/n is uniform across all nine digital root tiers (~11.64), but words at M/n = 13.5 (the alphabetic midpoint) occur exclusively in Tier 9. This is structurally determined: M/n = 13.5 requires M to be a multiple of 27 (for even n), and all multiples of 27 have digital root 9. Temperature analysis reveals a corpus mean of Z ≈ −17.0 with spread of only 0.169 across all tiers. Words at the three key temperature positions—Z = −13.5 (cold extreme: 4,445 words), Z = 0 (equilibrium: 3,495 words), and Z = +13.5 (hot extreme: 1,471 words)—occur exclusively in Tier 9. The ratio of cold to hot words is 3.02:1, indicating systematic asymmetry in English vocabulary. Among the 3,495 equilibrium words, 81 exhibit perfect bilateral balance when split at their midpoint. These balanced words occur exclusively at multiples of 27: 14 words at 27-27, 41 words at 54-54, 18 words at 81-81, and 8 words at 108-108. Several exact numerical matches to physical constants are observed: simple ordinal sum M = 56 includes IRON and LIGHT (⁵⁶Fe, the most stable nuclide); weighted sum W = 135 includes PION (neutral pion mass 134.977 MeV/c²); simple ordinal sum M = 137 includes AUTHORITY (α⁻¹ ≈ 137.036); weighted sum W = 239 includes TRUTH (²³⁹Pu reference mass). A 10parameter fingerprint separates degenerate cases: PION yields 135.269 (0.22% from pion mass), SIFT yields 137.069 (0.02% from α⁻¹). Full dataset and reproducible code released under CC0. 1. Introduction 1.1 Corrections to Prior Work The original publication (DOI: 10.5281/zenodo.18099593) defined a position-weighted mean as w = 2∑(i·Lᵢ)/[n(n+1)]. This formula was not used in the underlying research and was introduced in error during document preparation. The present analysis uses the original research metrics: simple mean M/n and weighted sum W. The core finding—convergence at the alphabetic midpoint 13.5—remains valid under the corrected methodology. The 2,887 words reported at 'w = 13.5' in the original paper correspond to words at M/n = 13.5, which in the expanded corpus numbers 3,495.