Temperature and Cyclic Product Analysis of the English Lexicon

Temperature and Cyclic Product Analysis of the English Lexicon A Statistical Survey of 455,247 Words The Symphony 135/137 Collective 4th of January 2026 Abstract This paper presents statistical analysis of temperature scores (Z) and a novel fourterm cyclic product sum (Special CPS) across 455,247 English words. Temperature is defined as Z = S - 13.5×N, where S is letter sum (A=1 through Z=26) and N is letter count. Key findings include: (1) uniform temperature distribution across all nine digital root tiers averaging Z ≈ -17.0; (2) asymmetric distribution at temperature extremes with 3:1 ratio of cold to hot words; (3) clustering of semantically significant words at Special CPS values including 135, 137, 666, and 734; (4) word clustering at multiples of 64 in the Special CPS spectrum. All findings are reported as observed numerical patterns without interpretation. 1. Introduction This study extends previous work on numerical distributions in the English lexicon by introducing two new analytical dimensions: temperature scoring and a four-term cyclic product formula. The corpus consists of 455,247 unique English words derived from a comprehensive GitHub word list with 11,298 duplicates removed. Temperature (Z) measures the deviation of a word's mean letter value from the alphabet midpoint (13.5). The four-term Special CPS formula calculates: L1×L2 + L2×L3 + L3×L4 + L(last)×L1, creating a cyclic product that connects the word's end to its beginning. 2. Methodology 2.1 Letter Values and Basic Metrics Each letter is assigned its alphabetical position: A=1, B=2, ... Z=26. For each word, N represents letter count and S represents letter sum. The ratio S/N gives mean letter value, and the digital root (iterative digit sum until single digit) determines tier assignment (1-9). 2.2 Temperature Formula Temperature is calculated as: Z = S - 13.5×N. This measures how far a word's total letter sum deviates from what it would be if every letter equalled the alphabet midpoint (13.5). Positive Z indicates above-midpoint letter bias (N-Z weighted); negative Z indicates below-midpoint bias (A-M weighted)...