Introduction: The Parameters of the Omnilexical Challenge
The inquiry presented posits a theoretical optimization problem at the extreme edge of computational linguistics and creative philology: the construction of a complete and coherent narrative detailing the history of the English language, utilizing every known word in the language (encompassing all dialects and colloquialisms) with a strict frequency floor of one and a ceiling of one hundred occurrences. This report offers a comprehensive analysis of this "Omnilexical Constraint," dissecting the interplay between vocabulary magnitude, syntactic probability, and the mathematical limitations of coherent narrative structures.
To answer "how many words it would take," one cannot simply sum the dictionary. One must solve for the structural "glue" required to bind a hyper-diverse lexicon into a legible story without violating the severe frequency restrictions imposed on the language’s most essential tools—its function words. The central conflict of this undertaking is the tension between the Zipfian distribution natural to English (where a tiny fraction of words accounts for the majority of usage) and the Uniform distribution imposed by the constraints (where high-frequency determiners and prepositions are capped, forcing a reliance on rare dialectal and archaic vocabulary).
This analysis proceeds in three phases: first, establishing the magnitude of the "known" lexicon (V) by integrating standard, archaic, dialectal, and technical vocabularies; second, modeling the "Function Word Bottleneck" that arises from the frequency constraint; and third, proposing a "Poly-Dialectal Syntactic Scaffold" that resolves these tensions, leading to a definitive word count estimate.
