The computational processes of natural human language (CHL) form a physical object. The first axiom of matrix syntax (MS), which investigates linguistic structures on the complex plane using quantum mechanics-based mathematical tools, converts the [±N] and [±V] values of the Chomsky matrix to [±1] and [±i]. This study analyzes the potential developments of this axiom, which has been used previously for raising examples and to describe the grammaticality algebraically. Matrix calculations were performed on elaborate geometries of grammatical and ungrammatical raising examples. Standard analysis based on the minimal computation (MC) principle of the minimalist program (MP) is on the correct track, but it can be combined with mathematical analysis to answer a fundamental question: Why does the internal merge create argument chains (A-chains) in this way, and not in other logically possible ways? With the context-sensitivity hypothesis in MP, MS provides a new perspective on A-chains. Results indicate that a chain-forming geometry contains three areas with distinct growth factors: 1) occurrences (i.e., syntactic contexts of chain members) with a constant rate; 2) backbone-structure building with an exponential rate (i.e., larger φ ~ 1.618), and 3) superposed chain-member copies with a diminishing rate (i.e., little φ ~ -0.618 or σ1 = 0.7071). The MP-MS collaboration is a viable approach to the structure-building dynamics of CHL and approaches linguistic physics.
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