maxPhonemes
plain-language theorem explainer
The definition sets the upper bound on natural language phoneme inventories at 45, matching the orbit count from the gap-45 construction. Linguists studying universal grammar constraints or empirical phoneme distributions would cite this constant. It is introduced by direct assignment to the numerical value fixed upstream in the gap derivation.
Claim. The maximum phoneme inventory size is defined to be $45$, where this value is the orbit count arising from the gap-45 structure.
background
The module develops bounds on phoneme inventories drawn from Recognition Science. It records that the cube of the two-element field forces a vertex count of 8, an edge count of 12, and an orbit count of 45. This produces a minimum inventory of 8 phonemes and a maximum of 45. Upstream, the gap definition from Gap45.Derivation is the product of closure and Fibonacci factors, and its main theorem asserts that the gap equals 45.
proof idea
This is a direct definition that assigns the constant 45 to the maximum phoneme count, drawing on the established result that the gap equals 45.
why it matters
This supplies the upper endpoint used in the band theorems and the certification structure that records the minimum less than the maximum, the minimum equal to 8, and the maximum equal to 45. It connects the linguistic bound to the orbit count of 45 from the Q3 structure. The module documentation further links it to a Zipf exponent in the empirical interval (0.45, 0.52).
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