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The aim is to prove Lehmer's Conjecture by establishing the Mahler measure as the minimum substrate expansion quantum in a defined lattice framework.

March 7, 2026Open Access

Lehmer's Conjecture: The Minimum Substrate Expansion Quantum

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The aim is to prove Lehmer's Conjecture by establishing the Mahler measure as the minimum substrate expansion quantum in a defined lattice framework.
Derivation within the Cymatic K-Space Mechanics framework.
Analysis of cyclotomic and non-cyclotomic polynomials' Mahler measures.
Quantification of expansion rates using modular closure constraints.
Examination of the implications of empirical falsification based on LIGO phase-error results.
Lehmer's polynomial reaches a Mahler measure of approximately 1.176280, confirmed as the minimum for non-cyclotomic polynomials.
Cyclotomic polynomials are shown to have a Mahler measure of 1, indicating pure rotation.
Minimum expansion rates constrained by W=32 and bilateral parity conditions.
Mathematical derivation of M_min as (φ^(1/5))^2, establishing topological necessity.

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Proves Lehmer's conjecture, demonstrating a minimum expansion quantum in quantum physics, suggesting significant implications.

Geoffrey Howland (2026) studied this question.

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