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Bibliographic Details
Main Author:	Bénard, J_T
Format:	Recurso digital
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Published:	Zenodo 2026
Online Access:	https://doi.org/10.5281/zenodo.19081422
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<h1>Abstract</h1> The Warburg effect — aerobic glycolysis in cancer cells despite oxygen availability — has been documented since 1927 and remains without a unified mechanistic explanation after a century of research. We propose that this phenotype is not a metabolic accident but an algebraic necessity: the obligatory consequence of a symmetry-breaking event in the Z₃ rotational group of the F₀F₁-ATP synthase. Within the T144 algebraic framework, normal oxidative phosphorylation corresponds to the F₀F₁ rotary motor operating in conformational state k = 1 (mod 3) — Z₃ conformity. Any perturbation displacing the motor to k ≠ 1 (mod 3) — Z₃ non-conformity — structurally precludes net ATP synthesis via OXPHOS. Glycolysis is the only available alternative. The Warburg phenotype follows by algebraic necessity, independently of the specific mechanism producing the perturbation. This result, derived from the T144 framework established in Papers 1–13, provides the first formal, mechanism-independent explanation of the Warburg effect. It unifies all known Warburg drivers — IF1 overexpression, oligomycin, hypoxia, mtDNA mutations, FBP accumulation — under a single algebraic descriptor: k ≠ 1 (mod 3). As a corollary of this central result, we resolve the fifteen-year Cuezva–Sgarbi controversy on the role of IF1 in cancer metabolism. We demonstrate that both experimental programs are correct and address orthogonal modes of F₀F₁: Cuezva demonstrates Z₃ non-conformity via IF1-driven hydrolytic reversal (k = 2); Sgarbi demonstrates IF1 inactivity in synthetic mode (k = 1) under normoxia — an orthogonal and equally valid observation. The apparent contradiction dissolves when k is introduced as the discriminating invariant.

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