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| Natura: | Recurso digital |
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Zenodo
2026
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| Accesso online: | https://doi.org/10.5281/zenodo.19242276 |
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Sommario:
- <p>This note establishes a structural overdetermination of the product flag manifold Fl₁,₂(ℂ³) × ℂP¹ from three independent physical requirements: gauge structure (irreducible weight lattice), fermion generations (Euler characteristic χ ≡ 0 mod 3), and Einstein gravity (Bochner-flat Marsden–Weinstein quotient).</p> <p>Working within the standard class of compact Kähler manifolds of complex dimension 4 with effective torus action, we show that any two of these three conditions are sufficient to determine the manifold uniquely. The third condition then follows as a prediction. This yields a consistency triangle in which gauge structure predicts gravity, gravity predicts generations, and generations predict gauge structure.</p> <p>The result provides a structural analogue of parameter-free prediction: independent physical sectors constrain the same geometric object from different directions, eliminating the need for tuning. The Bochner-flatness underlying Einstein dynamics is shown to follow from the same conditions that fix the gauge and generational structure, unifying these sectors at the level of manifold selection.</p> <p>This note complements prior work on polynomial truncation and Kähler reduction by identifying a consistency structure that links the emergence of physical law across regimes.</p>