Sheng Lu

Superposition State of the Continuum: External Countability and Internal Uncountability of the Cauchy Reals Rc in the Effective Topos

We do not claim that ℝ is countable in ZFC.In the Effective Topos (Eff), the Cauchy reals ℝc simultaneously admit two readings: externally, the global-section set satisfies |Γ(ℝc)| = ℵ₀ (countability); internally, in the Mitchell–Bénabou language, ⊨ ¬∃f : N → ℝ_c surjective (unco...

The Reals Are Countable: ZFC as a Special Case of the Effective Topos

This paper argues that ZFC can be viewed as a special case of the Effective Topos (Eff), providing a novel interpretation of the countability of the reals..We do not claim that ℝ is countable in ZFC.In the Effective Topos (Eff), the Cauchy reals ℝc simultaneously admit two readin...

Real Numbers Are Countably Infinite: The Fatal Defects of Cantor's Diagonal Argument and the Constructive Complexity Alternative

Cantor's diagonal argument is widely regarded as the definitive proof that the real numbers are uncountable. Within the framework of Bu Theory, this paper identifies three fatal defects: (1) conflating computability boundary with set-theoretic cardinality; (2) ignoring the legiti...

Parameter-Free Derivation of CKM Mixing Angles from Cayley-Dickson Topology and Möbius Fiber Spectrum

This paper constructs a canonical isomorphism between the Laplace spectrum on a Möbius fiber and the Cayley-Dickson nilpotent decomposition, proving that CKM matrix elements are topological invariants—specifically cross-ratios on the Fano plane—under this isomorphism. As a coroll...

Fiber Singularity Theory A Unified Framework of Fractal Geometry, Quantum Chaos, and Riemann ζ Zeros

Classical mathematics treats singularities (poles, essential singularities, discontinuities, non-differentiable points) as signs of theoretical failure. However, physical systems—from turbulence and black holes to quantum energy levels—frequently exhibit such structures, suggesti...

Fiber Singularity Theory A Unified Framework of Fractal Geometry, Quantum Chaos, and Riemann ζ Zeros

Classical mathematics treats singularities (poles, essential singularities, discontinuities, non-differentiable points) as signs of theoretical failure. However, physical systems—from turbulence and black holes to quantum energy levels—frequently exhibit such structures, suggesti...

Non-orientable Möbius Algebra and the Computable Origin of the Standard Model

Starting from the intuition that a Möbius strip has "one side marked 0 and the other marked 1," this paper sews zero and infinity together along a meridian via 0 ≅ ∞, and explicitly relaxes four implicit assumptions on which Hurwitz's theorem relies — that zero is a global absorb...