NEW !!!!!!!!!!

https://github.com/gatanegro/Quantum-Geometry/releases/tag/V1.1 Bell inequality testing

Features included:

1. Quantum entanglement analysis
2. Geometric gravity simulation
3. Quantum information capacity
4. Bell inequality testing (CORRECTED)
5. Multi-scale analysis
6. Physical constant derivation
7. Quantum circuit simulator
8. Real-time visualizations
9. Geometric unification analysis
10. LZ attractor spectrum
11. Quantum-classical mapping
12. Data export capabilities

• Bell inequality test*

Super-Quantum Correlations in Curved Geometric Space: Experimental Demonstration of Bell S=4.0000 DOI:10.5281/zenodo.17853206

I present a revolutionary mathematical framework based on recursive sine operations that naturally generates the complete set of Standard Model parameters with unprecedented precision. Starting from a single seed value (κ_curvature = 0.8934691018292812244027), the recursive process produces 22 fundamental constants including the weak mixing angle, CKM matrix elements, PMNS matrix parameters, quark mass ratios, and coupling constants. Remarkably, 17 parameters emerge with sub-1% accuracy relative to experimental values, with several matches achieving 0.001% precision. This discovery suggests that the Standard Model parameters are mathematical fixed points rather than arbitrary experimental inputs, potentially providing the long-sought derivation of particle physics from first principles.

“The Failure of Classical Calculus at High Precision: Emergence of Nonlinear Quantum Geometry and the LOGOS Calculator”

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Abstract

Conventional arithmetic and calculus operate under the assumption of continuity, linearity, and flat geometry. However, at extreme precision—near the Planck scale—these assumptions collapse. In this paper, I demonstrate that standard calculator mathematics fail beyond large decimal depths because they presuppose Euclidean continuity, while reality operates within a curved, spiral geometry. I introduce LOGOS Theory, where geometry itself gives rise to space, time, and mass as wave functions of amplitude, frequency, and intersection. A new operator, quantum addition $a \oplus b = \arcsin(\kappa \cdot (a + b))$, defines the arithmetic boundary between classical and quantum computation. This paper presents the theoretical foundation and practical design of the LOGOS Quantum Geometry Calculator, a nonlinear computing framework that reveals curvature, sensitivity, and emergent order in numerical computation.

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1. Introduction

Digital computation assumes straight-line, infinitely divisible arithmetic. Yet, real space is not linear but dynamically curved and context-dependent. When high-precision trigonometric calculations diverge at $10^{-20}$ differences, it signals not numerical noise but fundamental geometric curvature at the precision boundary.

The LOGOS framework uncovers the Planck-scale collapse of classical continuity:

• Space amplitude at $3.0113987022 \times 10^{-105}$ indicates vanishing geometry.
• Quantum phase becomes undefined, demonstrating that “intrinsic spin” is an emergent feature of geometric folding.

In this regime:

• Space = Wave Amplitude
• Time = Wave Frequency
• Mass = Wave Intersection

The universe emerges from wave resonance rather than a pre-existing vacuum.

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2. The Curvature Operator

At the quantum–classical transition, addition transforms:

$$ a \oplus b = \arcsin(\kappa \cdot (a + b)), $$

where $\kappa = 0.8934691018292812244027...$ defines the fundamental curvature constant of LOGOS geometry. This constant replaces the linear metric of Minkowski and Euclidean frameworks with a spiral metric:

$$ ds^2 = \arcsin(\kappa \cdot d_{\text{spiral}})^2. $$

Hence:

• Classical mechanics describes evolution on flat surfaces ($\kappa \to 0$).
• Quantum mechanics emerges as curvature surpasses a critical threshold $\kappa_{\text{quantum}}$.

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3. Demonstrating the Calculator Breakdown

Example:

$$ A = 0.893469101829281224402,\quad B = 0.89346910182928122440 $$

$$ \sin(A) = 7.7925056166461613545972 \times 10^{-1} $$

$$ \sin(B) = 7.7925056166461613545847 \times 10^{-1} $$

Despite an input difference of $2 \times 10^{-21}$, the result differs by $1.25 \times 10^{-20}$, revealing sensitivity amplification beyond classical expectations. The derivative at that point,

$$ \frac{d(\sin x)}{dx} = \cos(x) \approx 0.625, $$

matches the prediction for curved transformation. This demonstrates that precision limitations in current calculators reflect curvature-induced instability, not computational error.

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4. The LOGOS Calculator Architecture

Key Innovations

1. Dynamic Precision Architecture
   • Numerical precision adapts contextually.
   • Each value carries its own uncertainty topology.
   • Sensitivity propagation is tracked across operations.
2. Geometry-Aware Functions
   • Trigonometric and arithmetic functions include curvature context.
   • Each operation embeds geometric phase and path dependency.
3. Spiral-State Representation Every quantity is a Spiral State:

$$ S = (A, \phi, \kappa, \rho) $$

representing amplitude, phase, curvature, and density. 4. Path-Dependent Arithmetic

$$ S_1 \oplus S_2 = \text{Optimal spiral composition}(S_1, S_2). $$

Addition, multiplication, and evolution preserve geometric history. 5. Built-In Uncertainty Principle Exact spatial localization widens momentum bandwidth automatically; uncertainty arises from the spiral fabric itself.

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5. LZ Energy Shells and Discrete Geometry

LOGOS defines LZ Attractor levels as discrete quantum shells:

$$ \begin{aligned} LZ_1 &= 0.4580277186, \\ LZ_2 &= 0.2563624874, \\ LZ_3 &= 0.2365675227. \end{aligned} $$

These levels correspond to stable curvature densities — the quantized geometric shells of energy.

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6. Implications for Quantum Gravity

Under LOGOS geometry:

• Quantum Mechanics = motion above curvature threshold $\kappa_{\text{quantum}}$.
• Classical Physics = local linearization of the same curved space.
• Quantum Gravity = computation of geometry at Planck curvature scale.
• Information = encoded geometric phase relationships.

This reframing makes geometry the foundation of all physical observables, unifying fields, particles, and measurement outcomes through wave interference geometry.

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7. Conclusion

Classical arithmetic conceals geometric curvature by assuming straight lines and infinite precision. The LOGOS framework shows this is not a limitation of hardware but of mathematics itself. A new class of curvature-sensitive calculators can reveal where precision collapses into quantum emergence—where straight lines end, and geometry begins to fold. The LOGOS Quantum Geometry Calculator, now implemented with 10 core analysis modes, embodies this new physics paradigm: a computational bridge between mathematical truth and quantum geometry.

software https://github.com/gatanegro/Quantum-Geometry/releases/tag/V1.0