Chetansing Rajput

The Pythagorean Angle Lattice: A Unified Framework Connecting Geometry, Number Theory, and the Langlands Program

A single lattice built from primitive Pythagorean triples and Gaussian integers unifies metallic means, an Omni-Metallic Euler constant, explicit S₃ and holomorph Galois extensions of ℚ(i), closed geodesics on the modular surface, and Maass/Bianchi forms in one geometric-arithmet...

The Pythagorean Angle Lattice: Geometry, Algebra, and Hyperbolic Correspondence

A lattice built from the angles of primitive Pythagorean triples systematically generates algebraic, logarithmic and transcendental constants while revealing an S₃-Galois extension and a precise correspondence with closed geodesics on the modular surface : We study the Pythagorea...

The Pythagorean Angle Lattice: Arithmetic Structures and Spectral Geometry A Synthesis of the Omni-Metallic Framework, Non-Abelian Character Invariants, and the Geometry of Integer Triangles

A self-contained arithmetic–geometric framework linking primitive Pythagorean triples to zeta values, modular geodesics, and a conjectural cancellation of non-abelian Artin characters. We present a complete, self-contained unification of the Pythagorean Angle Lattice L and the Om...

Pi from the Pythagorean Angle Lattice: A Direct Geometric Sieve from Integer Right Triangles

π is recovered as the ratio of two full rotations (720°) to a universal constant that emerges from the asymptotic angles of primitive Pythagorean triples. We present a rigorous derivation of the constant π strictly from the geometry of primitive Pythagorean triples. By ordering t...

Pi from the Pythagorean Angle Lattice: A Direct Geometric Sieve from Integer Right Triangles

π is recovered as the ratio of two full rotations (720°) to a universal constant that emerges from the asymptotic angles of primitive Pythagorean triples. We present a rigorous derivation of the constant π strictly from the geometry of primitive Pythagorean triples. By ordering t...

The Pythagorean Angle Lattice: Arithmetic Structures and Spectral Geometry A Synthesis of the Omni-Metallic Framework, Non-Abelian Character Invariants, and the Geometry of Integer Triangles

A self-contained arithmetic–geometric framework linking primitive Pythagorean triples to zeta values, modular geodesics, and a conjectural cancellation of non-abelian Artin characters. We present a complete, self-contained unification of the Pythagorean Angle Lattice L and the Om...

The Pythagorean Angle Lattice: Angle Hierarchy and Spectral Structure

Every primitive Pythagorean triple generates an infinite angle-halving hierarchy that recovers the metallic means precisely when c−b equals 1, 2 or 8, and naturally produces a convergent spectral zeta function. We study the Pythagorean Angle Lattice, a countable set of real numbe...

The Pythagorean Angle Lattice: Angle Hierarchy and Spectral Structure

Every primitive Pythagorean triple generates an infinite angle-halving hierarchy that recovers the metallic means precisely when c−b equals 1, 2 or 8, and naturally produces a convergent spectral zeta function. We study the Pythagorean Angle Lattice, a countable set of real numbe...