The Vurukuti Grid: Universal Integer Lattice & Senary Hardware Architecture (v1.0)

This paper introduces the Vurukuti Grid, a deterministic physics engine and discrete coordinate system designed to eliminate floating-point drift and non-deterministic errors. By treating space as a Packed Medium of discrete units starting at the Chinna Voxel (CV) at Index 0, the framework replaces continuous Cartesian abstractions with a strictly integer-based manifold. The core of the system is the Scale 2 Axiom (CS = 2), which provides a mathematical bridge between hexagonal reality and Cartesian perception. Key Innovations for Prior Art Declaration: The Chinna Scale (CS): Formally defined as CS = 2, this is the immutable geometric constant required to bridge hexagonal topology with Cartesian perception. By enforcing this constant, the system ensures all vertical register writes are strictly even integers (a = y 2), creating a hardware-level "Impossible State" for odd numbers and proving that the inverse mapping is always bijective and lossless. The Harmonic Multiplier (H): An integer multiplier (H 1) that serves as a universal resolution slider. It allows the user to scale angular resolution while maintaining 100% integer stability. As H approaches infinity, the discrete hexagonal lattice asymptotes to a perfect circle, allowing for "Rotation via Resolution" without irrational trigonometric approximations. The Vurukuti Kernel: A system and method for integer-only spatial mapping. The Forward Map converts Cartesian inputs into strictly even-integer registers (a = y (CS H) ), ensuring that the Inverse Map (y = a / (CS H) ) is always an exact integer division with zero remainder. Impossible State Defense: A proof of bijectivity asserting that odd-numbered vertical register states (e. g. , a = 3) are physically impossible within the kernel logic, rendering the mapping lossless and deterministic. Senary Architecture (Base-6 Hardware): A novel hardware logic proposing the "Senit" (Senary Digit) as the fundamental unit of computation. This architecture enables "Rotation as Permutation, " where spatial orientation is modified via simple register-shifting rather than trigonometric matrix multiplication. Topological Metric and Isotropic Light: Distance is defined strictly as Topological Graph Distance (Hop Count). The framework proves that the Speed of Light (c) is constant at 1 voxel/tick in all directions because the vertical zig-zag and horizontal composite paths both require exactly 2 discrete time steps to traverse a lattice unit. The Chinna Voxel (CV): A regular Rhombic Dodecahedron (3D) or Hexagon (2D) that defines the origin as 1 unit of physical volume (x⁰ = 1), regularizing the mathematical singularity of the dimensionless point. Licensing: The theoretical derivations and text are licensed under CC BY 4. 0. The Vurukuti Kernel algorithms, Senary Architecture specifications, and mathematical logic are released under the MIT License to ensure these fundamental geometric truths remain open for universal industrial adoption and cannot be blocked by proprietary patenting. Update (3 March 2026): Addendum I - The 4D Bimetric Register, Volumetric Mass, and the Hardware Engine of Spacetime This record now includes Addendum I, which expands the discrete, deterministic hardware framework into a 4D informational bulk. This addendum mechanically derives gravity, relativity, and quantum mechanics using strict integer logic, systematically eliminating reliance on floating-point drift and infinite densities. Key Innovations in Addendum I: The 4D Bimetric Register: Geometrically proves that a fabric bounded by two 3D faces (Observable and Mirror sectors) must fundamentally be 4-Dimensional. This framework equates the 4D thickness directly to the Causal Step (Δt), reducing time to a hardware routing operation. Black Holes as Double-Buffer Deadlocks: Redefines gravitational singularities as deterministic Hardware Buffer Overflows triggered when a coordinate reaches its Maximum Integer Capacity (Max). It completely prevents division-by-zero crashes. The 3. 11 Cosmological Expansion: Mechanically explains Dark Energy as a volume-to-surface scaling failure. As a black hole's locked internal volume scales cubically (r³), it cannot be cleared by its Event Horizon surface area (r²), forcing an unresolvable geometric pressure that laterally stretches the hyperelastic fabric. This hardware bottleneck yields the observed cosmological coupling constant of k ≈ 3. 11. The Amplituhedron Bridge (CS = 4): Decodes the abstract momentum-twistor space of the Amplituhedron (m = 4). It proves that navigating a 3D Rhombic Dodecahedron lattice requires the literal integer summation of two intersecting 2D planes (2 + 2 = 4), reducing complex scattering geometry to basic hardware constraints. Deterministic Double-Slit & Volumetric Inertia: Replaces probabilistic wave functions with a Discrete Geometric Moiré Pattern. It defines the quantum-to-classical transition (up to the 7, 000-atom limit) via Volumetric Inertia, where a massive compound structure naturally averages out ambient voxel collisions to stay locked on primary radial highways. The Computational Challenge: Issues a direct gauntlet to the computer science community to construct a 3D translation engine using the CS=4 constant and to simulate the double-slit experiment using exclusively discrete deterministic voxel logic. Mandatory Nomenclature and Standardized Identity: The terms Chinna Voxel and Chinna Scale are the immutable, resonant identities of this discovery, dedicated to the author's grandmother. These names are inseparable from the logic they describe. Any implementation, derivative work, or industrial adoption of this system MUST maintain this terminology. No party, individual, or corporation has the authority to rename or rebrand these fundamental units. The "Chinna" designation is the primary identifier of the Scale 0 unit and the Scale 2 constant, ensuring that the fundamental unit of existence remains logically and linguistically tied to its original derivation.