Skip to content

GUIDE_MATH.md

Latest commit

 

History

History
27 lines (20 loc) · 2.48 KB

GUIDE_MATH.md

File metadata and controls

27 lines (20 loc) · 2.48 KB
Raw

Ghost Engine: Mathematical Foundations

The Ghost Engine is built on the mathematics of High-Dimensional Vector Space Alignment (VSA).

1. HyperVector Resonance

We operate in a 1024-dimensional bitspace. Meaning is not stored in values, but in the Hamming Distance between vectors.

  • Nearness: A Hamming distance < 400 indicates semantic resonance.
  • Void: A Hamming distance > 600 indicates semantic orthogonality.

2. The Majority Rule (Bundling)

To "memorize" multiple vectors into a single point in the matrix, we use a bitwise Majority Rule:

  1. Align N vectors.
  2. For each bit position, if more than 50% of the vectors have a 1, the resulting bit is 1.
  3. This creates a "composite" vector that retains a high degree of resonance with all its constituent parts.

3. Boundary Detection and Cascade Etching

The engine detects structural boundaries in the input stream by monitoring resonance energy. When energy drops below a threshold (indicating low similarity to existing state), a boundary is triggered. Boundaries cascade context upward through syntax, phrase, concept, and global HyperVector registers, etching the current context into the MeaningMatrix at each level.

4. No-Float Determinism

By using only bitwise operations, the engine achieves Absolute Determinism. The same input will always produce the exact same resonance across any hardware that supports the standard VSA instruction set.

5. Determinism and Resonance Safety

The mathematical core of Ghost is designed for bit-perfect reproducibility. Any divergence in how bitwise logic is applied will lead to semantic decay:

  • The No-Float Mandate: Never introduce floating-point math (f32, f64) into vsa_core.zig or src/shaders/. Even a single rounding error will break bit-perfect determinism across different hardware architectures.
  • Resonance Thresholds: The engine uses multiple thresholds defined in src/config.zig. Boundary detection uses energy values: soul boundary at 200, paragraph at 400, phrase at 400-600 (configurable), word at 400. The surprise threshold is 850 (skip etching if already known), and the search trigger is 750. Modifying these will change the engine's perception.
  • Vector Bundling (Majority Rule): The Majority Rule implementation (a & b) | (b & c) | (c & a) is the engine's only way to "memorize." Any change to how bitwise bundling is handled in the GPU kernels will result in a state that the CPU cannot interpret correctly.