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README.md

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+# NextTokenSystem: Deterministic Algebraic Prediction Engine
+
+## Overview
+This system is a novel approach to next-token prediction that replaces neural networks and stochastic sampling with deterministic algebraic transformations. It achieves high precision by mapping tokens to a numeric coordinate space and applying governing equations.
+
+## Core Algebraic Mechanism
+The engine utilizes three primary equation types to model token relationships:
+- **Linear**: $y = x + c$ (Constant shifts)
+- **Multiplicative**: $y = a * x$ (Scale transformations)
+- **Quadratic**: $y = x^2 + c$ (Non-linear jumps)
+
+## Temporal Dynamics
+To ensure contextual coherence and adaptation, the system implements:
+- **Equation Memory**: Successful equations accumulate strength over time.
+- **Decay**: Unused rules gradually lose influence to prevent stale logic.
+- **Reuse Bias**: Recently used equations receive a temporary bonus for style consistency.
+
+## Conflict Resolution
+- **Local Anchors**: Specific token-to-token mappings are 'anchored' using optimized parameters, taking precedence over global rules.
+- **Global Rules**: Weighted selection based on temporal dynamics and fit scores for general context.
+
+## Deterministic Precision
+- **Zero Neural Intervention**: No transformers, embeddings, or backpropagation are used.
+- **95%+ Precision Goal**: Through adaptive coefficient scaling and symbolic back-search, the system targets near-perfect accuracy on structured datasets.
+
+---
+
+%%writefile requirements.txt
+numpy