Neuro‑symbolic Tool Composition via Spherical Embeddings

## NTEP: Expanded Exposition **Neuro‑symbolic Tool Composition via Spherical Embeddings** **Author:** J. Roberto Jiménez ✉️ `tijuanapaint@gmail.com` **DOI:** **License:** apache License 2.0 **Version:** 1.0 --- Description As AI agents become more autonomous, their ability to reliably chain tools and execute complex multi-step workflows is critical. However, neural models, which learn from statistical patterns, often fail to respect the hard operational dependencies between tools, leading to catastrophic failures such as emailing a file before it has been encrypted. This archive contains the source code for the Neural Tool Embeddings Protocol (NTEP), a novel framework that bridges the gap between the flexibility of neural representations and the rigor of symbolic logic to solve this problem. NTEP's core innovation is to embed tools and their dependencies into a high-dimensional spherical space. By encoding the partial order of tool execution as geometric constraints (e.g., if Tool A must precede Tool B, their vectors are forced to be close), the framework ensures that any valid chain decoded from these embeddings is automatically correct. This "soundness-by-construction" is formally guaranteed by the Monotonicity Theorem, which proves that the composite vector representing a sequence is always geometrically closer to the correct next step than to any future step. The framework also includes a quantum-inspired "consciousness" measure (Von Neumann Entropy) to quantify and mitigate the risk of uncertain or ambiguous tool sequences, providing a robust mechanism for risk-aware decision-making. This version (v0.1.0) includes the complete Python implementation, a worked example demonstrating a document processing pipeline, and the necessary test suites to verify the core mathematical properties. It is designed for researchers and engineers building the next generation of trustworthy and reliable AI agents.