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{
  "mcpServers": {
    "puppeteer": {
      "command": "npx",
      "args": ["-y", "@modelcontextprotocol/server-puppeteer"],
      "env": {
        "PUPPETEER_LAUNCH_OPTIONS": "{\"headless\": \"new\", \"args\": [\"--no-sandbox\", \"--disable-setuid-sandbox\", \"--disable-dev-shm-usage\", \"--window-size=1280,720\"]}",
        "ALLOW_DANGEROUS": "true"
      }
    },

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Mathematical Foundations of the UOR-Prime Framework: A Technical Primer

Introduction:
This primer presents a comprehensive, textbook-style exploration of the mathematical foundations underlying the Universal Object Reference (UOR) and Prime Framework as described in the attached paper. Our goal is to equip the reader with deep technical mastery of all prerequisite disciplines, from fundamental definitions to advanced concepts, in a self-contained manner. We cover the following major areas, each chosen for its relevance to the UOR-Prime Template:

• Category Theory Fundamentals – including the language of objects, morphisms, functors, and terminal objects, which form the abstract backbone of the framework.
• Universal Properties – general constructions (like terminal objects) that guarantee uniqueness and canonicality in mathematical structures.
• Algebraic Structures – formal definitions and examples of groups, rings, fields, and algebras, including t

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Model-Context-Protocol (MCP) for Agentic AI Workflows

The Model-Context-Protocol (MCP) is an open standard introduced by Anthropic in late 2024 to enable AI systems (like large language model agents) to seamlessly connect with external data sources and tools. This report provides a deep dive into MCP’s architecture and its role in agentic workflows – multi-step, tool-using AI “agents” that coordinate tasks. We will cover MCP’s core concepts, how to develop MCP-compliant agents (both client and server sides), strategies for orchestrating multiple MCP-based agents (coordination, conversation state management, and tool chaining), ensuring interoperability and schema compliance, and finally compare MCP’s approach to other leading agent frameworks (LangGraph, CrewAI, OpenDevin, AutoGen, etc.), evaluating compatibility, strengths, and limitations.

MCP Architecture and Core Concepts in Agentic Systems

MCP Overview: MCP is not a programming framework or a single toolchain – it is a protocol (a

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Title: Toward a Deterministic, Semantic, and Dynamically Coherent LLM: Integrating Infomorphic Neurons, UOR Digest Encoding, and Hamiltonian Mechanics

Abstract

This paper introduces a unified theoretical and implementation framework for constructing advanced language learning models (LLMs) that transcend the limitations of token-based architectures. Integrating three frontier paradigms—(1) Infomorphic Neurons via Partial Information Decomposition (PID), (2) Universal Object Reference (UOR) with 512-bit Prime Digest Encoding, and (3) Hamiltonian Mechanics as a governing model of semantic trajectory dynamics—we propose a deterministic, reversible, and fully interpretable semantic engine. This triadic approach enables the construction of dynamic, on-the-fly evolving neural knowledge graphs with canonical semantic addressability, physically grounded coherence, and intrinsically lossless transformation.

1. Introduction

Language models have traditionally relied on probabilistic token prediction, which fragments

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BasedOn:

1. https://transformer-circuits.pub/2025/attribution-graphs/methods.html
2. https://gist.github.com/afflom/2698a9f0b5a88302008db624a05e6331#file-512-spectral-md
3. https://github.com/UOR-Foundation

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Universal Object Reference System (UORS)

Semantic Addressing Engine

The UORS Semantic Addressing Engine is a revolutionary framework that provides a mathematically coherent, multi-dimensional addressing system for digital objects. It enables universal, language-independent object references that remain stable across representations, languages, and domains.

This reference implementation demonstrates the core concepts of UORS using Clifford algebras, manifold structures, and coherence-based validation to create a robust semantic addressing system.

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Phase 1 MVP Implementation Tracker: Core Architecture and Provider Modules

Overview

This document tracks the implementation progress of the Phase 1 MVP for our new Infrastructure as Code (IaC) architecture. The goal of Phase 1 is to implement the full core module architecture and establish functional provider modules for AWS, Azure, and Kubernetes that comply with our design principles.

Last Updated: March 18, 2025

Milestone Summary

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The Prime Framework presents an innovative fusion of number theory, algebra, and geometry, proposing a novel way to encode natural numbers in Clifford algebras and interpret them within a fiber algebraic structure. While it introduces fresh perspectives on long-standing mathematical conjectures, its viability under the pressure of solving these problems must be critically assessed.

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Strengths of the Prime Framework

1. Unique Factorization and Number Embedding

The framework ensures a unique representation of numbers across all bases, reinforcing classical number theory results like the Fundamental Theorem of Arithmetic.

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Time-Based Signal Extraction, Compression, and Predictive Modeling in the Prime Compute Information System

By leveraging Fourier transforms, wavelet analysis, and other mathematical methods within the Prime Compute Information System (PCIS), we can detect high-value signals in massive datasets, optimize semantic coherence, compress information losslessly, and predict future states of objects and transformations.

1. Fourier Transform & Time-Series Signal Decomposition

The Fourier transform (FT) allows us to decompose the time-dependent evolution of the information system into frequency-domain components, helping us to:

Isolate high-value signals by filtering low-amplitude noise in high-dimensional data streams.

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Universal Object Reference (UOR) for Music Theory: A Rigorous Computational Framework

1. Introduction

Music, as a highly structured yet expressive system of organized sound, is fundamentally governed by mathematical principles. The Universal Object Reference (UOR) framework offers a robust unifying paradigm for encoding and generating music across distinct traditions by situating musical elements within a well-defined algebraic and geometric space. This document articulates an extensible UOR-based approach to music theory, emphasizing both theoretical rigor and computational applicability in music analysis, synthesis, and generative composition.

Framework Objectives

• Formalize music fundamentals using precise mathematical structures.
• Embed music theory in UOR through Clifford algebraic encodings, Lie group symmetries, and coherence norms.
• **Represent diverse musical systems (Western Classical, Hindustani Classical, and Gamelan) within a UOR framework, facilitating compa