ZDTP Chess

Multi-Dimensional Decision Intelligence Using Applied Pathological Mathematics

"Better math, less suffering" - Chavez AI Labs

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What Makes This Different

Traditional chess engines evaluate positions with a single number. Zero Divisor Transmission Protocol (ZDTP) evaluates positions across three dimensional layers simultaneously:

• 16D Tactical Layer - Immediate threats, hanging pieces, forcing sequences
• 32D Positional Layer - Piece coordination, pawn structure, gateway patterns
• 64D Strategic Layer - Long-term planning, endgame evaluation, strategic depth

Each position is analyzed through six mathematical gateways (King, Queen, Knight, Bishop, Rook, Pawn) derived from zero divisor patterns in higher-dimensional algebras. When multiple gateways converge on the same evaluation, you've found something objectively strong across independent mathematical frameworks.

This is infrastructure for AI systems, not a chess product. Chess is the proof of concept for multi-dimensional decision intelligence.

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Features

Gateway Convergence Detection

Six independent mathematical "gateways" (King, Queen, Knight, Bishop, Rook, Pawn) analyze each position. When multiple gateways converge on the same evaluation and recommendation, the system identifies framework-independent optimal moves with mathematical certainty.

Blunder Prevention

Industry-standard Static Exchange Evaluation (SEE) integrated with dimensional analysis to catch hanging pieces and catastrophic moves before they happen.

Educational Interface

Clear visualization of dimensional scores, gateway patterns, and convergence indicators help players understand not just what move to make, but why it's optimal across multiple mathematical frameworks.

Candidate Suggester (Session 2)

LLMs systematically miss pawn moves, defensive resources, and quiet positional moves when playing chess. They fixate on "obvious" piece moves while overlooking quiet pawn advances, pawn captures, and defensive interpositions. No amount of prompting fixes this because the bias operates below the reasoning layer.

The chess_suggest_candidates tool solves this by categorizing every legal move by tactical function before the LLM makes any recommendation:

Category	When It Appears	Subcategories
Forcing	Always	checks, captures, promotions, threatens promotion
Defensive	Only when pieces are attacked	escape, pawn defends, piece defends, counterattack
Developing	Always	castling, center pawn advance, minor piece development, rook activation
Quiet	Only on request	everything else

Each move includes a Static Exchange Evaluation (SEE) safety assessment so the LLM sees material-loss warnings inline before recommending a move.

Master Dampener (Session 0.1)

Formally verified fortress draw detection. When structural signals (locked pawns, opposite-color bishops, insufficient material) combine with temporal stasis (evaluation unchanged over 4+ moves), the Master Dampener pulls evaluation toward 0.0 (draw). Formula: Consensus × (1 - FortressSignal)

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Prerequisites

Required Software

• Python 3.10 - 3.13 - Python 3.14+ currently has compatibility issues
  • Download: https://www.python.org/downloads/
  • Windows users: During installation, check "Add Python to PATH"
• Claude Desktop with MCP support
  • Download: https://claude.ai/download

Optional (Recommended)

• Git for cloning repository
  • Download: https://git-scm.com/downloads
  • Alternative: Download ZIP file directly from GitHub (see Installation)

Verify Your Installation

# Check Python version (should show 3.10-3.13)
python --version

# Check pip is available
python -m pip --version

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Installation

Quick Start (All Platforms)

1. Download ZDTP Chess
2. Install Python dependencies
3. Configure Claude Desktop
4. Restart Claude Desktop

Detailed platform-specific instructions below.

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Installation on Windows

Step 1: Download ZDTP Chess

Option A: Using Git

git clone https://github.com/pchavez2029/zdtp-chess.git
cd zdtp-chess

Option B: Download ZIP (No Git Required)

1. Visit https://github.com/pchavez2029/zdtp-chess
2. Click the green "Code" button
3. Select "Download ZIP"
4. Extract to a permanent location (e.g., C:\Users\YourName\Documents\zdtp-chess)
5. Open PowerShell in the extracted folder:
   • Navigate to the folder in File Explorer
   • Hold Shift + Right-click in the folder
   • Select "Open PowerShell window here"

Step 2: Fix PowerShell Execution Policy (One-time Setup)

If you encounter "cannot be loaded because running scripts is disabled" errors:

# Run PowerShell as Administrator
# Right-click PowerShell in Start Menu -> "Run as Administrator"

Set-ExecutionPolicy -ExecutionPolicy RemoteSigned -Scope CurrentUser
# Type 'Y' and press Enter when prompted

This is a one-time Windows security setting required for Python packages.

Step 3: Install Dependencies

# Important: Use 'python -m pip' on Windows (not just 'pip')
python -m pip install -r requirements.txt

You may see warnings about scripts not on PATH - these are non-critical and can be ignored.

Step 4: Configure Claude Desktop MCP Server

1. Open Claude Desktop
2. Navigate to Settings -> Developer -> Edit Config
   • This opens claude_desktop_config.json in your default text editor
3. Add the ZDTP Chess configuration:

{
  "mcpServers": {
    "zdtp-chess": {
      "command": "python",
      "args": ["-m", "zdtp_chess_mcp"],
      "cwd": "C:\\Users\\YourName\\Documents\\zdtp-chess",
      "env": {
        "PYTHONPATH": "C:\\Users\\YourName\\Documents\\zdtp-chess"
      }
    }
  }
}

Critical Configuration Notes:

• Replace C:\\Users\\YourName\\Documents\\zdtp-chess with your actual installation path
• Use double backslashes (\\) in Windows paths for JSON format
• Both cwd and PYTHONPATH must point to the same directory
• The args must be ["-m", "zdtp_chess_mcp"] NOT ["-m", "zdtp_chess_mcp.zdtp_chess_server"]
• If you have other MCP servers, add zdtp-chess inside the existing mcpServers object

4. Save the config file
5. Completely close and restart Claude Desktop
   • Quit the application entirely, don't just close the window
   • On Windows: Right-click system tray icon -> "Quit"

Step 5: Verify Installation

1. Open Claude Desktop
2. Go to Settings -> Developer
3. Check MCP Servers list:
   • zdtp-chess should show as "connected"
   • If it shows "failed", see Troubleshooting section below

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Installation on macOS/Linux

# Clone repository
git clone https://github.com/pchavez2029/zdtp-chess.git
cd zdtp-chess

# Install dependencies
pip install -r requirements.txt

Configure Claude Desktop by editing:

• macOS: ~/Library/Application Support/Claude/claude_desktop_config.json
• Linux: ~/.config/Claude/claude_desktop_config.json

Add to configuration:

{
  "mcpServers": {
    "zdtp-chess": {
      "command": "python",
      "args": ["-m", "zdtp_chess_mcp"],
      "cwd": "/absolute/path/to/zdtp-chess",
      "env": {
        "PYTHONPATH": "/absolute/path/to/zdtp-chess"
      }
    }
  }
}

Replace /absolute/path/to/zdtp-chess with your actual installation path. Restart Claude Desktop completely.

Requirements

• python-chess>=1.999 - Chess move generation and board representation
• mcp>=0.9.0 - Model Context Protocol server
• hypercomplex>=0.3.4 - Hypercomplex number systems (Sedenions, Pathions, Chingons)

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Troubleshooting

"ModuleNotFoundError: No module named 'zdtp_chess_mcp'"

Causes & Solutions:

1. Missing cwd or PYTHONPATH in config

   • Verify your config has BOTH cwd AND PYTHONPATH set to the installation directory

2. Incorrect path format (Windows)

   • Use double backslashes (\\) in JSON paths
   • Wrong: "C:\Users\YourName\Documents\zdtp-chess"
   • Correct: "C:\\Users\\YourName\\Documents\\zdtp-chess"

3. Claude Desktop not restarted

   • Completely quit and restart Claude Desktop (not just close window)

"Server disconnected" Error

1. Wrong Python version

   • Check: python --version (must be 3.10-3.13, NOT 3.14+)
   • Solution: Install Python 3.13 from https://www.python.org/downloads/

2. Dependencies not installed

   • Run: python -m pip install -r requirements.txt

3. Wrong command in config

   • Use: "args": ["-m", "zdtp_chess_mcp"]
   • NOT: "args": ["-m", "zdtp_chess_mcp.zdtp_chess_server"]

4. Python not in PATH

   • Use full Python path in config:

"command": "C:\\Users\\YourName\\AppData\\Local\\Programs\\Python\\Python313\\python.exe"

• Find your Python path: where.exe python (Windows) or which python (macOS/Linux)

Multiple Python Installations

If packages install but you still get ModuleNotFoundError:

# Windows - see all Python installations
where.exe python

# Check which Python pip uses
python -m pip --version

Use the full path to your Python 3.13 installation in the config:

"command": "C:\\Users\\YourName\\AppData\\Local\\Programs\\Python\\Python313\\python.exe"

PowerShell "running scripts is disabled"

# Open PowerShell as Administrator
Set-ExecutionPolicy -ExecutionPolicy RemoteSigned -Scope CurrentUser
# Type 'Y' and press Enter

Can't Find Config File

Easy method: Settings -> Developer -> Edit Config (works on all operating systems)

Manual paths:

• Windows: C:\Users\YourName\AppData\Roaming\Claude\claude_desktop_config.json
• macOS: ~/Library/Application Support/Claude/claude_desktop_config.json
• Linux: ~/.config/Claude/claude_desktop_config.json

Note: On Windows, the AppData folder is hidden by default. Use Settings -> Developer -> Edit Config instead.

Python 3.14 Compatibility

If you see:

pip._vendor.pyproject_hooks._impl.BackendUnavailable: Cannot import 'setuptools.build_backend'

Python 3.14 has breaking changes in setuptools. Use Python 3.13 or earlier:

1. Download Python 3.13 from https://www.python.org/downloads/
2. Install with "Add to PATH" checked
3. Reinstall dependencies: python -m pip install -r requirements.txt

Getting Help

If you encounter issues not covered here:

1. Check the logs: Claude Desktop -> Settings -> Developer -> View logs
2. Verify installation:

python --version
python -m pip list | findstr "chess mcp hypercomplex"

3. Create a GitHub Issue: https://github.com/pchavez2029/zdtp-chess/issues
   • Include your OS, Python version, and error messages from Claude Desktop logs

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The Math Section

"I was told there would be no math." - Anonymous Student

Sorry, but there's math. Here's the minimal math you need to understand how this works:

Zero Divisors

In normal arithmetic, if A × B = 0, then either A = 0 or B = 0 (or both). This is the zero-product property you learned in algebra.

In higher-dimensional algebras, however, this breaks down with amazing annihilation.

Starting in 16D sedenions and continuing upward to 32D pathions, and 64D chingons, you can find non-zero elements P and Q where:

P × Q = 0

even though P ≠ 0 and Q ≠ 0

These are called zero divisors, and mathematicians traditionally have dismissed them as "pathological", wrongly demeaning them as algebraic structures that make systems "unusable."

Why Zero Divisors Are Actually Useful

Key insight: Zero divisors can encode information about dimensional collapse and information loss in algebraic systems. In chess decision-making, this maps to:

• Tactical collapse (16D) - Positions where forcing sequences eliminate options
• Positional transformation (32D) - How piece coordination changes across moves
• Strategic encoding (64D) - Long-term plan evaluation through dimensional reduction

When you analyze a chess position in 16D and transmit it to 32D and 64D via ZDTP, zero divisor patterns preserve the decision-relevant structure with lossless information movement between dimensional spaces.

Example: The Canonical Six

We discovered six fundamental zero divisor patterns that appear consistently across 16D/32D/64D spaces. (Reference: https://zenodo.org/records/17402495)

Each pattern provides a different "lens" for evaluating positions. When multiple patterns converge on the same evaluation, you've found framework-independent optimality.

That's the math. The rest is engineering.

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How It Works

Zero Divisor Transmission Protocol (ZDTP)

ZDTP enables lossless data movement between higher-dimensional mathematical spaces:

1. Encoding (16D) - Chess position → 16D sedenion representation

   • Material balance, piece mobility, tactical threats
   • Encoded using basis elements e₀ through e₁₅

2. Transmission (32D) - 16D data → 32D pathion space via gateway patterns

   • Six independent gateways process position simultaneously
   • Zero divisor patterns preserve decision-relevant structure
   • Positional factors (coordination, structure) emerge in 32D

3. Strategic Analysis (64D) - 32D data → 64D chingon space

   • Long-term planning, endgame evaluation
   • Strategic depth analysis through dimensional expansion

4. Convergence Detection - Compare all gateway outputs

   • If multiple gateways agree (within threshold), move is framework-independent optimal
   • Disagreement indicates tactical complexity requiring deeper analysis

Why this matters: Traditional dimensional reduction loses information. ZDTP uses zero divisor patterns to preserve decision-relevant structure across dimensional transformations. Information moves losslessly between 16D, 32D, and 64D spaces.

Game Flow

1. You play White against a computer opponent (Black)
2. After each move, ZDTP analyzes the position through an adaptive gateway
3. Dimensional scores show tactical (16D), positional (32D), and strategic (64D) evaluation
4. Positive scores = advantage for White (you)
5. Gateway convergence alerts you when multiple frameworks independently agree

MCP Tools

ZDTP Chess provides the following tools through the Model Context Protocol:

• chess_new_game - Start a new game
• chess_suggest_candidates - Categorize all legal moves by type (forcing/defensive/developing/quiet)
• chess_make_move - Execute a move (requires explicit user confirmation)
• chess_analyze_move - Preview move consequences without executing (what-if analysis)
• chess_get_board - Display current position and game state
• chess_get_dimensional_analysis - Detailed breakdown of current position
• chess_check_gateway_convergence - Check multiple gateways for framework-independent optimization
• chess_load_position - Load a position from FEN or the Stressor Library (Session 0.1)
• chess_list_stressors - List curated test positions for dimensional analysis stress testing

Recommended workflow: Call chess_suggest_candidates first to see the full tactical landscape, then use chess_analyze_move to deep-dive promising candidates, then execute with chess_make_move.

Example Analysis Output

╔══════════════════════════════════════════════════════════════╗
║  BLACK RESPONDS: Nf6                                         ║
╚══════════════════════════════════════════════════════════════╝

Analysis Gateway: Knight (discontinuous gateway - non-linear patterns)
Position Evaluation: +0.94 (White's perspective)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  MULTI-DIMENSIONAL POSITION ANALYSIS
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

🎯 16D TACTICAL LAYER (Immediate Threats & Material)
   Score: +0.87 (White's perspective)
   • Material balanced
   • White has better mobility (3 more legal moves)
   • No immediate threats detected

🏗️ 32D POSITIONAL LAYER (Structure & Coordination)
   Score: +2.91 (White's perspective)
   • Gateway Pattern: Discontinuous Gateway (Knight)
   • Strong center control for White
   • Well-coordinated piece development

🌟 64D STRATEGIC LAYER (Long-term Planning)
   Score: +1.23 (White's perspective)
   • White's central pawns provide middlegame flexibility
   • Favorable pawn structure approaching
   • Long-term endgame potential

CONSENSUS EVALUATION: +0.94 (slight advantage: WHITE)

💡 SUGGESTED MOVES: Nf3 (develop), c4 (Queen's Gambit), Bf4 (bishop out)

Example: Using the Candidate Suggester

After starting a game and reaching a complex middlegame position, ask Claude to survey your options:

You: "What are my best options here?"

Claude calls chess_suggest_candidates and responds with the full tactical landscape:

Claude:

Here's what I see across all 41 legal moves:

Forcing moves:

• dxc6 (pawn capture) - Safe trade, wins a pawn
• Qxa5 (piece capture) - WARNING: Your queen hangs after recapture (loses 5.8 material)

Defensive moves:

• h3 - Moves your pawn off the attacked h2 square
• e4 - Your pawn now defends the d5 pawn that's under pressure

Developing moves:

• e3 - Center pawn advance, strengthens your pawn chain
• Rec1 - Rook activates on the semi-open c-file

The quiet pawn capture dxc6 stands out - it's safe and wins material. Want me to run a deeper ZDTP analysis on it?

Without the Candidate Suggester, the LLM would likely recommend the flashy queen capture and miss the safe pawn win entirely.

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Architecture

ZDTP Chess combines standard chess engine components with novel multi-dimensional analysis:

Standard Components

• Legal move generation (python-chess library)
• Material evaluation
• Blunder detection using Static Exchange Evaluation (SEE)
• Basic tactical analysis

These components ensure ZDTP Chess meets baseline requirements for chess programming and can be validated against traditional engines.

ZDTP Innovation

• 16D Tactical Analysis - Sedenion-based immediate threat detection
• 32D Positional Analysis - Pathion gateway patterns for structural evaluation
• 64D Strategic Analysis - Chingon-based long-term planning
• Gateway Convergence - Framework-independent optimality detection

The ZDTP layers run after standard blunder detection, adding strategic insight beyond traditional evaluation functions.

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Mathematical Foundation

ZDTP Chess is built on research into Cayley-Dickson algebras and zero divisor patterns:

Research Publication: Framework-Independent Zero Divisor Patterns in Higher-Dimensional Cayley-Dickson Algebras: Discovery and Verification of The Canonical Six - Zenodo DOI: 10.5281/zenodo.17402495

Formal Verification (Session 0.1)

ZDTP Chess v2.0 features are grounded in machine-verified proofs from ChavezTransform_Specification_aristotle.lean:

• Theorem 5 (Bilateral Kernel Bound): K_Z(P,Q,x) ≤ 4(||P||² + ||Q||²)||x||²

  • Ensures tactical noise is mathematically contained
  • Implementation: Dim 52 tactical_ceiling computes saturation ratio

• Theorem 3 (Dimensional Weight): (1 + ||x||²)^(-d/2) ≤ 1 for d > 0

  • Provides decay function for piece influence based on board density
  • Implementation: Dim 54 mobility_occlusion uses this decay

• Stability Constant M: M = (||P||² + ||Q||²) · √(π/α)

  • Threshold for detecting evaluation stasis (fortress positions)
  • Implementation: Master Dampener uses practical threshold M = 0.5

The Lean 4 proofs were generated by Aristotle (Harmonic) and compile with Mathlib.

The Six Gateways

Each gateway represents a different zero divisor pattern from 32D pathion algebra:

1. King Gateway - Master gateway, holistic evaluation
2. Queen Gateway - Multi-modal gateway, tactical complexity
3. Knight Gateway - Discontinuous gateway, non-linear patterns
4. Bishop Gateway - Diagonal gateway, long-range planning
5. Rook Gateway - Orthogonal gateway, file control
6. Pawn Gateway - Incremental gateway, structural analysis

When multiple gateways independently arrive at the same evaluation and recommendation, the move is considered framework-independent optimal.

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Applications

Chess (Current Proof of Concept)

• Zero Divisor Transmission Protocol moves position information with no data loss from 16D to 32D to 64D
• Multi-dimensional position evaluation across tactical/positional/strategic layers
• Framework-independent move quality assessment through gateway convergence
• Real-time blunder detection with dimensional analysis
• Educational tool for understanding multi-perspective decision-making

AI Infrastructure (Platform Vision)

• Decision Intelligence - Multi-framework validation for complex AI decisions
• Quantitative Finance - Portfolio analysis through dimensional risk assessment (CAILculator in development)
• Medical Diagnostics - Multi-framework symptom evaluation with convergence validation
• Strategic Planning - Business decisions analyzed across multiple independent frameworks
• AI Safety - Catching edge cases that single-model systems miss

For Developers & Researchers

• Multi-Framework Analysis - Reference architecture for combining independent mathematical approaches
• Applied Pathological Mathematics - Demonstration that "unusable" mathematical structures have practical value
• Framework-Independent Optimization - Study convergence patterns across different algebraic systems

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Roadmap

Phase 1: Chess (Complete - v1.0)

• ✅ Core dimensional analysis engine (16D/32D/64D)
• ✅ Six gateway patterns implemented
• ✅ ZDTP protocol for lossless dimensional transmission
• ✅ Gateway convergence detection
• ✅ Blunder detection with SEE integration
• ✅ MCP server with user confirmation safeguards

Session 0.1: Formal Verification (Complete - v2.0)

• ✅ Lean 4 Grounded Features - Theorems verified by Aristotle (Harmonic)
  • Theorem 5: Bilateral Kernel Bound → Dim 52 (tactical_ceiling)
  • Theorem 3: Dimensional Weight → Dim 54 (mobility_occlusion)
  • Stability Constant M → Master Dampener threshold
• ✅ Master Dampener - Fortress draw detection with formula: Consensus × (1 - FortressSignal)
• ✅ Zugzwang Coefficient - Non-commutativity measure |P·x - x·P| (Dim 63)
• ✅ Stressor Position Library - Curated test positions for dimensional analysis validation
• ✅ Temporal Confirmation - 4-eval history check for fortress stasis detection

Session 2: Candidate Suggester (Complete)

• ✅ Move Categorization Engine - Every legal move classified into forcing/defensive/developing/quiet
• ✅ SEE Safety Per Move - Inline material-loss warnings using battle-tested Static Exchange Evaluation
• ✅ Attacked Piece Detection - Identifies all friendly pieces under attack with attacker/defender counts
• ✅ Workflow Integration - System prompt updated to call chess_suggest_candidates before recommending moves
• ✅ 12-Test Validation Suite - Covers starting position, hanging pieces, checks, captures, promotions, castling, and JSON structure

Phase 2: Financial Infrastructure (In Development)

• CAILculator - Quantitative finance application via MCP server
• Portfolio risk assessment across dimensional frameworks
• Multi-asset correlation analysis through gateway patterns
• Framework-independent optimization for trading strategies

Phase 3: Platform Expansion

• Strategic business planning tools
• AI safety validation frameworks
• Natural language processing with dimensional embeddings
• Extended dimensional analysis (128D, 256D layers)

Chess Enhancements (Ongoing)

• Gateway selection strategy optimization
• Position-type adaptive gateway weighting
• Performance optimization (parallel gateway evaluation)
• PGN export with dimensional annotations

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About Chavez AI Labs

Mission: "Better math, less suffering"

Chavez AI Labs applies pathological mathematics - mathematical structures traditionally dismissed as unusable - to create practical AI systems and decision-making tools.

Founder: Paul Chavez

• 30+ years journalism experience (Associated Press, LA Times)
• UCLA alumnus (Political Science, 1989)
• Published research with CERN DOI on zero divisor patterns

Products:

• CAILculator - MCP server for high-dimensional mathematical analysis
• ZDTP Chess - Proof of concept for applied pathological mathematics
• Additional applications in quantitative finance, data analysis, and AI infrastructure

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Contributing

For collaboration inquiries, research partnerships, or commercial licensing:

• Contact: iknowpi@gmail.com
• Company: Chavez AI Labs (California-licensed AI company)
• Research: See published paper on framework-independent zero divisor patterns

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License

Apache License 2.0 with patent protection.

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Acknowledgments

• Python-chess library - Foundation for chess logic and board representation
• Anthropic MCP - Model Context Protocol implementation
• CERN - Digital Object Identifier (DOI) for research publication
• Chess community - Inspiration and education during development

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Citation

If you use ZDTP Chess in academic research, please cite:

Chavez, P. (2025). ZDTP Chess: Multi-Dimensional Analysis Through Zero Divisor Patterns.
Chavez AI Labs. https://github.com/pchavez2029/zdtp-chess

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Chavez AI Labs - Applied Pathological Mathematics