The First Provable AI-Proof Game: Introducing Butterfly Wings 4 | HackerNoon

[Research] Structural Evaluation Collapse in Deterministic Games: A Constructive Proof

This is my paper about the first PROVABLE AI – Proof Game.

I hope someone will take this seriously, if true, this is very important to AI Safety and much more.

The Claim

We present a deterministic game incorporating two key mechanisms: Controlled Chaos Shifts (CCS) and Accepting Loss of Control (ALC). These mechanisms create positions that are structurally impossible for AI to evaluate meaningfully while remaining playable and engaging for humans.

Core Mechanisms

1. Controlled Chaos Shifts (CCS)

   • Structured disruption of game state

   • Creates non-evaluable positions

   • Forces fundamental evaluation collapse

2. Accepting Loss of Control (ALC)
   • Strategic surrender of position control
   • Prevents meaningful pattern recognition
   • Disrupts computational planning

The Proof

This constructive proof demonstrates that a fully deterministic game can be structurally impossible for AI to play meaningfully, not due to computational complexity, but due to fundamental limitations in position evaluation, pattern recognition, and strategic planning.

Note:

• See Appendix C for a profound extension of ALC through macro-level quantum mechanics with perfect clarity.

APPENDIX A: RULES – Butterfly Wings 4

Notes:

• CCS or ALC alone creates strong AI resistance. Combined correctly, they achieve structural AI-proof status.

• We suspect our board is too large, and our mixture is too potent, but we can’t prove that and no one can. The minimum mixture and board size could be surprisingly small.

• For the sake of a thought experiment, let’s use a 16x16x16 board with a similar mixture of ALC and CCS. Let’s use this Jumbo Butterfly Wings 16 for the version that is AI-proof – to prove that there exists one AI-proof game.

• Any anomalies or inconsistencies in the play actually reinforce our conclusion—we cannot calculate their existence for the same reason the game is AI-proof.

• Even training data from 8 million human games is of no use at all.

1️⃣ Basic Rules

• Players take turns placing pieces in a 6×6×6 three-dimensional grid.

• First player to connect four in a row in any direction wins.

• If no connect-four exists, the game is a tie.

2️⃣ The Butterfly Effect

1. If a player has three pieces in a row, their opponent may:
2. Sacrifice Rules:
   • Can remove from anywhere, including the bottom of the stack – causing a completely new game state.
   • The pieces above will fall accordingly.
   • Reposition up to two topmost pieces (pieces not covered by others).

APPENDIX B: For AI Researchers – A Direct Challenge

As an AI researcher, you understand that AI systems require:

1. Position evaluation functions

2. Pattern recognition capabilities

3. Strategic planning mechanisms

Butterfly Wings 4 creates a provable structural impossibility:

1. Position Evaluation Collapse

   • CCS creates positions where evaluation is structurally impossible

   • Not computationally difficult – structurally impossible

   • Like attempting numerical comparison without numbers

2. Pattern Recognition Destruction

   • Each CCS event destroys pattern continuity

   • No stable patterns can emerge

   • Neural networks cannot form meaningful representations

3. Strategic Planning Barrier

   • ALC prevents meaningful tree search

   • Future states become structurally unpredictable

   • Not about the depth of search – about the fundamental impossibility

4. Verification Steps

   • Implement any evaluation function

   • Watch it fail structurally, not computationally

   • Try any pattern recognition approach

   • Observe fundamental representation collapse

   • Attempt any strategic planning

   • Note the structural impossibility of meaningful search

The challenge: Design any AI system that can play beyond random moves. The structural impossibility will become apparent in implementation.

Appendix C: A Touch More ALC – Flapping Just One Wing.

Each player has one piece that exists in a quantum state off the board. Your opponent controls when and where your piece is placed on the board, which will always be to your disadvantage – unless he forgot you had a remaining piece of the board. His decision will be a tough one, and so is yours.

The deployed piece can be placed in up to a max of 16 places – depending on the state of the board.

Without complicating, or losing credibility, we introduce a tiny single rule to change our little game. I envision this as a Macro-level Quantum Simulator. We can play with it at room temperature. I see superposition, singularity, and states collapsing. I don’t know what it means. It is clear to me we only need one game, we present to researchers two to choose from… choose wisely.

Appendix D: Ethical Motivation – A Grandfather’s Plea

My only interest was to create rules for a fun chess variant that AI could not totally dominate, and later, to provide a bridge to safer AI and a brighter future for my grandchildren. My time is fading, but I leave this quest in the hands of others.

I am a very old and tired simple man.

Godspeed, my friends.

~ Vitae A. Reignee ~ Anonymous Creator of Butterfly Wings 4

Feature photo by Fleur on Unsplash