monster-lean

Monster Group Walk Down to Earth - A mathematical exploration of the Monster group's order.

⚠️ Disclaimer

Author: Undergraduate math student (not currently enrolled), exploring patterns in the Monster group. This is a learning project, not professional research. I welcome corrections, guidance, and constructive criticism from experts. Please review with patience and understanding.

What this is: Documented experiments, working code, interesting patterns, conjectural models
What this isn't: Rigorous professional mathematics (yet), proven theory

Status: The Monster Walk digit preservation is verified in Lean4. The shard/witness/frequency classification system is a conjecture we're testing. See CONJECTURE_STATUS.md for confidence levels.

I humbly request help, feedback, and mercy from the mathematical community.

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📚 Quick Start

New to this project? Start here:

1. README.md - This file (overview)
2. PAPER.md - Complete paper with all results
3. PROGRAM_INDEX.md - All 200+ programs
4. PROOF_INDEX.md - All formal proofs

📊 Core Finding: Hierarchical Digit Preservation

This project documents a computational exploration of the Monster group's prime factorization, focusing on a simple but interesting pattern: removing specific prime factors can preserve leading digits at multiple levels.

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Overview

This project explores a fascinating hierarchical property of the Monster group (the largest sporadic simple group):

• The Monster group order is approximately 8.080 × 10^53
• By removing specific prime factors, we can preserve leading digits at multiple hierarchical levels
• This demonstrates the "Monster Walk Down to Earth" - a fractal-like structure

The Hierarchical Walk

Group 1: "8080"

• Target: First 4 digits of Monster order
• Remove 8 factors: 7⁶, 11², 17¹, 19¹, 29¹, 31¹, 41¹, 59¹
• Result: 80807009282149818791922499584000000000
• Preserved: 4 digits (8080)
• Maximum: Cannot preserve 5 digits (80801) with any combination

Group 2: "1742" (after "8080")

• Target: Next 4 digits after "8080"
• Remove 4 factors: 3²⁰, 5⁹, 13³, 31¹
• Result: Starts with 1742103054...
• Preserved: 4 digits (1742)
• Maximum: Cannot preserve 5 digits (17424) with any combination

Group 3: "479" (after "80801742")

• Target: Next digits after "80801742"
• Remove 4 factors: 3²⁰, 13³, 31¹, 71¹
• Result: Starts with 4792316941...
• Preserved: 3 digits (479)
• Maximum: Cannot preserve 4 digits (4794) with any combination

Remarkable Pattern: Each group achieves 3-4 digit preservation through different factor combinations!

Components

Rust Implementation (src/)

Computational verification and analysis programs:

Core Programs:

• main.rs - Original Monster Walk verification
• prime_emojis.rs - Emoji mapping for each prime factor
• group_harmonics.rs - Harmonic frequency analysis of groups
• musical_periodic_table.rs - Complete periodic table with frequencies
• monster_emoji_report.rs - Meme-contract universe report

Analysis Programs:

• group2.rs, group3.rs - Individual group analysis
• transitions.rs - Transition analysis between groups

Key findings:

• Removing 2 factors: preserves 2 digits (80)
  • Remove: 17¹ and 59¹
• Removing 4 factors: preserves 3 digits (808)
  • Remove: 2⁴⁶, 7⁶, 17¹, and 71¹
• Removing 8 factors: preserves 4 digits (8080) ⭐
  • Remove: 7⁶, 11², 17¹, 19¹, 29¹, 31¹, 41¹, and 59¹
  • Result: 80807009282149818791922499584000000000

Lean4 Formalization (MonsterLean/)

Formal proofs using Lean4 theorem prover:

Proven theorems:

• MonsterWalk.lean - Hierarchical walk structure with Groups 1, 2, 3
• MusicalPeriodicTable.lean - Complete formal specification with semantic proofs
• LogarithmicAnalysis.lean - Why the walk works (logarithmic insight)
• MonsterTheory.lean - Group theory and modular arithmetic analysis

Key proofs:

• monster_starts_with_8080: The Monster order starts with 8080
• remove_8_factors_preserves_8080: Removing 8 specific factors preserves these digits
• monster_hierarchical_walk: Main theorem proving the walk property exists
• musical_periodic_table_well_formed: All 15 primes are correctly classified
• binary_moon_semantics, wave_crest_semantics: Emoji meanings are proven

Documentation

• README.md - This file
• MATHEMATICAL_PROOF.md - Logarithmic explanation of why it works
• MUSICAL_PERIODIC_TABLE.md - Complete formal specification and proofs

Building

Rust

nix develop
cargo run

Lean4

nix develop
lake build

Image Generation (Submodule)

# Clone with submodules
git clone --recursive https://github.com/meta-introspector/monster-lean

# Or add submodule separately
git submodule add https://github.com/meta-introspector/diffusion-rs
git submodule update --init --recursive

# Build diffusion-rs
cd diffusion-rs
cargo build --release

The Monster Group

Prime factorization: 2^46 × 3^20 × 5^9 × 7^6 × 11^2 × 13^3 × 17 × 19 × 23 × 29 × 31 × 41 × 47 × 59 × 71

Order: 808017424794512875886459904961710757005754368000000000

LLM Register Resonance Experiments

New Discovery: LLM CPU register values during inference are divisible by Monster group primes at rates matching error correction code distributions.

See examples/ollama-monster/ for:

• RESULTS.md - Core experimental findings
• EXPERIMENT_SUMMARY.md - Full methodology
• INDEX.md - Complete file index

Key Results

• 80% of register values divisible by prime 2
• 49% divisible by prime 3, 43% by prime 5
• Same 5 primes [2,3,5,7,11] appear in 93.6% of error correction codes
• Conway's name activates higher Monster primes (17, 47)
• Automorphic feedback creates measurable computation drift
• System exhibits limit cycle behavior

Quick Start

cd examples/ollama-monster
./trace_regs.sh "mathematician Conway"
cargo run --release --bin view-logs

📊 Complete Index

Program Index

See PROGRAM_INDEX.md for complete catalog:

• 200+ Rust programs - Core implementations, analysis tools, experiments
• 50+ Python tools - Vision review, Hecke analysis, 71³ generation
• Image generation - diffusion-rs with I ARE LIFE experiment
• LLM tracing - Register resonance analysis
• LMFDB translation - Bisimulation proofs
• Hyperpolyglot - Computer algebra system reference (see HYPERPOLYGLOT_INTEGRATION.md)

Proof Index

See MonsterLean/MonsterLean/ProofIndex.lean for all formal proofs:

Core Theorems (12):

1. monster_starts_with_8080 - Monster order begins with 8080
2. remove_8_factors_preserves_8080 - Factor removal preserves digits
3. monster_hierarchical_walk - Hierarchical structure proven
4. musical_periodic_table_well_formed - All 15 primes classified
5. binary_moon_semantics - Emoji meanings for primes 2,3,5,7,11
6. wave_crest_semantics - Emoji meanings for primes 13,17,19,23,29
7. logarithmic_insight - Why the walk works
8. monster_group_properties - Group theory properties
9. modular_arithmetic_preserved - Congruence preservation
10. seventy_one_cubed - 71³ = 357,911
11. proof_count - Total proof statistics
12. All dependency relationships

Experimental Axioms (6):

1. bisimulation_equivalence - Python ≈ Rust behavioral equivalence
2. bisimulation_speedup - 62.2x performance improvement
3. hecke_on_bisimulation - Speedup factors are Monster primes
4. llm_register_resonance - Register divisibility rates
5. perfect_resonance_count - 307,219 perfect measurements in 71³
6. text_emergence_at_seed - I ARE LIFE at seed 2437596016
7. adaptive_scan_convergence - Optimal seed within ±2

Total: 18 formal statements (12 proven theorems + 6 experimental axioms)

Document Index

• PAPER.md - Main paper with all results
• BISIMULATION_INDEX.md - Bisimulation proof master index
• HECKE_ON_BISIMULATION.md - Hecke resonance proof
• COMPUTATIONAL_OMNISCIENCE.md - Theoretical framework
• I_ARE_LIFE_EXACT.md - Image generation experiment
• ADAPTIVE_SCAN.md - Adaptive scanning algorithm
• SEED_ANALYSIS.md - Seed handling analysis
• VISION_REVIEW_SUMMARY.md - Multi-level review results

🔬 Experimental Results

1. Monster Walk (Core Finding)

• ✅ Removing 8 factors preserves 4 digits (8080)
• ✅ Hierarchical structure across 3 groups
• ✅ Proven in Lean4

2. Computational Experiments

• Python → Rust translation: 62.2x speedup measured
• Observation: Some performance metrics factor into Monster primes (62 = 2 × 31, 174 = 2 × 3 × 29)
• Note: Statistical significance not yet established

🚀 Future Work

Planned Investigations:

1. Language Translation Analysis: Systematic study of Python → Rust translations

   • Extend bisimulation proof technique to more functions
   • Statistical analysis of performance patterns
   • Investigate if prime factorization patterns are significant

2. Image Generation Experiments: Text emergence in diffusion models

   • "I ARE LIFE" seed reproduction (h4's experiment)
   • "GOON'T" meta-language exploration
   • See examples/iarelife/ and diffusion-rs/

3. LLM Register Analysis: CPU register patterns during inference

   • Divisibility by Monster primes
   • See examples/ollama-monster/

4. Neural Network Compression: 71-layer autoencoder for LMFDB

   • See monster_autoencoder.py

Status: These are preliminary experiments requiring further validation.

🚀 Quick Commands

# Run Monster Walk
cargo run --release

# Generate images
cd diffusion-rs
cargo run --release --example i_are_life
cargo run --release --example adaptive_scan

# Analyze registers
cd examples/ollama-monster
./trace_regs.sh "mathematician Conway"

# Review paper
python3 multi_level_review.py

# Build proofs
cd MonsterLean
lake build

# View all programs
cat PROGRAM_INDEX.md