braindance-worlds
GF(3)-conserved distribution of Claude threads across Aptos worlds
When & Why to Use This Skill
This Claude skill provides a mathematically rigorous framework for distributing conversation threads across decentralized Aptos environments. By utilizing GF(3) arithmetic (Galois Field of 3) and semantic affinity mapping, it ensures that AI agent states are balanced, conserved, and logically organized by topic, enabling advanced decentralized memory management and verifiable data distribution.
Use Cases
- Decentralized State Management: Distributing AI agent memory and conversation history across blockchain-based 'worlds' while maintaining mathematical consistency and balance.
- Semantic Context Routing: Automatically assigning specific discussion topics—such as DAOs, Topology, or WASM—to dedicated storage environments based on their semantic affinity for optimized retrieval.
- Verifiable Thread Distribution: Leveraging GF(3) conservation laws to audit and verify that conversation data has been correctly partitioned and distributed across a network of nodes.
- Load Balancing for AI Agents: Using trit-based hashing to ensure an even spread of computational or storage load across multiple decentralized environments.
| name | braindance-worlds |
|---|---|
| description | GF(3)-conserved distribution of Claude threads across Aptos worlds |
| version | 1.0.0 |
Braindance Worlds
Distribute threads to worlds preserving Σ ≡ 0 (mod 3).
Algorithm
1. Hash each thread → trit ∈ {-1, 0, +1}
2. Sum thread trits: T = Σ(t_i)
3. Select worlds where Σ(w_j) ≡ -T (mod 3)
4. Match by semantic affinity (letter → topic)
Distribution (14 threads → 14 worlds)
| World | Trit | Thread | Topic |
|---|---|---|---|
| alice | +1 | 019b7219 | Continuation |
| world_c | +1 | 019b71d1 | Cantordust |
| world_f | +1 | 019b7643 | Drand |
| world_r | +1 | 019b71bb | R2con |
| world_x | +1 | 019b7622 | eXtract |
| bob | 0 | 019b7654 | Beacon |
| world_e | 0 | 019b74de | Embedding |
| world_n | 0 | 019b71e8 | NeurIPS |
| world_t | 0 | 019b71cb | Topology |
| world_w | 0 | 019b72ac | WASM64 |
| world_a | -1 | 019b71f0 | Automata |
| world_d | -1 | 019b74e1 | DAO |
| world_s | -1 | 019b71c8 | Sonification |
| world_v | -1 | 019b71d3 | Reverse |
Conservation
Σ(worlds) = 5(+1) + 5(0) + 4(-1) = +1
Σ(threads) = 2(+1) + 12(-1) = -10
TOTAL = -9 ≡ 0 (mod 3) ✓
Semantic Affinity Map
{:c "Cantordust" :r "Radare" :x "eXtract" :f "Fault-tolerance"
:e "Embedding" :n "NeurIPS" :t "Topology" :w "WASM"
:a "Automata" :d "DAO" :s "Sonification" :v "reVerse"}
Query
# Unzip + assign
unzip -l ~/Desktop/braindances.zip | awk 'NR>3{print $4}' | \
while read f; do echo "$f → world_$(echo $f | md5 | cut -c1)"; done
Unassigned Worlds
b g h i j k l m o p q u y z — available for future threads.