aptos-gf3-society

# aptos-gf3-society Skill


> *"The society that sums to zero is the society that sustains."*

## Overview

**Aptos GF(3) Society** implements on-chain triadic coordination using Move smart contracts. Every operation maintains GF(3) conservation: the sum of all trit assignments is congruent to 0 (mod 3).

## GF(3) Trit Encoding (Move 1.x Compatible)

```move
const TRIT_ERGODIC: u8 = 0;  // COORDINATOR (0)
const TRIT_MINUS: u8 = 1;    // VALIDATOR (-1)
const TRIT_PLUS: u8 = 2;     // GENERATOR (+1)
```

| Role | Trit | u8 | Function |
|------|------|-----|----------|
| GENERATOR | +1 | 2 | Creates, proposes, stakes |
| COORDINATOR | 0 | 0 | Mediates, balances, votes |
| VALIDATOR | -1 | 1 | Verifies, challenges, audits |

## Denotation

> **This skill generates Aptos Move modules that implement GF(3)-balanced governance, staking, and asset management with automatic conservation enforcement.**

```
Society : (Members × Roles) → OnChainState
Invariant: ∀ state ∈ Society: Σ(trits) ≡ 0 (mod 3)
Effect: Proposals, votes, and stakes all preserve GF(3) balance
```

## Core Modules

### 1. PyUSD Staking (`pyusd_staking.move`)

```move
module aptos_society::pyusd_staking {
    struct StakingPool has key {
        generator_stake: u64,   // trit = PLUS (2)
        coordinator_stake: u64, // trit = ERGODIC (0)
        validator_stake: u64,   // trit = MINUS (1)
    }

    /// GF(3) balance check: generator ≈ validator stakes
    fun check_gf3_balance(pool: &StakingPool): bool {
        let gen = pool.generator_stake;
        let val = pool.validator_stake;
        if (gen == 0 && val == 0) { return true };
        ((larger - smaller) * 100 / larger) <= 10  // 10% tolerance
    }
}
```

### 2. IECsat Tiles (`plus_codes.move`)

Plus Code tiles with 69-byte mutual awareness:

```
69 = 3 × 23 (triadic structure)

Per tile:
  PLUS (+1):    23 bytes → GENERATOR state
  ERGODIC (0):  23 bytes → COORDINATOR state
  MINUS (-1):   23 bytes → VALIDATOR state
```

### 3. Audit Database (`aptos_audits.duckdb`)

18 audit reports from 6 auditors, all GF(3) balanced:

```sql
SELECT * FROM gf3_audit_triads;
-- auditor(+1) ⊗ protocol(0) ⊗ report(-1) = 0 ✓
```

## Officially Audited Modules

From `aptos_audits.duckdb`, safe for production use:

| Module | Verification | Requirement |
|--------|--------------|-------------|
| `coin` | Move Prover | Conservation: result.value == amount |
| `account` | Move Prover | exists<Account>(new_address) |
| `timestamp` | Move Prover | Monotonicity: new >= current |
| `stake` | Move Prover | Validator management |
| `fungible_asset` | Move Prover | Supply conservation |

## Storage Cost Analysis

```
Precision | Tiles           | Storage    | APT Cost    | USD Cost
----------|-----------------|------------|-------------|------------
10-char   | 4.1 trillion    | 286 TB     | 2.9M APT    | $34 billion
11-char   | 83 trillion     | 5.7 PB     | 57M APT     | $687 billion
17-char   | 5.3 sextillion  | 366 ZB     | 3.7 quad    | $44 quint
```

**Strategy**: Hierarchical lazy loading
- On-chain: 10-char root tiles + Merkle roots
- Off-chain: 11-17 char tiles in Arweave/IPFS
- Proof: Merkle path from root → leaf

## GF(3) Triads

```
pyusd_staking (+1) ⊗ datalog-fixpoint (0) ⊗ merkle-validation (-1) = 0 ✓
aptos-gf3-society (+1) ⊗ move-narya-bridge (0) ⊗ move-smith-fuzzer (-1) = 0 ✓
```

## Invariant Set

| Invariant | Definition | Enforcement |
|-----------|------------|-------------|
| `GF3Conservation` | Σ(trit) ≡ 0 (mod 3) | Runtime assert |
| `TriadCompleteness` | Every action requires G+C+V | Vote counting |
| `StakeNonNegative` | Stakes ≥ 0 | u64 type |
| `CooldownEnforced` | 24h minimum stake | Timestamp check |

## Commands

```bash
# Query audit database
duckdb src/nickel/aptos_society/aptos_audits.duckdb \
  -c "SELECT * FROM formally_verified_modules"

# Build Move contracts
cd src/nickel/aptos_society && aptos move compile

# Deploy to testnet
aptos move publish --profile testnet

# Check GF(3) conservation
duckdb aptos_audits.duckdb -c "SELECT * FROM gf3_audit_triads"
```

## Files

```
src/nickel/aptos_society/
├── Move.toml                 # Package config
├── aptos_audits.sql          # Audit schema
├── aptos_audits.duckdb       # Queryable audit data
├── aptos_llms_acset.clj      # Lazy docs ACSet
└── sources/
    ├── pyusd_staking.move    # GF(3) staking
    ├── society.move          # Governance
    └── gf3_move23.move       # Move 2.3 primitives
```

## References

- [Aptos Framework Formal Verification](https://medium.com/aptoslabs/securing-the-aptos-framework-through-formal-verification)
- [Move Prover Documentation](https://aptos.dev/build/smart-contracts/prover)
- [PyUSD Contract Addresses](https://www.paypal.com/us/digital-wallet/manage-money/crypto/pyusd)

---

**Skill Name**: aptos-gf3-society
**Type**: On-Chain Governance / Smart Contracts
**Trit**: +1 (PLUS - GENERATOR)
**GF(3)**: Creates societies that maintain conservation


## Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

### Graph Theory
- **networkx** [○] via bicomodule
  - Universal graph hub

### Bibliography References

- `general`: 734 citations in bib.duckdb

## Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the Prof home:

```
Trit: 0 (ERGODIC)
Home: Prof (profunctors/bimodules)
Poly Op: ⊗ (parallel composition)
Kan Role: Adj (adjunction bridge)
```

### GF(3) Naturality

The skill participates in triads where:
```
(-1) + (0) + (+1) ≡ 0 (mod 3)
```

This ensures compositional coherence in the Cat# equipment structure.