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)

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)

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:

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

# 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
• Move Prover Documentation
• PyUSD Contract Addresses

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

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.