aptos-gf3-society

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Original

English

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Translation

Chinese

aptos-gf3-society Skill

Aptos GF(3) 社群Skill

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

"求和为零的社群才是可持续的社群。"

Overview

概述

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).

Aptos GF(3) 社群使用Move智能合约实现链上三元协作。所有操作都保持GF(3)守恒：所有trit赋值的总和与0同余（模3）。

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

GF(3) Trit编码（兼容Move 1.x）

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

move

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

角色	Trit	u8	功能
GENERATOR	+1	2	创建、提案、质押
COORDINATOR	0	0	调解、平衡、投票
VALIDATOR	-1	1	验证、质询、审计

Denotation

说明

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

本Skill可生成Aptos Move模块，实现具备自动守恒强制机制的GF(3)平衡治理、质押与资产管理。

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

Core Modules

核心模块

1. PyUSD Staking (

pyusd_staking.move

)

1. PyUSD质押（

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
    }
}

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

)

2. IECsat瓦片（

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

具备69字节互感知能力的Plus Code瓦片：

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

)

3. 审计数据库（

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 ✓

来自6家审计机构的18份审计报告，全部符合GF(3)平衡：

sql

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

Officially Audited Modules

官方审计模块

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

来自

aptos_audits.duckdb

，可安全用于生产环境：

模块	验证方式	要求
`coin`	Move Prover	守恒：result.value == amount
`account`	Move Prover	exists<Account>(new_address)
`timestamp`	Move Prover	单调性：new >= current
`stake`	Move Prover	验证者管理
`fungible_asset`	Move Prover	供应量守恒

Storage Cost Analysis

存储成本分析

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

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

策略：分层懒加载

链上：10字符根瓦片 + Merkle根
链下：存储在Arweave/IPFS中的11-17字符瓦片
证明：从根到叶子的Merkle路径

GF(3) Triads

GF(3)三元组

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

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

不变量集合

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

不变量	定义	执行方式
`GF3Conservation`	Σ(trit) ≡ 0 (mod 3)	运行时断言
`TriadCompleteness`	每个操作都需要生成者(G)+协调者(C)+验证者(V)	投票计数
`StakeNonNegative`	质押额 ≥ 0	u64类型
`CooldownEnforced`	最低质押冷却期24小时	时间戳检查

Commands

命令

bash

undefined

bash

undefined

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"

undefined

duckdb aptos_audits.duckdb -c "SELECT * FROM gf3_audit_triads"

undefined

Files

文件结构

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

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

参考资料

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

Skill名称：aptos-gf3-society 类型：链上治理 / 智能合约 Trit：+1（PLUS - 生成者） GF(3)：创建保持守恒的社群

Cat# Integration

Cat# 集成

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)

本Skill在Prof范畴中映射为双余模Cat# = Comod(P)：

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

GF(3) Naturality

GF(3) 自然性

The skill participates in triads where:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.

本Skill参与以下三元组：

(-1) + (0) + (+1) ≡ 0 (mod 3)

aptos-gf3-society

Original

Translation

aptos-gf3-society Skill

Aptos GF(3) 社群Skill

Overview

概述

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

GF(3) Trit编码（兼容Move 1.x）

Denotation

说明

Core Modules

核心模块

1. PyUSD Staking (pyusd_staking.move)

1. PyUSD质押（pyusd_staking.move）

2. IECsat Tiles (plus_codes.move)

2. IECsat瓦片（plus_codes.move）

3. Audit Database (aptos_audits.duckdb)

3. 审计数据库（aptos_audits.duckdb）

Officially Audited Modules

官方审计模块

Storage Cost Analysis

存储成本分析

GF(3) Triads

GF(3)三元组

Invariant Set

不变量集合

Commands

命令

Query audit database

Query audit database

Build Move contracts

Build Move contracts

Deploy to testnet

Deploy to testnet

Check GF(3) conservation

Check GF(3) conservation

Files

文件结构

References

参考资料

Cat# Integration

Cat# 集成

GF(3) Naturality

GF(3) 自然性

1. PyUSD Staking (
`pyusd_staking.move`
)

1. PyUSD质押（
`pyusd_staking.move`
）

2. IECsat Tiles (
`plus_codes.move`
)

2. IECsat瓦片（
`plus_codes.move`
）

3. Audit Database (
`aptos_audits.duckdb`
)

3. 审计数据库（
`aptos_audits.duckdb`
）