iecsat-storage Skill
"69 bytes of mutual awareness per tile. 3 × 23. Triadic by design."
Overview
IECsat Storage calculates on-chain storage costs for Plus Code tiles with GF(3)-conserved mutual awareness. Each tile maintains exactly 69 bytes of state.
The 69-Byte Structure
69 = 3 × 23 (triadic decomposition)
┌─────────────────────────────────────────────────────────┐
│ 69-BYTE TILE STATE │
├─────────────────────────────────────────────────────────┤
│ PLUS (+1) │ ERGODIC (0) │ MINUS (-1) │
│ 23 bytes │ 23 bytes │ 23 bytes │
│ GENERATOR │ COORDINATOR │ VALIDATOR │
├────────────────┼────────────────┼──────────────────────┤
│ state_hash │ neighbor_refs │ proof_data │
│ (20 bytes) │ (20 bytes) │ (20 bytes) │
│ trit (1 byte) │ trit (1 byte) │ trit (1 byte) │
│ flags (2 B) │ flags (2 B) │ flags (2 B) │
└────────────────┴────────────────┴──────────────────────┘
Σ(trit) = +1 + 0 + (-1) = 0 ✓ CONSERVED
Plus Code Precision Levels
| Length | Tiles | Resolution | Example | |--------|-------|------------|---------| | 2 | 162 | 2,226 km | Global quadrant | | 4 | 64,800 | 111 km | Country region | | 6 | 25.9M | 5.6 km | City district | | 8 | 10.4B | 278 m | City block | | 10 | 4.1T | 14 m | Building | | 11 | 83T | 70 cm | Room | | 13 | 33Q | 14 cm | Object | | 15 | 13 quint | 5.6 mm | Component | | 17 | 5.3 sext | 223 μm | Microstructure |
Storage Cost Analysis (Aptos Mainnet)
Pricing assumptions:
- Storage cost: 0.00001 APT per byte
- APT price: $12 USD
- Bytes per tile: 69
Cost formula:
APT = tiles × 69 × 0.00001
USD = APT × 12
Cost Table
| Precision | Tiles | Storage | APT | USD | |-----------|-------|---------|-----|-----| | 10-char | 4.15T | 286 TB | 2.86M | $34.3B | | 11-char | 82.9T | 5.7 PB | 57.2M | $687B | | 12-char | 1.66Q | 114 PB | 1.14B | $13.7T | | 13-char | 33.2Q | 2.29 EB | 22.9B | $275T | | 17-char | 5.31S | 366 ZB | 3.66Q | $44 quint |
Hierarchical Strategy
┌─────────────────────────────────────────────────────────┐
│ ON-CHAIN (APTOS) │
│ 10-char root tiles: 4.1T × 69B = 286 TB │
│ Cost: 2.86M APT ($34B) │
│ Contains: Merkle roots for child tiles │
├─────────────────────────────────────────────────────────┤
│ OFF-CHAIN (ARWEAVE) │
│ 11-17 char tiles: Content-addressed │
│ Proof: Merkle path from root → leaf │
│ Cost: ~$0.005/MB permanent storage │
└─────────────────────────────────────────────────────────┘
Denotation
IECsat : PlusCode → (TileState × MerkleProof)
where:
TileState = { plus: 23B, ergodic: 23B, minus: 23B }
MerkleProof = Path from 10-char root to target tile
Invariant: ∀ tile: Σ(trit) ≡ 0 (mod 3)
Practical Applications
Battery Cell Tracking (238.8B cells)
Cells: 238,800,000,000
Storage: 238.8B × 69B = 16.5 TB
APT: 165M APT
USD: $1.98B
Fraction of APT supply: 16.5%
Global Building Coverage (10-char)
All buildings worldwide: ~1 billion
Storage: 1B × 69B = 69 GB
APT: 690K APT
USD: $8.3M
Move Implementation
struct TileState has store, copy, drop {
// PLUS (+1) - 23 bytes
generator_hash: vector<u8>, // 20 bytes
generator_trit: u8, // 1 byte
generator_flags: u16, // 2 bytes
// ERGODIC (0) - 23 bytes
coordinator_refs: vector<u8>, // 20 bytes
coordinator_trit: u8, // 1 byte
coordinator_flags: u16, // 2 bytes
// MINUS (-1) - 23 bytes
validator_proof: vector<u8>, // 20 bytes
validator_trit: u8, // 1 byte
validator_flags: u16, // 2 bytes
}
public fun is_gf3_conserved(state: &TileState): bool {
let sum = (state.generator_trit as i8 - 1) + // 2 → +1
(state.coordinator_trit as i8) + // 0 → 0
(state.validator_trit as i8 - 1); // 1 → -1 (adjusted)
sum == 0
}
Commands
# Calculate storage for N tiles
python3 -c "
tiles = 4_147_200_000_000 # 10-char
bytes_per_tile = 69
apt_per_byte = 0.00001
apt_price = 12
total_bytes = tiles * bytes_per_tile
total_apt = total_bytes * apt_per_byte
total_usd = total_apt * apt_price
print(f'Tiles: {tiles:,}')
print(f'Storage: {total_bytes/1e12:.2f} TB')
print(f'APT: {total_apt/1e6:.2f}M')
print(f'USD: \${total_usd/1e9:.2f}B')
"
GF(3) Triads
iecsat-storage (0) ⊗ aptos-gf3-society (+1) ⊗ merkle-validation (-1) = 0 ✓
iecsat-storage (0) ⊗ plus-codes (+1) ⊗ content-addressing (-1) = 0 ✓
Skill Name: iecsat-storage Type: Storage Cost Estimation / On-Chain Economics Trit: 0 (ERGODIC - COORDINATOR) GF(3): Mediates between tile generation and validation
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.