Decay Mechanics Reference

Sigmoid Decay Function

The decay rate for a wallet is calculated using a sigmoid curve applied to its concentration ratio:

concentration_ratio = wallet_balance / total_supply
decay_rate = max_decay_rate * sigmoid(concentration_ratio, threshold, steepness)

Fixed-Point Implementation

All calculations use u64 with 10^8 precision factor (PRECISION = 100_000_000).

The sigmoid is implemented as a precomputed lookup table with 1024 entries covering the [0, 1] range of concentration ratios. Linear interpolation between table entries.

// Lookup table entry
struct SigmoidEntry {
    input: u64,    // concentration_ratio * PRECISION
    output: u64,   // sigmoid_value * PRECISION
}

Parameters (Phase 1 defaults)

• MAX_DECAY_RATE: 5% per block period (5_000_000 in fixed-point)
• THRESHOLD: 1% of supply (1_000_000 in fixed-point)
• STEEPNESS: 10 (1_000_000_000 in fixed-point)

Cluster Index

Detects coordinated wallet groups attempting to evade decay by splitting holdings.

Algorithm

1. Build transaction graph for trailing CLUSTER_WINDOW blocks
2. Identify connected components (wallets that transact with each other)
3. Score each cluster: cluster_balance = sum(member_balances)
4. Apply decay to cluster_balance instead of individual balances
5. Distribute proportionally: each member decays by (member_balance / cluster_balance) * cluster_decay

Invariants

• Cluster merge must be commutative: merge(A, B) == merge(B, A)
• Cluster merge must be associative: merge(merge(A, B), C) == merge(A, merge(B, C))
• Singleton clusters (one wallet) must produce identical results to non-clustered decay

Decay Pool

Decayed tokens flow to the decay_pool. Miners receive: block_reward = base_reward + (decay_pool * REDISTRIBUTION_RATE).

Critical invariant: total_effective_supply + decay_pool == total_mined_supply must hold after every block.

See references/sigmoid-table-generator.md for the table generation algorithm.