Epoch Decay

Emissions decrease over time through epoch-based decay, ensuring long-term sustainability.

Epoch Definition

epoch_index = floor(total_rounds_since_genesis / epoch_rounds)

Where:
- epoch_rounds = 525,600 (default)
- At ~2 min/round: 1 epoch ≈ 2 years

Decay Formula

Emissions follow a geometric decay:

E(n) = E₀ × r^n

Where:
- E(n) = emission at epoch n
- E₀ = base emission (250 PORB)
- r = retention rate (0.85 = 85%)
- n = epoch_index

Decay Visualization

PORB per Emission
250 │●
    │  ●
212 │    ●
    │      ●
180 │        ●
    │          ●
153 │            ●
    │              ●
130 │                ●
    └──────────────────────────
     E0  E1  E2  E3  E4  E5
          Epoch (2 years each)

Implementation

fn apply_decay(base: u128, epoch: u32, decay_bps: u16) -> u128 {
    if epoch == 0 {
        return base;
    }

    let mut result = base;
    for _ in 0..epoch {
        result = result * decay_bps as u128 / 10_000;
    }

    result
}

// Examples (base = 250, decay_bps = 8500):
// Epoch 0: 250 PORB
// Epoch 1: 250 × 0.85 = 212.5 PORB
// Epoch 2: 250 × 0.85² = 180.6 PORB
// Epoch 3: 250 × 0.85³ = 153.5 PORB

Emission Schedule

Epoch	Years	Per Emission	~Annual Emissions
0	0-2	250 PORB	6.5M PORB
1	2-4	212 PORB	5.5M PORB
2	4-6	180 PORB	4.7M PORB
3	6-8	153 PORB	4.0M PORB
4	8-10	130 PORB	3.4M PORB
5	10-12	111 PORB	2.9M PORB
10	20-22	49 PORB	1.3M PORB
20	40-42	10 PORB	0.3M PORB

Cumulative Distribution

Year	Cumulative Emissions	% of Budget
2	~6.5M PORB	6.5%
4	~12.0M PORB	12.1%
10	~24.1M PORB	24.2%
20	~37.0M PORB	37.2%
∞	~43.8M PORB	44.0%

The system never depletes the full 99.5M budget, ensuring extreme longevity.

Epoch Rollover

When a new epoch begins:

fn check_epoch_rollover(root: &mut RootAccount) {
    let new_epoch = (root.total_rounds_since_genesis / root.epoch_rounds) as u32;

    if new_epoch > root.epoch_index {
        emit!(EpochRolled {
            old_epoch: root.epoch_index,
            new_epoch,
            total_rounds: root.total_rounds_since_genesis,
        });

        root.epoch_index = new_epoch;
    }
}

Decay Constants

Constant	Value	Description
EPOCH_ROUNDS_DEFAULT	525,600	Rounds per epoch
DECAY_BPS_DEFAULT	8,500	85% retention (15% decay)
EMIT_BASE_DEFAULT	250 PORB	Base emission

Mathematical Proof

Theorem: Total emissions converge to a finite value.

Proof:

Total = Σ(n=0 to ∞) E₀ × r^n × N
      = E₀ × N × (1 / (1 - r))
      = 250 × 26,280 × 6.67
      ≈ 43.8M PORB

Where N ≈ 26,280 emissions per epoch (average gap = 10 rounds).

This is well under the 99.5M budget. ∎

Why Decay Matters

Sustainability

• Prevents rapid token depletion
• Ensures rewards for future players
• Creates predictable economics

Scarcity

• Early participants get higher rewards
• Creates natural value appreciation pressure
• Rewards early adoption

Balance

• Fast enough to be meaningful
• Slow enough to last 100+ years
• Gradual transition, no sudden drops

Next Steps

• Supply Mechanics - Full supply structure
• Liquidity Management - LP operations
• Economic Sustainability - The value loop