Chapter 4: MeriToken Model

4.1 Model Overview

MeriToken is the core measurement unit of GMC. Its design must answer a key question: How can contribution measurement reflect current activity while also respecting historical contributions?

The answer is: exponential decay + non-zero floor value.

4.2 Two Key Values

Each MeritPocket maintains two core values:

• curMerit (current MeriToken): The real-time contribution measurement value; decays over time and grows with new contributions
• minMerit (floor value): The lower bound of decay, representing the long-term sediment of historical contributions; only increases (except under penalties)

curMerit ≥ minMerit ≥ e (initial value)

4.3 Acquisition

MeriToken is acquired through contributions; the system mints new Tokens:

Acquisition Method	Description	Trigger Condition
Objective measurement	Automatically calculated based on verifiable metrics	System automatically records threshold met
Task bounty	Preset Merit for a specific task	Stakeholders vote to approve upon completion
Initial allocation	Granted upon network registration	Identity registration completed

Initial value = e ≈ 2.718 (the natural constant, naturally aligned with the exponential decay model).

4.4 Decay Model

Core Idea

Each Merit acquisition batch has an independent influence duration. The influence duration reflects the timeliness of that contribution — a contribution with 100 days of influence has its Merit fully decayed within 100 days.

Single-Batch Decay Formula

MeriToken_i(t) = (V_i - B_i) × e^(-λ_i × t) + B_i

• V_i: Initial Merit value of the batch
• B_i: The batch's contribution to the floor value
• λ_i: Decay coefficient, determined by influence duration T_i (λ_i = k / T_i, where k is a constant)
• t: Time elapsed since acquisition

Total Current MeriToken

curMerit = Σ MeriToken_i(t)  (sum of all active batches)

When all batches have fully decayed, curMerit approaches minMerit.

4.5 Floor Value (minMerit)

Update Rule

Each time new Merit is acquired, the floor value is updated:

Let current curMerit = M, newly acquired Merit = x, current floor value = B, then:

New floor value B' = (x + M) × B / M

Meaning: The floor value grows in proportion to the new Merit's share of the total.

Properties

• Starting value = e ≈ 2.718
• Only increases (except under penalties)
• Represents the indelible sediment of historical contributions
• Even if contributions cease entirely, curMerit will ultimately never fall below minMerit

Edge Case

When curMerit = minMerit (i.e., at the floor state) and new Merit x is acquired:

B' = (x + B) × B / B = x + B

The floor value increases directly by x — meaning Merit acquired while at the floor state is entirely deposited as floor value.

4.6 Implementation of Per-Batch Independent Decay

Challenges

• Each MeritPocket must maintain a list of Merit batches
• Querying the current value requires iterating over all batches that have not fully decayed
• On-chain storage and computation costs grow linearly with the number of batches

Optimization Strategies

1. Batch merging: Batches with similar influence durations are periodically merged to reduce active batch count
2. Off-chain computation: Use Rollup to compute real-time values off-chain; only store snapshots and proofs on-chain
3. Batch sedimentation: When the maximum active batch count is exceeded, the oldest batches are automatically sedimented into the floor value
4. Lazy computation: Precise values are only calculated when needed (e.g., during voting or queries)

4.7 Design Philosophy

Why Exponential Decay?

• Incentivizes continuous contribution rather than a single large contribution followed by inactivity
• Reflects the timeliness of contributions — more recent contributions have greater impact on current reputation
• Naturally simulates the decay of social memory
• Decays rapidly at first and slows later, aligning with intuition

Why a Non-Zero Floor?

• Acknowledges the long-term value of historical contributions — past efforts do not completely zero out
• Prevents long-term contributors from losing all voting power due to a brief pause
• The floor value grows with cumulative contributions, rewarding sustained participation

Why Independent Influence Duration Per Batch?

• Different contributions naturally have different timeliness
• A single customer service interaction may have an influence of only 30 days
• Maintaining an open-source project may have an influence lasting years
• A uniform decay rate would distort the value of different types of contributions

4.8 Discussion Notes

Key decisions in the MeriToken model:

• Exponential decay + non-zero floor: Strikes a balance between "incentivizing continuous participation" and "respecting historical contributions"
• Independent influence duration per batch: Increases implementation complexity but more accurately reflects differences in contribution timeliness
• Floor value only increases (except under penalties): Protects the fundamental rights of long-term contributors
• Initial value of e: Combines mathematical elegance with practical significance

To be further examined: Whether the floor value update formula behaves reasonably under extreme conditions