> For the complete documentation index, see [llms.txt](https://pijschain.gitbook.io/whitepaper/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://pijschain.gitbook.io/whitepaper/tokenomics/emission-model-and-daily-reward-formula.md).

# Emission Model & Daily Reward Formula

PIJSChain adopts a mathematically constrained emission model designed to balance early participation incentives with long-term economic sustainability. Rather than relying on fixed APR promises or discretionary reward adjustments, the protocol enforces a transparent, formula-driven daily reward mechanism tied directly to network participation and time-based decay.

The daily reward allocation is governed by the following formula:

&#x20;                           DailyReward = E . min( 1,(S / C. T)<sup>β</sup> ) . e<sup>−λt</sup>

Where:

* E represents the maximum daily token emission, set at 45,890 PIJS
* T denotes the maximum staking emission supply, equal to 117.3 million PIJS, representing 51% of total token supply
* S is the current effective staking amount across the network
* C is an efficiency coefficient dynamically adjusted based on total effective stake
* β (beta) controls the sensitivity of emission growth relative to staking participation
* λ (lambda) is the emission decay rate
* t represents time elapsed since network genesis

This formulation introduces three critical economic controls:

First, participation-sensitive issuance. When the network’s effective staking participation is low, emissions scale proportionally rather than releasing the full daily allocation. This prevents over-incentivization during periods of insufficient security contribution.

Second, controlled emission saturation. The min(1, …) constraint ensures that daily issuance never exceeds the protocol-defined maximum, regardless of excessive stake concentration. This preserves long-term supply discipline and prevents short-term reward inflation.

Third, time-based decay. The exponential decay factor ensures that rewards gradually decrease as the network matures, reinforcing the principle that early commitment is rewarded while long-term sustainability is protected.

Together, these mechanisms align economic output with real network contribution, ensuring that rewards are earned through participation, not speculation. Emissions are predictable, transparent, and resistant to manipulation—forming the economic backbone of PIJSChain’s commitment-first Proof-of-Stake model.


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