> For the complete documentation index, see [llms.txt](https://docs.getrekt.trade/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.getrekt.trade/mint-curve.md).

# mint curve

The new emissions curve depends on cumulative eligible losses, not LP balance. This replaces the old LP-threshold curve in the product specification; implementation remains outstanding.

## Marginal rate

Let L be prior cumulative eligible losses in USDC and H = 10,000,000 USDC:

```
epoch(L) = floor(L / H)
rate(L) = 10,000 / 2^epoch(L)
```

For a new gross eligible loss B, integrate that rate from L to L+B. Every portion of B uses the epoch it falls into. Cash and debt losses use this same formula and same platform-wide counter.

| Prior L    | New loss B | Ideal reward          |
| ---------- | ---------- | --------------------- |
| 0          | 100        | 1,000,000 $REKT       |
| 9,999,990  | 20         | 150,000 $REKT         |
| 10,000,000 | 100        | 500,000 $REKT         |
| 0          | 25,000,000 | 162,500,000,000 $REKT |

The last row illustrates multiple boundaries mathematically; it does not imply a single position of that size is permitted.

## Theoretical total

Each complete epoch emits half as much as the previous one:

```
100 billion + 50 billion + 25 billion + ...
= 200 billion $REKT
```

This is an asymptote under the stated curve, no premint and no other issuance. It is not evidence of a deployed max-supply check. Upgrade authority and implementation precision still matter.

## Proposed exact integer specification

The current reward ledger and USDC both use six decimal places. To prevent splitting a loss into smaller settlements from changing total platform issuance, the proposed implementation uses differences of a globally rounded cumulative supply. It must not round the per-USDC rate to an integer first.

Let l be cumulative loss in micro-USDC, h = 10,000,000,000,000 micro-USDC, n = floor(l/h), and q = l mod h. Let A = 200,000,000,000,000,000 reward atoms.

```
C(l) = A − ceil(((2 × h − q) × 10,000) / 2^n)
minted_atoms(l, b) = C(l + b) − C(l)
```

C is the cumulative ideal supply rounded down to whole reward atoms. Carrying the global fractional remainder means a settlement can receive one more atom than rounding its own reward independently. Total issuance depends only on total eligible loss; individual users' amounts still depend on settlement order and the epoch reached.

Use checked wide-integer arithmetic, not floating point. Very large epochs need an explicit safe branch: with these constants, n ≥ 58 gives C(l) = A − 1, so no unbounded bit shift is needed. Under this exact proposal, finite cumulative issuance reaches at most 199,999,999,999.999999 $REKT. It never needs to round upward to 200 billion.

{% hint style="warning" %}
This rounding rule is a proposed implementation specification, not current contract behavior. Validate the smallest loss unit, both sides of every boundary, multi-epoch losses, different settlement partitions, duplicate closes and global-counter migration before release. [Implementation status](broken://pages/c7eabe8af8c3f2ae7c1c1dce69dad717e5d1ac7a).
{% endhint %}


---

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