# Seigniorage Tax

HOLI staking emission is neither an OHM-style free rebase nor a bond sale. Stakers accrue newly minted HOLI through the rising HOLI-per-sHOLI ratio, but that emission remains **untaxed protocol inventory** until the staker pays a USDG-denominated **seigniorage tax** to release it.

The distinction is deliberate:

* **Free rebase:** newly minted tokens become the staker's property without payment.
* **Bond:** a buyer first contributes an asset and receives newly issued tokens under separate sale terms.
* **HOLI seigniorage tax:** only stakers accrue emission; deposited principal remains theirs, while the newly minted portion becomes withdrawable only when its USDG tax is paid.

USDG tax proceeds enter Treasury **undeployed reserves**. The launch inflation pause is [7-Day Quiet Period](/launch/quiet-period). sHOLI balances, cooldown receipts, and entry-ratio accounting are [Staking](/staking).

## Premium and emission gate

Let <Md expr="P_t" /> be the HOLI/USDG TWAP and <Md expr="n_t" /> current NAV. The market premium is

<Eq expr="\pi_t = \frac{P_t}{n_t} - 1" />

New staking emission runs only when:

<Eq expr="P_t > 1.45\,n_t" />

If the gate fails, the emission rate is zero. After the launch quiet period, sHOLI governance controls whether emission is on and its rate. The gate remains an automatic upper constraint on that decision.

For an emission interval <Md expr="\Delta t" /> and approved HOLI-per-second rate <Md expr="r_t" />:

<Eq expr="E_t = \begin{cases} r_t\Delta t, & P_t > 1.45\,n_t \\ 0, & \text{otherwise} \end{cases}" />

Treasury mints <Md expr="E_t" /> HOLI into the sHOLI contract. It does not mint sHOLI. With effective sHOLI shares <Md expr="S_t^s" /> unchanged, the global HOLI-per-sHOLI ratio rises from <Md expr="R_t" /> to

<Eq expr="R_{t+1} = R_t + \frac{E_t}{S_t^s}" />

A position with <Md expr="s_i" /> effective shares therefore accrues

<Eq expr="\Delta X_i = E_t\frac{s_i}{S_t^s}" />

No MasterChef allocation, reward debt, harvest action, or priced emission receipt is required. The ratio performs the pro-rata allocation.

## Separating principal from newly minted HOLI

Each account has one weighted-average entry ratio <Md expr="R_{0,i}" /> after its matured receipts have been merged. At current ratio <Md expr="R_t" />, <Md expr="s_i" /> sHOLI represents

<Eq expr="G_i = s_iR_t" />

of gross HOLI. Its deposited principal and newly minted portion are

<Eq expr="B_i = s_iR_{0,i}" />

<Eq expr="X_i = s_i(R_t-R_{0,i})" />

Only <Md expr="X_i" /> is subject to seigniorage tax. Deposited principal is not taxed.

## USDG tax

Let <Md expr="\tau = 0.69" /> be the seigniorage-tax multiplier. The USDG tax price per newly minted HOLI is

<Eq expr="P_{\mathrm{tax}} = \max(n_t,\;\tau P_t)" />

For a withdrawal that contains <Md expr="X" /> newly minted HOLI:

<Eq expr="T_{\mathrm{USDG}} = X P_{\mathrm{tax}}" />

HOLI uses 18 decimals and USDG uses 6; implementation rounds the USDG payment up so a withdrawal cannot underpay because of integer division.

The 69% tax multiplier and the 45% premium gate are the same boundary viewed from two sides:

<Eq expr="\frac{1}{0.69} \approx 1.4493" />

At the gate, <Md expr="0.69P_t \approx n_t" />. Above it, the tax can add more than current NAV per released HOLI. The <Md expr="\max" /> protects Treasury if price or NAV changes between emission accrual and withdrawal.

After the user pays <Md expr="T_{\mathrm{USDG}}" />, the contract burns the withdrawn sHOLI and releases both principal and the taxed emission:

<Eq expr="\text{HOLI out} = B + X = sR_t" />

The released HOLI is transferable, sellable, or stakeable again. Restaking starts a new seven-day cooldown for that deposit.

## Partial withdrawal

Burning <Md expr="b" /> sHOLI removes the same proportion of principal and emission:

<Eq expr="B_b=bR_0,\qquad X_b=b(R_t-R_0)" />

The user pays <Md expr="X_bP_{\mathrm{tax}}" /> USDG and receives <Md expr="bR_t" /> HOLI. The remaining position keeps exactly the same <Md expr="R_0" />. Partial withdrawal does not create a new entry ratio.

If the user does not pay the seigniorage tax, the newly minted portion cannot leave the contract. A principal-only exit may return <Md expr="B_b" /> and leave <Md expr="X_b" /> as untaxed sHOLI inventory for the remaining pool; it must never hold deposited principal hostage.

## Supply and NAV timing

Emission HOLI minted into sHOLI is not yet externally released. Let <Md expr="U_t" /> be untaxed emission inventory held by sHOLI. Formal external supply excludes <Md expr="U_t" /> until the corresponding tax is paid. Deposited principal remains an external claim throughout staking and is **not** subtracted again.

On taxed withdrawal, two changes happen atomically:

1. <Md expr="X" /> HOLI leaves untaxed inventory and enters external supply.
2. <Md expr="XP_{\mathrm{tax}}" /> USDG enters Treasury assets.

Because <Md expr="P_{\mathrm{tax}}\ge n_t" />, releasing the emission does not issue it below current NAV. The complete denominator is [NAV Definition](/nav/definition).

The SHYT [green channel](/launch/green-channel) remains a separate market path: SHYT buys HOLI from SHYT/HOLI at the pool price. Seigniorage tax is the standing USDG inflow attached specifically to staking emission.