# NAV Definition

Let <Md expr="A_t" /> be the marked external-asset total at <Md expr="t" />: USDG, SHYT, eligible RWA, and the **external legs of LPs**. The protocol holds **only governance-approved assets**. Official NAV is **1×** those external legs. Do not 2× an LP. The **SHYT in the green-channel (SHYT/HOLI) pool counts in NAV**; HOLI in that pool is in <Md expr="S_t^{\mathrm{treas}}" />, out of <Md expr="N_t" />, not added to <Md expr="A_t" />. Do not count Treasury-held HOLI again.

Let <Md expr="S_t" /> be on-chain HOLI total supply, <Md expr="S_t^{\mathrm{treas}}" /> Treasury-held HOLI — **including HOLI in protocol LP** — <Md expr="G_t" /> unsold HOLI still sitting on HOLIGenesis (`unsoldHoli()`), and <Md expr="U_t" /> untaxed staking-emission HOLI held inside sHOLI.

The protocol records **no book liabilities**. Formal NAV uses **external supply** — HOLI already released outside protocol inventory, not total issuance — as the denominator:

<Eq expr="N_t = S_t - S_t^{\mathrm{treas}} - G_t - U_t,\qquad n_t = \frac{A_t}{N_t}" />

Treasury-held HOLI is not an asset in <Md expr="A_t" /> and not a claim in <Md expr="N_t" />. It is dropped from both. Unsold Genesis inventory is also excluded until it is credited or sold. HOLIGenesis `holiCredit` is user-owned escrow: those tokens remain on Genesis until `withdraw`, but they already count in <Md expr="N_t" />. TreasuryNav adds only `unsoldHoli()` to Treasury-held HOLI. Untaxed sHOLI emission stays out of <Md expr="N_t" /> until released.

Do not subtract all HOLI held by the sHOLI contract. Deposited principal remains an external holder claim throughout staking and stays in <Md expr="N_t" />. Only the separately tracked untaxed-emission inventory <Md expr="U_t" /> is excluded. When <Md expr="X" /> emission is released, <Md expr="U_t" /> falls and <Md expr="N_t" /> rises by <Md expr="X" /> in the same transaction that USDG tax enters <Md expr="A_t" />.

Opening full-quota is one instance of this identity. Sizes live on the [opening balance sheet](/launch/opening-balance-sheet). This page is the identity.

How lines in <Md expr="A_t" /> are marked is [asset valuation & price sources](/nav/valuation). The dashboard **reads on-chain** and **updates NAV automatically**. [Transparency](/treasury-mgmt/transparency).

## POL accounting

### Uniswap V4 LP valuation

Protocol LP positions use a Uniswap V4 **full-range hook**. Treasury assets and positions are read and marked automatically by the contracts. Every LP in NAV pairs an independently priced external asset <Md expr="X_j" />—USDG, SHYT, a stock token, or another eligible asset—with HOLI; the protocol holds no StockA/StockB direct LPs. RWA enters as these external LP legs, not idle inventory.

Formal NAV counts **only the external-asset leg** of each LP in <Md expr="A_t" />. The SHYT/HOLI green-channel LP is a Treasury asset, and its SHYT counts at **1×**. HOLI in that pool is Treasury inventory, out of <Md expr="N_t" />, and is not added to <Md expr="A_t" />.

### External quantity and mark

For LP <Md expr="j" />, the contract reads the Treasury's current full-range V4 position liquidity and pool price to derive its current amounts. The current hook has no V4 LP fee: the only swap charge is the HOLI sell burn, which never becomes a position balance. If <Md expr="\alpha_{j,t}" /> is the position share and <Md expr="R_{j,t}^{X}" /> the external reserve, then

<Eq expr="q_{j,t}^{X} = \alpha_{j,t}\, R_{j,t}^{X}" />

and its external-leg mark is

<Eq expr="V_{j,t}^{\mathrm{ext}} = q_{j,t}^{X}\, p_{j,t}^{X}" />

<Md expr="p_{j,t}^{X}" /> is the USDG mark from the held pool's direct market quote, converted through the HOLI route. HOLI in that pool is already excluded from the denominator, so it must never be added to the numerator.

### Registration and sum

A Treasury pool is registered automatically when the Treasury creates it: Genesis SHYT/HOLI, the completed-Genesis HOLI/USDG pool, and later `deployLiquidity` HOLI pairs. The registry stores the external-leg address (`address(0)` for native ETH); a legacy Treasury position can be added only through the multisig migration function. A directly held ERC-20 is a separate multisig-controlled entry: the contract reads its `decimals()` itself and rejects unsupported precision. A direct balance needs a valid HOLI-route mark; direct dust for an automatic LP asset is counted once, not twice.

Let <Md expr="A_t^{\mathrm{nonLP}}" /> be undeployed reserves and other non-LP assets after removing double counts:

<Eq expr="A_t = A_t^{\mathrm{nonLP}} + \sum_j V_{j,t}^{\mathrm{ext}}" />

SHYT is fully circulating, so its market cap equals FDV for this mark. The sell-HOLI charge and slippage affect a trade fill, not the NAV print.