Market anatomy

A market is one account plus a handful of vaults, and one identity that every instruction must preserve.

The live reserve

For each side $i$ of the market (base or quote) the program stores a live reserve:

$$R_i = C_i + D_i^{f} + D_i^{\ell} + H_i$$

On the books

CCash

DLent out

HhLP's part

In the vault

CCash

BhLP backing

FFees held

ZRecenter funds

• $C_i$ is accounted cash. It is the only term that can leave in a swap or a withdrawal.
• $D_i^{f}$ and $D_i^{\ell}$ are cash-backed debt: public lending debt and isolated leverage debt. Each was created by handing cash to a borrower, so cash fell and debt rose by the same amount. Together they are $D_i^{cb}$.
• $H_i$ is the hLP live reserve, the part of the reserve owned by the two hedged vaults. It is a balanced liquidity coordinate, not a per-asset liability.

hLP funding debt $D_i^{h}$ affects utilization and the vaults' equity but is not added to the identity again; it is already represented through $H$. Without hLP the identity collapses to V1's: live reserve equals cash plus debt.

Borrow neutrality

A cash-backed borrow of $a$ moves $C_i \to C_i - a$ and $D_i^{cb} \to D_i^{cb} + a$, so $R_i$ does not change. Lending does not move the price. Trading does: a swap changes the inventory on both sides.

Unpaid interest is not inventory

Interest accrues into the debt balances. Writing $P$ for the principal counters, the unpaid interest on a side is

$$J_i = \max(D_i^{f} - P_i^{f},\,0) + \max(D_i^{\ell} - P_i^{\ell},\,0)$$

and the executable reserve the curve is built on is $X_i = R_i - J_i$. A receivable is not something a trader can buy. Quoting swaps from $R_q / R_b$ would be wrong twice over: it would count receivables as inventory and it would ignore the concentrated geometry.

Cash versus custody

Accounted cash is one claim on the physical reserve vault; it is not the only one. The vault must hold at least:

$$V_i^{\text{reserve}} \ \ge\ C_i + F_i^{\text{custody}} + B_i^{b} + B_i^{q} + Z_i$$

where $F$ is claimable swap-fee yield held outside executable reserves, $B^{b}, B^{q}$ is inventory backing the two hLP vaults, and $Z$ is surcharge retained to fund the curve's next recentering. Tokens donated to the vault outside an instruction do not become executable liquidity. Interest owed to lenders lives in a separate interest vault per asset, with its own accounting.

Shares

srLP is a fungible, market-wide, two-sided claim. For a supply of $S$ reserve shares and a burn of $s$, each side pays out

$$a_i = \left\lfloor \frac{s\,(R_i - J_i)}{S} \right\rfloor$$

that is, a proportional share of the reserve with unpaid interest left out, subject to cash, market-health and slippage checks. The unpaid interest belongs to whoever held the shares while it accrued: the market's income books pay it to them when borrowers pay, even after they have withdrawn. A deposit mints against the same basis, so new principal cannot buy interest that accrued before it arrived.

Owning a share is not an unconditional promise of redemption while the cash behind it is lent out. The program checkpoints published yield before any eligible balance changes, so a principal withdrawal never forfeits an unharvested claim.

jrLP is the first-loss tranche of the same reserve shares. Junior LP owns $S_J$ of the $S$ shares at its own exchange rate, absorbs funded losses before srLP, and takes the governed junior income share; srLP stays one-for-one with the other $S - S_J$. Senior and junior tranches covers both tranches.

The two hLP mints are shares of the aggregate hedged vaults. Their srLP ownership and funding debt are reconstructed algebraically at every trade's endpoint, which is why the total srLP supply $S$ and the ordinary supply $S_o$ held outside the vaults are tracked separately. The srLP the vaults hold is senior.

All four mints, srLP, jrLP and the two hLP, are Token-2022 tokens with transfer hooks, so a transfer can keep yield accounting correct. A direct burn bypasses the hooks; withdraw through the program instead. A direct jrLP burn becomes part of the permanent junior seed.

Accounts

Vaults per side: a reserve vault (cash, custody), a collateral vault (lending collateral), a leverage collateral vault, an interest vault. The accounts reference lists every field and the seeds that derive each address.

Invariants the program keeps

• srLP supply is backed by reserve-side principal; no instruction mints srLP without corresponding reserve value.
• Junior reserve shares never exceed the reserve shares outstanding. A tranche conversion moves ownership between srLP and jrLP and never moves an asset.
• Reserve principal excludes reserve-custodied swap-fee liabilities and interest-vault balances.
• Physical custody covers cash, fee custody, hLP backing inventory and protected recenter reserves; transitions conserve the accounted amount exactly.
• Only hLP transitions change $H_i$; hLP debt shares stay matched to aggregate vault funding debt, and hLP never uses srLP-denominated debt.
• Isolated leverage debt counts toward utilization but never enters a public borrower's health check.
• Leverage collateral vault balances match the collateral accounted across open leverage positions.
• Referral binding never changes principal, debt, interest, health or liquidation terms.