Paired L+S tokens

Mint produces matched long and short tokens. Here’s why, and how the two settle against the underlying.

A Continuum position is a pair of SPL tokens: one long (L), one short (S). They are minted and redeemed at the protocol’s NAV, but trade independently on the protocol’s native per-side books and committed-order venue.

What “paired” means

When you call mint_paired(amount), the protocol:

1. Reads L_NAV from the oracle.
2. Derives S_NAV = (initial_l × initial_s) / L_NAV (constant-product inverse).
3. Splits amount (after fees) in half by value, not quantity.
4. Mints (amount / 2) / L_NAV long tokens and (amount / 2) / S_NAV short tokens.

The two quantities differ - usually by a lot. For QQQ at L_NAV = 480, S_NAV = 0.00208, a 100 cUSDC mint produces ~0.104 QQQL and ~24,038 QQQS.

The value of each leg at mint time is identical (50 cUSDC each, before fees). As the underlying price moves, the long leg’s value rises while the short leg’s falls reciprocally.

Why pairs, not single sides

A user-facing single-sided mint is unsafe. Minting only L without an offsetting S deposit creates an unbacked claim against the collateral vault. If 1,000 users each minted L-only at NAV, the vault would be drained on redemption while the short side’s mints would have nothing to settle against.

Paired mint sidesteps this: every cUSDC of collateral is matched by tokens whose combined value is exactly that cUSDC (modulo fees). The vault’s solvency is structural, not dependent on price.

The keeper has a fee-free single-sided mint/redeem path - but it’s gated by signer match against market.keeper_authority, and used only inside arb cycles that net back to cUSDC. See Solvency invariants.

The constant-product invariant

L_NAV × S_NAV = initial_l × initial_s  (always)

This is the heart of Continuum. It means:

• As L_NAV rises, S_NAV falls reciprocally, not linearly.
• Combined pair value L_NAV + S_NAV is bounded; it has a minimum at L_NAV = S_NAV = √(initial_l × initial_s) (geometric mean) and grows as either NAV moves away from that point.
• The short side asymptotically approaches zero but never crosses below - short-token holders never owe more than they paid.
• The long side can appreciate unboundedly while the short side provides diminishing counterpart.

→ Full NAV math

P&L of a paired position

Suppose you mint at QQQ = 480 (L = 480, S = 1, paired value 481):

Mint: 100 cUSDC → 0.104 QQQL @ 480 + 49.95 QQQS @ 1

If QQQ rises 10% to 528:

L_NAV = 528             (proportional)
S_NAV = 480 × 1 / 528 = 0.909
Position value = 0.104 × 528 + 49.95 × 0.909
              = 54.91 + 45.40
              = 100.31 cUSDC

If QQQ falls 10% to 432:

L_NAV = 432
S_NAV = 480 × 1 / 432 = 1.111
Position value = 0.104 × 432 + 49.95 × 1.111
              = 44.93 + 55.49
              = 100.42 cUSDC

The paired position has near-zero net delta. It’s essentially neutral - the value drift is just the geometric-mean curvature of the constant product. To actually take a directional view, you sell one of the legs.

Selling a leg

Each side has its own native book (QQQL/cUSDC and QQQS/cUSDC), plus the committed-order path for size:

• Sell QQQL (or buy QQQS) to express a bearish view; buy QQQL (or sell QQQS) for bullish.
• Small amounts hit the book instantly; large amounts route as committed orders filling at the next oracle print at NAV ± 10bps.

A common flow:

1. mint_paired(100 cUSDC)              → 0.104 QQQL + 49.95 QQQS
2. sell the S leg: 49.95 QQQS → ~50 cUSDC
                                       → net: 0.104 QQQL + 50 cUSDC
                                       (long-only position, fully funded)

You started with 100 cUSDC and now hold a long-only QQQ position worth ~100 cUSDC plus 50 cUSDC of dry powder. The 50 cUSDC came from selling the short leg into the protocol’s standing bid.

The reverse - sell QQQL, hold QQQS - gives you a short-only exposure.

What if NAV and book price disagree?

In v2 they can’t disagree by much, by construction: every venue prices off the same NAV. The instant oracle swap quotes NAV directly; committed orders fill at a price set after the commitment; and the books are re-pinned to NAV whenever drift exceeds the per-market gate. Any residual gap is bounded by max(reposition gate, half-spread) + the paired-arb fee hurdle - see Peg maintenance.

If a fast move does leave a book stale for one keeper cycle, an arber can lift the in-the-money bins - the loss is capped at those bins’ deliberately lean depth, and the next cycle re-pins. Anyone can run that arb; the books charge real bin-ladder slippage, so near NAV there is rarely anything to take.

Decimals and minimums

Token	Decimals	Minimum mint
cUSDC (collateral)	6	10_000_000 lamports = 10 cUSDC
L tokens	6	n/a (derived from cUSDC)
S tokens	6	n/a (derived from cUSDC)

The minimum is enforced by the program (InvalidAmount / BelowMinimum errors).

Token metadata

Long and short SPL mints have Metaplex token metadata (name, symbol, image). Wallets and explorers display them as e.g. “QQQ Long” / “QQQS” with the Continuum logo.

→ Live markets table lists every long/short mint pubkey.

Common questions

Q: Are paired tokens ERC-20-style approval-required? No. They are SPL tokens. Solana uses Associated Token Accounts (ATAs); there is no approve step.

Q: Can I transfer the paired position to another wallet? Yes. Both L and S are standard SPL tokens. Transfer them like any other Solana token. The receiver can independently redeem at NAV.

Q: Do I have to redeem in pairs? No. Mint must be paired; redeem can be any combination of L and S the user holds. Redemption is value-weighted, not quantity-paired.

Q: What happens if I lose access to half the pair? The other half is still redeemable on its own. Solvency invariant 1 (paired-only mint) doesn’t apply to redeem - see Solvency.

Q: Are there fees on transfers? No. Continuum’s fees are at mint and redeem (mint_fee_bps, redeem_fee_bps, both ~10 bps). Transfers are free at the protocol layer; you pay normal Solana fees only.