TWAP and Executable Capacity

Mature TWAP confirmation, immediate spot constraints, and lending inventory jointly determine maximum executable short-selling capacity.

Three Distinct Constraints

Constraint	Question answered	Data source
Risk Curve	How much theoretical net selling is currently permitted?	Fixed-parameter model
TWAP + spot	Which price increases are confirmed, and does the current price contract capacity?	V2 cumulative prices and live reserves
Borrowable Token / exact output	Can inventory actually be sold for this much USDC?	Engine ledger, Token balance, live Pair

The amount that can ultimately be opened depends on all three, not on a single market-cap table.

1. Cumulative Prices and TWAP

V2 records cumulative prices in external6 / token18 . Let A(t) be the cumulative value scaled by 2¹¹² , with Δt:

{\overset{―}{P}}_{raw, X 112} = ⌊ \frac{A (t_{1}) - A (t_{0})}{Δ t} ⌋

Converting to native18 market cap:

M_{TWAP} = ⌊ \frac{{\overset{―}{P}}_{raw, X 112} S 10^{12}}{2^{112}} ⌋

2. A Minimum Window Is Not a Fixed Rolling Window

The reference Engine family uses a minimum observation window of 300 seconds:

Δt < 300 seconds: Observation updates neither writes observation state nor raises the confirmed ceiling.
Δt ≥ 300 seconds: the average covers the entire period.

3. The Confirmed Ceiling Can Only Rise

At initialization, the capacity ceiling starts from fixed M₀ and C(M₀) , rather than zero capacity. No elapsed-time TWAP sample exists yet.

For a mature sample, the candidate market cap is:

M_{candidate} = max (M_{0}, min (M_{TWAP}, M_{t}))

The historical ceiling rises only when the candidate exceeds it. Let H be the confirmed market-cap ceiling and $C_H$ the confirmed capacity ceiling:

H^{'} = max (H, M_{candidate}), C_{H}^{'} = max (C_{H}, C (H^{'}))

Ordinary price declines do not reduce these two historically confirmed ceilings. Actual available capacity is still immediately limited by spot.

4. Immediate Spot Constraints

M_{s} = min (max (M_{spot}, M_{0}), M_{t})

M_{effective} = min (H, M_{s})

C_{effective} = min (C_{H}, C (M_{effective}))

If total net sold across all existing positions is O = totalOpenShortNative:

C_{remaining} = max (C_{effective} - O, 0)

Spot falls: capacity for new positions contracts immediately, without waiting for a new TWAP.
Spot recovers: capacity can recover immediately within the confirmed ceiling.
Spot reaches a new high: the portion above the confirmed ceiling still requires mature TWAP confirmation.
Spot falls below M₀: the model still has an M₀ floor; this does not mean that all market risk disappears.

Scenario Example

Assume a historically confirmed market-cap ceiling of 10,000,000 USDC and existing net sold of 8,000 USDC:

Current spot market cap	Effective capacity (approx. USDC)	Remaining net-sale capacity for new positions (approx. USDC)
25,000,000	55,056.240673	47,056.240673; the increase above the old ceiling has not been released
1,000,000	10,518.095455	2,518.095455; immediate contraction
10,000,000	55,056.240673	47,056.240673; recovery within the old ceiling

This example calculates only the risk layer. Token lending constraints for the actual Pair may further reduce the final executable amount.

5. Token Inventory Constraints

L_{available} = L_{0} - L_{bad} - L_{borrowed}

The Engine's actual Token balance must also be at least its ledger balance available for lending. Additional Token transfers do not automatically increase L₀; if the balance is insufficient, the Quoter returns an error instead of continuing to show apparently available capacity.

Let T be the Pair's Token18 reserve,R its external6 USDC reserve, and L the Token18 available for lending. To ensure that V2's exact-output input calculation does not exceed L, the maximum external6 net sale amount permitted by inventory is:

E_{L} = ⌈ \frac{L \cdot 9,970 \cdot R}{T \cdot 10,000 + L \cdot 9,970} ⌉ - 1

L = 0 returns zero separately in that case.

Round this preview capacity down to external6, then take the smaller value:

E_{exec} = min (⌊ \frac{C_{remaining, preview}}{10^{12}} ⌋, E_{L})

Q_{sold, \max} = E_{exec} 10^{12}

N_{max} = ⌈ \frac{(Q_{sold, \max} + 1) 10,000}{9,900} ⌉ - 1

If Qsold,max = 0, notional principal is also zero. Adding 1 and subtracting 1 here are raw native18 integer units, not 1 USDC.

6. A Quote Is Not an Execution Guarantee

Preview and confirmed state are distinct fields and should be displayed separately.
Swaps, other users' position openings, tax-Token conversions, or the passage of time may occur after a quote.
Executable notional is still not a complete trade quote: the user must also meet collateral, maximum Token borrowing, and six-decimal exact net-output requirements.