I almost fell off my chair reading your post on X, since I have been working on a closely related problem, with some subtle but important differences, for almost 5 years.
The way I like to frame P + N = 1 is that we change the “contract” between traders and LPs. Instead of creating a strict USD liability that has to be defended by liquidation, we let the payoff itself absorb the stress. The system stays fully collateralized because the two sides are always just splitting the same collateral.
In your construction this is done with expiring option-like claims:
P + N = 1
and at maturity:
P = min(1, S/x)
N = max(0, 1 - S/x)
That removes the need for liquidation and allows much slower oracle assumptions. But as you point out, the cost shows up elsewhere: rebalancing, slippage, expiry management, and tracking drift.
A novel approach
I would like to propose a closely related construction. It follows the same spirit as OP, but replaces expiring options with a perpetual liquidity-backed payoff.
Let x be the ETH/USD price. Let l be the target leverage, and let y be what I call the saturation price. Unlike the strike S in the option construction, y is not a price where one side expires worthless. It is the boundary between the convex zone and the saturation zone.
Define the trader side P, denominated as a share of the ETH collateral reserve, as:
P = (1/l) (x/y)^(l-1) when x <= y
P = 1 - ((l-1)/l) (y/x) when x >= y
and as before:
P + N = 1
Here P is the pooled trader side going long ETH/USD, and N is the LP side. Notice that 0 <= P <= 1. Also, neither side is wiped out at an ordinary strike. P goes to 0 only as ETH/USD goes to 0, and P goes to 1 only as ETH/USD goes to infinity.
At x = y: P = 1/l
and therefore: N = (l-1)/l
So the saturation price is the point where:
N = (l-1)P
In other words, it is the point where the LP side is exactly large enough to support leverage l.
Convex zone
For x <= y, the trader side follows a power-law payoff:
P'/P = (x'/x)^(l-1)
Since P is denominated in ETH collateral units, the USD value of the trader side scales as:
(x'/x)^l
So while the vault remains under saturation, the trader gets the path-independent payoff of constant leverage. There is no liquidation and no volatility decay in this region. Profitability depends only on the entry price, the exit price, and the upfront fee.
This is the region I call the convex zone. It is the payoff we would ideally want from constant leverage if it could be maintained perfectly without liquidations.
Saturation zone
For x >= y, the payoff becomes:
P = 1 - ((l-1)/l) (y/x)
so:
N = ((l-1)/l) (y/x)
This means the LP side is fixed in USD terms:
N * x = ((l-1)/l) y
So above saturation, LPs are no longer providing additional convexity. Their claim becomes fixed in the quote asset, and traders receive the residual ETH upside. This resembles a feeless margin trade or perp-like position.
This is where the system has run out of unused LP inventory. The position does not liquidate, but the payoff is no longer the ideal power payoff. Above saturation, returns become path-dependent and volatility decay can appear.
Oracle tradeoff
Your approach maximizes oracle safety. Because settlement happens at maturity, the oracle can be slow and dispute-friendly. The cost is that users or wrappers have to roll options and rebalance across strikes and maturities.
This construction makes a different tradeoff. It is perpetual and users can mint/burn continuously, so it needs an oracle for accounting. But because there are no liquidations, the oracle is not deciding when to forcibly close positions. It is only used for minting, burning, and reserve accounting.
That makes slower TWAPs much more acceptable, especially for deep pairs like ETH/USD. A manipulated oracle can still create bad entry or exit terms, but it does not trigger a liquidation cascade.
In the implementation I have been working on, SIR, this is done with Uniswap v3-style TWAPs, fee-tier selection by liquidity, and price truncation against multi-block manipulation.
Best-effort convexity
The protocol does not promise infinite free convexity.
As more traders enter, P grows relative to N. This pushes the saturation price y downward, which shrinks the convex zone. In other words, the more demand there is for convexity, the less convexity the vault can offer at the margin.
That is the self-balancing part. LPs are not forced to sell unlimited perpetual optionality at a fixed price. The payoff degrades when LP depth is insufficient.
So I think the two constructions are very close in spirit, but make different choices around expiry.
Your design gets the strongest slow-oracle guarantees by settling at maturity. The tradeoff is rolling, rebalancing, and expiry management.
This construction gives up some of that oracle purity in exchange for perpetual positions, continuous mint/burn, no expiry, no ongoing funding fee, and path-independent leverage as long as the vault remains below saturation.
The failure mode is also different. In the option construction, the cost shows up through tracking drift and rebalancing slippage. Here it shows up through LP-depth constraints: once the vault saturates, convexity degrades instead of pretending the system can provide unlimited constant leverage.
For context, this is live already. I can share Dune charts of our synthetic assets by DM or other information if interested.