Exogenous collateral · negative feedback · full reserve

The oil peg as a
control system.

An oil-backed token can be algorithmic, mint and redeem are a feedback law around a price the protocol does not set. Crude already has a world market. The token is pinned to that market by arbitrage, inventory constraints, and a fee schedule that is a function of tank state, not of belief.

1 obl ≡ 1 quality-equivalent barrel · 42 US gal after grade adjustment
Status: formal sketch · no deployment · no encumbered oil · not an offer

$ mint --bbl 1.0 --grade WTI --hub cushing

✓ assayed q = 1.004 · tanked 0.996 bbl → 1 obl

$ redeem --token 1 --hub rotterdam

✓ burned 1 obl → netback 0.981 bbl after freight & queue

invariant: supply ≤ Σ qᵢ vᵢ · token arrival ≠ barrel arrival

01 — Thesis

Why an algorithmic oil peg is even a coherent sentence.

Call a peg algorithmic when the restoring force is a published function of state, not a discretion of an issuer. Three objects are enough.

Exogenous spot $S_t$World liquids demand is on the order of 100 million barrels a day. A token float of even several billion dollars is hours of physical flow. $\partial S / \partial P \approx 0$. The collateral price is not a function of the token price.

Endogenous inventory $I_t$Tanks, not a treasury. Float cannot exceed assayed, unencumbered stocks. This is the anti-reflexivity constraint algorithmic coins delete.

Policy $\pi(I, Q)$Mint cost and redeem cost are functions of fill and of the redemption queue. The algorithm does not set the oil price. It sets the width of the no-arbitrage band.

ArbitrageursThe actuators. If they have capital and a legal path to a hub, the band is enforced. If they do not, the algorithm is a PDF.

Terra failed because collateral value was an increasing function of token demand. Oil demand from refineries does not read the obl order book.

The comparison case is not Tether and not USO. Tether is a claim on dollars held off-system. USO was a claim on futures rolls, and the roll — not the barrel — dominated the return. obl as specified is a warehouse receipt with a burn right. Its dollar volatility should match crude. Stability is against oil, not against the dollar. Anyone selling dollar-stability is selling a second instrument: a hedge, with margin, which this note refuses to hide inside the token.

02 — Objects

A quality-equivalent barrel, not “oil” as a vibe.

Crude is not homogeneous. The mint function first maps a cargo to benchmark-equivalent volume. API gravity, sulfur, and basic sediment & water are the first-order basis.

$$ q(g) = 1 + \alpha(\mathrm{API}-\mathrm{API}_0) - \beta(S-S_0) - \gamma\,\mathrm{BSW} $$

A delivery of physical volume $v$ mints $n = v\, q(g)$ tokens, and only if $q(g)$ clears a floor. Off-spec crude does not enter the float at par. Redemption inverts the map at the chosen hub:

$$ v_{\mathrm{out}} = \frac{n}{q(g_{\mathrm{hub}})} - \text{shrinkage} - \text{freight in kind} $$

Location is priced by netback, not by a slogan that all hubs are one good. Let $f_{h,h^\star}$ be the cost of moving a barrel from hub $h$ to the holder’s hub. The redeemable packet is the solution of a tiny linear program over hubs that currently have free stock:

$$ h^\star = \arg\max_h \big( q_h v_h - f_{h,h_{\mathrm{ask}}} \big) \quad \text{s.t.}\quad v_h \le I_h $$

That program is the algorithm. It is operations research. It does not require a new monetary theory.

03 — The band

No arbitrage is the peg. The fee schedule is the algorithm.

Let $P_t$ be the token price in dollars per obl, $S_t$ the benchmark spot, $c_m$ the all-in cost of creating a token, $c_r$ the all-in cost of destroying one. Any price outside the band is a free lunch for someone who can touch a tank.

$$ S_t - c_r(I_t, Q_t) \;\le\; P_t \;\le\; S_t + c_m(I_t) \tag{1} $$

Inside the band, arbitrage is idle. The token may wander. That wandering is not a broken peg; it is the bid-ask of the physical world. A design that displays a flat dollar price through a pipeline outage is lying.

The algorithmic part is how costs depend on state. Fill fraction $\phi = I / I_{\max}$. Queue depth $Q$ in barrels waiting on trucks or berths.

$$ c_m(\phi) = c_0 \,(1-\phi)^{-\eta}, \qquad \eta > 0 \tag{2} $$

$$ c_r(Q) = c_1 + \lambda Q \tag{3} $$

Equation (2) is a soft capacity constraint. As tanks fill, minting becomes uneconomic before the tank is physically full, so the float cannot be forced through the walls by a mint rush. Equation (3) prices congestion instead of freezing redemptions. A freeze is how commodity schemes become banks. A queue fee is how they stay warehouses.

Carry sits under the band, not inside a hidden yield. Working’s storage relation, in continuous form:

$$ F_{t,T} = S_t \, e^{(r+u-y)(T-t)} \tag{4} $$

$u$ is proportional storage cost,

The oil peg as acontrol system.

Why an algorithmic oil peg is even a coherent sentence.

A quality-equivalent barrel, not “oil” as a vibe.

No arbitrage is the peg. The fee schedule is the algorithm.

The oil peg as a
control system.