The mechanism

The curve, and the floor beneath it

How x·y=k works, why the last token can never be bought, and where the permanently un-buyable floor comes from.

The equation#

Every ODIN pool is a Uniswap V2 constant-product market. Two reserves — x (ODIN) and y (the paired asset) — hold:

x \cdot y = k

k changes only when liquidity is added or removed — never from a swap. A trade moves reserves along the curve; the fee stays inside the pool, nudging k up.

ODIN's LP tokens are unreachable, so liquidity can never be removed. k has one direction:

\frac{dk}{dt} \geq 0 \quad \text{always}

Spot price is the reserve ratio, p = y/x. Real size costs more, because the curve bends — to buy Δx ODIN you deposit:

\Delta y = \frac{k}{x - \Delta x} - y

The last token cannot be bought#

As ODIN is bought, the remaining reserve shrinks and each token costs disproportionately more. Push Δx → x and the cost Δy → ∞.

The last token in a pool cannot be bought at any finite price. The reserve is an asymptote.

DeFi slang calls this a "bonding curve." Strictly it's a constant-product AMM curve, not a Bancor supply-mint curve. In ODIN discussion, "bonding curve" means this.

Sixteen automated holders#

Each pool behaves like a non-human market participant that always quotes both sides:

Not smarter than passive holders — immortal, unemotional, and self-deepening.

The floor: k ÷ max supply#

A capped counter-asset can never exceed its maximum supply, so nobody can ever add more than that much y to a pool. The ODIN reserve can never fall below:

\text{ODIN}_{\text{floor}} = \frac{k}{\text{counter-asset max supply}}

Extracting past that point would require more of the paired asset than will ever exist. That residual ODIN is permanently un-extractable — stranded by arithmetic, not merely expensive to reach.

Worked example — ODIN/TSUKA

At a snapshot with roughly 7.21M ODIN against 8.96M TSUKA, k ≈ 6.46 × 10¹³. TSUKA's max supply is 1,000,000,000.

Even if every TSUKA that will ever exist were funnelled into this pool:

x_{\min} = \frac{6.46 \times 10^{13}}{10^{9}} \approx 64{,}000 \text{ ODIN}

Roughly 64,000 ODIN in that pool can never be unlocked, by anyone, at any price.

Reserves drift, so recompute from current reserves rather than reusing these figures — that's the point of showing the method.

And the floor rises. k only ratchets up from fees, so k ÷ max_supply only grows — the one strictly monotonic quantity in the whole picture.

Which pairs qualify#

Ten of the sixteen carry a real cap and therefore a real floor:

SOJ · TSUKA · OHMI · PEAS · WAIT · DBI · APU · APE · SHIB · LINK

Why the other six are excluded

They can still mint, so there's no fixed ceiling to divide by:

  • WETH — mints on deposit
  • WBTC, OHM, DAI — mint selectors present in bytecode
  • PAXG — upgradeable proxy

These give a soft, asymptotic floor rather than an exact one. No cap, no exact number, no line on the ledger.

The sink pool is excluded for a different reason: its ODIN is already counted on the pValhalla line. See burn accounting.

PEAS is the interesting case. It's deflationary, so its cap falls over time — the floor rises on both sides of the fraction: k up, max_supply down.

SOJ is the extreme#

SOJ's entire supply was paired with ODIN from launch. With y capped at the whole supply, the floor is essentially k itself: every fee that lands in the pool becomes stranded ODIN. A one-way absorber. The other capped pairs work identically, just less completely.

Why this matters#

The floor is the strongest single fact ODIN has, because it needs no trust at all. Not a policy, a lock, or a commitment — a quantity of ODIN removed from circulation by two hard-capped supplies and one immutable invariant, computable from public state at any block, with no discretion anywhere in the derivation.

It's also what bounds Liquidity-to-Float from below, and why that ratio has a rising minimum it can never fall through.