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f(o)

The FOMO Experiment · On-Chain · Permissionless
L(t) = L₀ · e−λt // liquidity as function of time
ΔL = L(t_prev) − L(t_now) // settlement delta
λ = const // immutable decay constant
∀ t : settlement is permissionless // anyone can crank
CA — coming soon —
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Protocol
f(o)
Mechanism
Exponential
Settlement
Permissionless
Decay λ
Immutable
// The Decay Function
L(t) = L₀ · e⁻ˡᵗ
0 t L₀ L(t) t₁ t₂ t₃
Definition
L(t) = L₀ · e−λt
Liquidity at time t. A fixed reservoir decays exponentially from genesis. The curve is determined entirely at deployment.
Settlement
ΔL(t) = L(t_prev) − L(t_now)
Each crank computes elapsed time against the curve and moves exactly the delta into market liquidity. The amount is deterministic.
Decay Constant
λ ∈ ℝ⁺, immutable after genesis
Set once at deployment. Never changes. The program-owned PDA holds the reservoir and the constant. Neither is mutable.
Permissionless
∀ caller : crank() → valid
Anyone can execute the settlement crank. The caller controls timing, not quantity. The amount is already written into the curve.
// f(o) a thread
(1/2)
liquidity as a deterministic function of time.

the fomo experiment is built around an on-chain anchor program that makes liquidity a deterministic function of time.

a fixed reservoir is committed to a program-owned pda at genesis alongside an immutable decay constant, giving the program everything required to derive where that reservoir should be at any future point.

L(t) = L₀ · e−λt where L₀ = genesis reservoir λ = immutable decay constant t = elapsed time since deployment

the curve is written once. it cannot be rewritten. every future state of the protocol is already encoded in these two values.

(2/2)
settlement is permissionless. nobody chooses the amount.

each crank resolves elapsed time against the exponential curve, computes the difference between theoretical and settled state, and moves exactly what is owed into market liquidity.

ΔL = L(t_prev) − L(t_now) crank() → transfers ΔL to market caller controls: when caller controls: nothing else

anyone can choose when to execute it, but nobody gets to choose the amount.

the experiment asks a simple question: what happens when liquidity is a law, not a decision?

// Mechanism
Genesis
The reservoir is committed.
At deployment, L₀ is transferred to a program-owned PDA. λ is written to program state. Neither changes again. The future is already determined.
init(L₀, λ) → PDA
Crank
Anyone can settle. No one can alter.
The settlement function is permissionless. Any caller can invoke crank() at any time. The output — ΔL — is computed from the curve alone. The caller is irrelevant to the amount.
crank(t) → ΔL = L(t_prev) − L(t)
Outcome
Liquidity as law, not discretion.
Market liquidity grows according to the exponential curve. Early cranks capture larger deltas. Late cranks capture smaller ones. The integral converges to L₀. Nothing is left over.
∫₀^∞ λL₀e−λtdt = L₀
// The experiment is live

f(o)

liquidity as a deterministic function of time.
settlement is permissionless.
nobody gets to choose the amount.

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