hooke: an elastic floor
for memecoins
A memecoin's creator fees usually leave the chart. hooke keeps them inside it. Every coin launched here routes its creator fees into a reserve called tension. Tension sits still while price holds above an anchor. When price falls below the anchor, the reserve buys back and burns, and the size of each buy follows Hooke's law: it grows in proportion to how far price has fallen. A shallow dip gets a light touch. A crash gets the full spring. This paper defines the anchor, the release rule, the damping that stops the spring from overshooting, the price impact of a release, and the holder roots that share the rest of the fees.
1The law
Robert Hooke published it in 1678 as an anagram, then solved it: ut tensio, sic vis. As the stretch, so the force. A spring pushes back in proportion to how far you move it from rest.
hooke reads the displacement from price. When price P sits above the anchor L, the spring is at rest. Below it, displacement is the fractional distance down.
Stiffness scales with stored tension, so a loaded spring hits harder than an empty one.
The release B is the force, capped by what the spring holds.
| symbol | meaning | value |
|---|---|---|
| P | price, read every keeper pass | live |
| L | anchor, the spring's rest point | 0.8 · TWAP72 |
| T | tension, SOL stored from creator fees | live |
| κ | stiffness, chosen at launch | 1.5 / 2.5 / 4.0 |
| ζ | damping ratio | 0.7 |
| φ | share of fees loaded into tension | 80% |
| R | SOL reserve of the coin's pool | live |
At κ = 2.5, a 10% drop releases 25% of tension, a 20% drop releases half, and a 40% drop empties the spring. A flat floor spends the same amount on every dip. A spring saves its weight for the dips that matter.
2Tension
Tension fills from fees and drains only through buys. Let f(t) be the coin's creator fee rate.
The energy stored in a displaced spring grows with the square of the displacement. Deep dumps meet large buys because the energy is already there, waiting.
Volume feeds tension, so busy coins carry stiff springs. A coin that trades $250K in a day at a 1% creator fee loads roughly $2,000 of tension that day.
3The anchor
The anchor sits at 80% of the 72-hour time-weighted price and only ratchets up.
A pump that holds for three days moves the anchor. A one-candle wick does not. Because the anchor never falls, the spring stays set against the best level the coin has held, and every new high in the average lifts the rest point with it.
4Damping
A spring with no friction overshoots. It buys too hard, price spikes past the anchor, sellers take the gift, price falls back, and the cycle repeats. hooke adds a damping term that reads the velocity of the displacement.
While price is still falling, the damper adds pressure. Once price turns up, it backs off and lets the recovery breathe. The displacement then follows the damped oscillator solution.
At ζ = 0.7 the overshoot is e^(−πζ/√(1−ζ²)) ≈ 4.6%. Price returns to the anchor in about one cycle and settles there. Less damping rings. More damping crawls.
5Recoil
Every release lands in a constant-product pool. Buying B SOL into a pool holding R SOL moves price by
Recoil depends on the ratio of tension to depth. A 5 SOL release into an 85 SOL pool lifts price 12.1%. Thin pools recoil hard. Deep pools need more tension for the same move. Tension grows with volume and volume deepens pools, so the two scale together.
6Roots
The other 20% of fees goes to holders, weighted by balance and by how long they have held. A wallet's roots deepen every day it holds and tear out the moment it sells.
b is balance and t is time since the wallet's last sell or transfer out, with τ = 24 hours. Roots grow fast at first, then slowly. A week of holding carries three times the weight of one day. A month carries five times. Any sell resets t to zero.
7Invariants
The engine holds five properties on every pass, for every coin.
8What the spring is not
It is not a guarantee. A spring holds what you load into it. If sellers outweigh tension, price goes through the anchor and stays there until new fees reload the spring. The keeper holds each coin's fee wallet, so a process enforces these rules, not a contract. Every claim, release and burn is public with its transaction, and each coin's page shows its anchor, its tension and every release as it lands.