The RICCI Model, in Full

1Discrete curvature

For the canonical V3 pool with sqrt-price s (Q64.96), the oriented displacement since the previous cycle is measured in parts-per-million of the squared sqrt-price:

The sign is oriented so that positive r always means the token rose against WETH, whichever pool slot it occupies. Squared sqrt-price is exactly the pool's rational price, so r is a pure integer computation — no floating point ever touches a decision.

2Flow pressure and the adaptive dead zone

Interval WETH volume against in-range liquidity L gives a flow pressure, which widens the dead zone in loud markets so that noise cannot trigger the policy:

The dead zone therefore lies between 0.15% and 0.65% of squared price, tightening when the pool is quiet and relaxing when it churns.

3Cubic response

Only curvature in excess of the dead zone earns size, and it earns it cubically:

Every action is bounded to 0.25%–12.5% of the relevant reservoir. A marginal breach trades the minimum; a violent dislocation deploys the cap and never more.

4The one-sided solvency cone

5Calm allocations

Inside the dead zone (|r| ≤ d) the reservoir refuses to sit on surplus:

• burn — token value above twice WETH: 6.25% of token inventory is transferred to 0x…dEaD. Total supply is untouched on paper; circulating float is not.
• lock lp — balanced inventories under material flow (q ≥ 2000): 10% of each asset mints a fresh live-tick-centred V3 position whose half-width grows with flow pressure, and its NFT is transferred to 0x…dEaD. Not burned — ownership-locked: the liquidity and all its future fees become permanently inaccessible, so each allocation mints a new NFT. The original launch position is explicitly rejected.
• airdrop — WETH above twice token value: 6.25% of WETH is split equally among 1–10 holders sampled uniformly from a finalized on-chain holder index. The eligible set and a future anchor block are committed before that block's hash exists; after 12 confirmations, rejection sampling from the hash stream picks unique recipients without modulo bias. No operator lists, no JavaScript randomness.

6The cycle

Every cycle claims available creator fees first (NoFeesToCollect is ordinary), observes the pool, takes exactly one action, and persists the next start time — drawn uniformly from [10, 15] minutes — before the economic action executes, so a restart can neither reset the clock nor double-fire a cycle.

7Safety model

• Dry-run is the default. Live signing requires the key-derived address to exactly equal the fee recipient.
• Native ETH is gas only; strategy capital is exclusively WETH plus the token.
• Swaps use fresh quotes, 0.75% minimum-output tolerance, pre-broadcast simulation, a 20% gas buffer, exact temporary approvals, and receipt/balance reconciliation with at most one retry.
• Prepared transactions are persisted before broadcast; restarts recover them exactly and refuse overlapping cycles.
• Airdrops persist per-recipient state and resume only unpaid entries.

8Why “Ricci”?

Ricci flow, ∂g/∂t = −2 · Ric(g), deforms a metric so that regions of high curvature relax toward uniformity — it is the equation Perelman used to settle the Poincaré conjecture. RICCI does to a price path what Ricci flow does to a manifold: it measures discrete curvature and applies a bounded, deterministic counter-flow until the geometry calms. The reservoir is the metric; the fees are the flow.