> ## Documentation Index
> Fetch the complete documentation index at: https://docs.morpheum.org/llms.txt
> Use this file to discover all available pages before exploring further.

# ReClamm Glide Mechanics – Explained Step by Step

> Glide (gradual recentering): goal, variables, centeredness, update rule, typical values, and engineering trade-offs

## Overview

**ReClamm** (Re-Centering Liquidity AMM) introduces a mechanism called **glide** (also referred to as gradual / time-proportional recentering) whose goal is:

> Automatically and smoothly move the virtual liquidity center of the pool toward a target price **without** creating large, sudden arbitrage opportunities and **without** requiring active LP management.

This is one of the biggest differences compared to classic Uniswap v3 concentrated liquidity (which is static until the LP manually moves ranges) and classic constant-product AMMs (which have no concept of preferred center at all).

***

## Core idea in one sentence

**The pool slowly "glides" its virtual balances toward a target price center using an exponential decay function — the farther the current price is from the target, the faster it wants to move back, but the movement is always gradual and time-proportional.**

***

## Key concepts and variables

| Symbol     | Meaning                                                     | Typical default / range             | Controls what?                            |
| ---------- | ----------------------------------------------------------- | ----------------------------------- | ----------------------------------------- |
| **T**      | Target price (the "desired" center of the pool)             | oracle price, TWAP, governance vote | where the pool wants to be                |
| **Vₐ, Vₓ** | Current virtual balances of token A and token B             | dynamic                             | virtual liquidity depth on each side      |
| **Rₐ, Rₓ** | Real (actual deposited) balances of token A and token B     | real LP deposits                    | real economic exposure                    |
| **c**      | Centeredness metric (how balanced the virtual liquidity is) | 0 … 1 (ideal = 1)                   | trigger condition for glide               |
| **m**      | Minimum centeredness margin                                 | 0.75 – 0.85                         | when glide is activated                   |
| **τ**      | Daily shift exponent / decay rate                           | 0.3 – 0.7                           | how aggressive the recentering is per day |
| **Δt**     | Time elapsed since last glide (in days)                     | fraction of day                     | controls speed of movement                |

***

## Centeredness formula (the trigger)

Most implementations use one of these two equivalent definitions:

$$
c = \min\left( \frac{R_a \cdot V_b}{R_b \cdot V_a},\ \frac{R_b \cdot V_a}{R_a \cdot V_b} \right)
$$

or the more symmetric version

$$
c = \frac{2}{\frac{R_a V_b}{R_b V_a} + \frac{R_b V_a}{R_a V_b}}
$$

* **c ≈ 1** → virtual liquidity is well balanced
* **c ≪ 1** → the pool is very imbalanced (one side has almost all virtual liquidity)

**Glide is only activated when c \< m** (e.g. c \< 0.80–0.85).

***

## The glide update rule (core mathematics)

When glide is triggered, the virtual balances are updated using **exponential decay** toward the target:

$$
V_{a,\ \text{next}} = T_a + (V_{a,\ \text{current}} - T_a) \cdot (1 - \tau)^{\Delta t}
$$

$$
V_{b,\ \text{next}} = T_b + (V_{b,\ \text{current}} - T_b) \cdot (1 - \tau)^{\Delta t}
$$

Where usually **Tₐ** and **Tₓ** are chosen such that

$$
\frac{T_a}{T_b} = \text{target price (in token B / token A)}
$$

**Most important properties of this formula**

1. **Asymptotic convergence** → Vₐ and Vₓ approach Tₐ and Tₓ exponentially
2. **The larger the deviation** (|V – T|), **the larger the absolute step** → strong restoring force
3. **The step size decays exponentially** → movement becomes slower and slower → **no sudden jump**
4. **Time-proportional** → twice the time → roughly twice the distance covered (in log scale)

***

## Typical values seen in production designs

| Parameter             | Conservative (stable pairs) | Aggressive (volatile / meme) | Very aggressive (new launch) |
| --------------------- | --------------------------- | ---------------------------- | ---------------------------- |
| m (min centeredness)  | 0.82 – 0.87                 | 0.75 – 0.80                  | 0.65 – 0.75                  |
| τ (daily exponent)    | 0.30 – 0.45                 | 0.50 – 0.70                  | 0.80 – 1.00                  |
| Min glide interval    | 4–12 hours                  | 1–4 hours                    | 15 min – 1 hour              |
| Max glide per trigger | \~3–8% of virtual depth     | 10–25%                       | 30–50%                       |

***

## Visual intuition – how the glide looks

Imagine the virtual price starts **below** the target and moves **up** over time. Think of the target as the top rung and the glide as climbing toward it: each step is **largest** when you are far away and **smallest** when you are almost there.

```mermaid theme={null}
flowchart BT
  T[["Target price"]]
  N3[["Nearly there"]]
  N2[["Closer"]]
  N1[["Virtual price now"]]
  N1 -->|largest moves| N2
  N2 -->|smaller moves| N3
  N3 -->|slowest near target| T
```

**Time** runs along the journey (left to right in the story, bottom to top in the diagram): the farther below target you start, the faster the **absolute** correction feels at first; near the target, movement **asymptotically** slows so there is no sudden snap.

***

## Why this is powerful (ReClamm advantages)

| Property                          | Classic Uniswap v3 | Classic x\*y=k | ReClamm glide                      |
| --------------------------------- | ------------------ | -------------- | ---------------------------------- |
| Needs active LP to re-range?      | Yes                | No             | **No** — automatic                 |
| Sudden large arb opportunity?     | When LP moves      | Always         | **Very small** — gradual           |
| Capital efficiency during drift   | Drops fast         | Constant       | **Stays high** — virtual recenters |
| Good for trending markets?        | Poor               | Poor           | **Good** — follows slowly          |
| Good for range-bound stablecoins? | Good               | Ok             | **Excellent** — stays centered     |
| Good for high-vol meme launches?  | Very poor          | Poor           | **Very good** — damps extremes     |

***

## Most important engineering trade-offs

1. **Too high τ** → pool chases price too aggressively → large arb during strong trends
2. **Too low τ** → pool stays imbalanced for too long → bad capital efficiency
3. **Too low m** → glide almost always active → unnecessary state writes / computation
4. **Too high m** → glide almost never triggers → defeats the purpose

**Sweet spot (most production designs)**\
→ m ≈ 0.78–0.84\
→ τ ≈ 0.45–0.65 (daily)\
→ glide triggered at most once per 1–4 hours

***

## Further exploration

Related topics you can go deeper into:

* How the glide affects **effective slippage** in different market regimes
* A numerical example with concrete numbers over 3 days
* How to choose τ and m given historical volatility of the pair
* Main failure modes / attack vectors when implementing glide

See the internal ReClamm design docs for deeper detail.