# ARC-Forge Dynamic Build Times

To begin fabricating parts on any **AXIS ARC-Forge**, it must be staked with the Alloy Space token. This brings the ARC **Online** and enables building.

The staked token has a steady and slow ***Idle*** **Consumption rate** $$(I)$$ when it is online but not building, meaning the token slowly depletes over time.&#x20;

{% hint style="info" %}
Note that there are performance benefits to remaining online for longer. Idle consumption rate is a low percentage of the ***Active*** **Consumption Rate,** when an ARC is actively building. You will be provided with the **Daily Consumption Rate** $$(D)$$per Arc, which is just the Active Consumption Rate per hour x 24.
{% endhint %}

> The formula for the *Active* Consumption Rate $$(A)$$**:**
>
> $$A = D / 24$$ (Alloy Token per hour)

> The formula for the *Idle* Consumption Rate $$(I)$$ with Idle Consumption Factor $$F\_I < 1$$**:**
>
> $$I = A\*F\_I$$ (Alloy Token per hour)

Keep in mind:

* More or less token can be **staked** at any time.
* To avoid running out of staked token mid-build, an **AXIS ARC-Forge** cannot begin fabrication unless it has enough staked token to at least cover the max Build Time of that ARC.
* A Multi-Build also cannot be started unless there is enough staked token to cover at least ***N** times* max Build Time.
* An ARC-Forge consumes token at a slower rate when it is **idle** (*staked but not building*).
* When an ARC runs out of staked token, it is immediately taken Offline, which brings the **Online Time** to 0 and clears any earned **Contract Bonus**.
* The Initial Daily Consumption Rate ( $$D\_{\rm INIT}$$) is created at time of minting an ARC. While $$D\_{\rm INIT}$$ is the initial value, but the current daily consumption rate $$D$$  can be different due to upgrades.
* Note that $$D\_{\rm INIT}$$ is also important because it is used to calculate the **Flat Rate** payable to users by Echo-9 for Unprocessed Parts and Consumables.

### ARC-Forge Dynamic Build Times

As an ARC is used over time, it loses efficiency, so that the minimum and maximum build time *increases with the number of completed builds*. The ARC can be **Refurbished** to restart this increasing build time, however it will never be as good as a brand-new ARC.

{% hint style="info" %}
Note that failed builds and cancelled builds will also add to the wear and tear of the ARC, and therefore also add one each to the total builds tally.
{% endhint %}

Malfunctions increase the number of builds tally by more than an ordinary failed print, by a value $$Z = 2$$ for the AXIS-REC, and $$Z$$ equal to the ARC class number for the higher classes (e.g. $$Z = 5$$ for the AXIS-E9). However, using a **Mechikit** in a timely fashion can reduce or even eliminate this count towards the build. If the total Malfunction waiting time is $$T$$ hours, and the Mechikit is applied at time $$t < T$$ before the waiting time runs out, then the new number added to the build tally will be $$ZZ = {\rm FLOOR}(Z\*t/T)$$.\
Catastrophic Malfunctions cause **double** the build tally increase of ordinary malfunctions.

{% hint style="info" %}
For example, if an AXIS-E9 experiences Malfunction, then $$Z = 5$$. If the Mechikit is used within 6 hours of a 12 hour malfunction waiting period, then\
$$ZZ = {\rm FLOOR}(Z \* t/T) = {\rm FLOOR}(5 \* 6/12) = {\rm FLOOR}(2.5) = 2$$So, $$n$$ is increased by $$ZZ = 2$$.

If, however, the failure was catastrophic, then $$n$$ is increased by $$2 \* Z = 2 \* 5 = 10$$ (unless prevented by an **Xtended** warranty upgrade, in which case it is just a normal malfunction)
{% endhint %}

> Effective use of **Mechikits** and **Xtended** Warranties will keep your ARCs running efficiently for much longer!

### Build Time Multiplier&#x20;

Let the number of builds completed since being minted (or refurbished) be $$n$$, and $$e ≅ 2.71828$$ being Euler's number, then the build time multiplier $$M(n)$$ as a function of $$n$$ is:

$$M(0) = {\rm mult\_init}$$

$$M(n) = {\rm mult\_init} + \frac{(h - 1)}{1+e^{(-k(n/d - T))}} + n^q - c$$

The current parameter values are as follows (subject to change before launch):\
\
$${\rm mult\_init} = 1$$

$$h = 4$$

$$d = 2$$&#x20;

$$k = 0.02$$

$$T = 100$$

$$c = 1.35$$

$$q = 0.02$$

The current minimum and maximum build time after upgrades and contract bonus (CB) is then modified as:

**final minimum build time** = $$M(n)$$ \* min build time after upgrades and CB\
**final maximum build time** = $$M(n)$$ \* max build time after upgrades and CB\
\\

<figure><img src="https://2111160599-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Ffggipod3jU8OdLSacyrb%2Fuploads%2FbdVn0Pk0SFtHvVTjUGnO%2FScreenshot%202023-03-13%20at%2008.23.49.png?alt=media&#x26;token=242f5d95-4719-49f5-b4d2-ce6d8ed140d5" alt=""><figcaption><p>AXIS-REC Dynamin Build Time</p></figcaption></figure>

<figure><img src="https://2111160599-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Ffggipod3jU8OdLSacyrb%2Fuploads%2F4qYUou1WcVYFnb9iSDcS%2FScreenshot%202023-03-13%20at%2008.24.09.png?alt=media&#x26;token=171a0ea7-cc35-46de-8fee-cf963db9ff9e" alt=""><figcaption><p>AXIS-E9 Dynamic Build Time</p></figcaption></figure>

### **ARC-Forge Refurbishment**

ARC Refurbishment is the complete repair and replacement of faulty parts, including rejuvenating the alchemical converter. This restores an ARC to its initial build tally $$n=0$$ and build times are reset. The additional effect of each refurbishment is to increase the value of $${\rm mult\_init}$$ for the particular ARC by 1%, i.e. $${\rm mult\_init} = {\rm mult\_init} + 0.01$$&#x20;

{% hint style="info" %}
It is important to note that refurbishment takes an ARC-Forge offline, which means that you lose your accumulated online time that counts towards your contract bonus.\
\
You can only pay for refurbishment in Alloy Token from your wallet. The refurbishment cost equals the following amount of Alloy Token which depends on current multiplier $$M(n)$$ and ARC class:
{% endhint %}

$$R\_{\rm REC}(n) = {\rm max}(250,  15 \* M(n)^W)​$$

$$R\_{\rm H}(n) = {\rm max}(350,  20 \* M(n)^W)​$$

$$R\_{\rm S}(n) = {\rm max}(400,  25 \* M(n)^W)​$$

$$R\_{\rm PRO}(n) = {\rm max}(500,  30 \* M(n)^W)​$$

$$R\_{\rm E9}(n) = {\rm max}(600,  35 \* M(n)^W)​​$$

*Note that the use of the max function is equivalent to having a minimum fee for Refurbishment.* The refurbishment exponent $$W$$ is the same across all ARC classes. Note that the values above are subject to change before launch!

Note also that the player can Refurbish an ARC at any time when the printer is Idle or Offline (i.e. not building a part). Refurbishment takes the same number of hours as the Class number (Rec, 1 hour; Hobby, 2 hours; Serious, 3 hours; etc) and once completed takes the ARC into Idle Refurbished state if it has staked Alloy Token, or Offline if it has none.

#### Refurbishment Taxes

The Alloy Token paid for refurbishment is burnt via a wallet transaction, and a 4.5% tax of the refurbishment fee is added to the Smelter Extraction pool.
