How far can Ark scale Bitcoin payments?

Disclaimer: The following answer was created with the help of LLM, but I checked and verified it as best I could

• to each roundthe user “consumes” one or more vTXOs and receives a new vTXO (recipient + typically modified vTXO). Conceptually, this mirrors the UTXO on L1. That is, the input is discarded and the output is created. (Arc Protocol)
• Who is at the forefront of output? ASP does. user Confiscation When you input vTXO into ASP, ASP “fronts” the on-chain liquidity backing all assets. new vTXO created in that round. What ASP can do is unlock (recover) the confiscated value laterwhen the forfeited vTXO expires. Think of this as the ASP prepaying short-term working capital and receiving an IOU that matures when the vTXO expires. (Arc Protocol)
• Expiration date/period: vTXO includes absolute time lock. The reference documentation says: 14th;In some articles (and implementations), ~4 weeks. The mechanism is the same. Users must roll their vTXO into a new round before it expires. After expiration, the ASP can mop up the funds and restore the prepaid liquidity. In other words, ASP liquidity is roughly tied up Until expiry date For input for that round. (Arc Protocol)

yes. A single payment typically:

1. consumes one or more input vTXOs,
2. Create at least two Output: Receiver vTXO and Change sender vTXO (unless it’s completely accurate). Because ASP needs to provide funding, for each new output Rounds (including change) allow ASP liquidity to be consumed on every payment greater than the payment amount. This “amplification of change” is extremely important. (Blog – Ark Research Institute)

Practical mental models:

• define M = total user funds “in this ASP’s ark” (total user vTXO).
• define V = “Speed” within validity period = Total value spent divided by each user in that window M.
• primary demand The working capital for the entire ASP window is High x Medium (The value of the output that ASP needs to front for internal transfer during that window).
• but Because most payments create a receiver output and Change output, ASP front more It’s not just the remittance amount. With simple division, the multiplier can be several times higher. Ark Labs’ specific simulations show cases where up to 0.33 BTC of 1 BTC balance needs to be spent. 2.67BTC ASP liquidity increased (about 8 times the actual transaction amount), but liquidity worsened (about 25 times) when there were more small splits. This is the “change amplification” effect. (Blog – Ark Research Institute)
• tenor: Liquidity is tight Until the confiscated input expires (vTXO expiry time, e.g. ~14 days / ~4 weeks), at which point the ASP can reuse it. Therefore, the “peak liquidity” of ASP is maximum net value of new output created minus Value of forfeitures that have already matured – measured over the maturity period. (Arc Protocol)

• For each small payment, two New output (receiver + change). if they play table tennis within the same expiration dateASP retains placket Inputs from previous rounds are forfeited, but more outputs are obtained. not yet mature.
• Net effect: ASP’s outstanding working capital has generally continued to increase over the years. Number of times the coin circulates during the window, multiplied Due to fluctuation amplification factor due to inappropriate denomination/coin selection. That is precisely the pathological case highlighted in the article on liquidity. (Blog – Ark Research Institute)

TL;DR answer

• How much liquidity is there and for how long? is enough to cover sum of all new outputs Inputs are created in rounds (receivers + changes) throughout the expiration window until they are forfeited. Expired Can be swept by ASP. tenor ≈ vTXO expiration date (e.g. approximately 14 days or approximately 4 weeks, depending on policy/implementation). (Arc Protocol)
• What happens if two users send small amounts back and forth? Each small payment generates multiple outputs, which can significantly increase liquidity requirements. ASP continues to output while forfeiture is unavailable. This may require Multiple of actual transaction amount In the window. (Blog – Ark Research Institute)
• Are the requirements proportional to the amount paid within the vTXO timelock? almost proportional Increase the volume on the window (Velocity x total user funds), but amplified Due to change/fragmentation. Good denominations and policies can bring it closer to a straight line. (Blog – Ark Research Institute)