Binary search always splits the range in half. That is a fine guess when you know nothing, but Lightning nodes probing a channel's hidden balance usually know something. Splitting where the balance probably is makes probing 3 to 6% more efficient in production.

Our researchers built Bayesian Binary Search: it learns where balances are likely to sit, then splits the range where the probability is, not at the midpoint.

The paper was published in the peer-reviewed journal Algorithms (MDPI, 2025), in collaboration with Stillmark. It runs in production at Amboss today.

The plain-English overview and the paper are in the reply.

Overview and paper: https://amboss.tech/blog/bayesian-binary-search

Lightning Network, week of 2 to 8 November: public capacity held at 3,235 BTC, only 0.3% below the week before, and the average public channel grew 1.5% to 0.098 BTC. That held through the busiest day of forced closes in three years.

On 8 November, 1,549 public channels were force-closed, more than double the previous one-day high of 687 on 24 October 2024. They were small: together they held 1.46 BTC, about 94,000 sats each. Losing them barely moved total capacity, and it raised the average size of the channels that remain.

The rest of the week looked like October. From Monday to Saturday, 86.2% of closes were cooperative, against 86.1% across October, and node operators opened 1,473 new channels over the seven days.

1.46 BTC force-closed in one day, against 3,235 BTC of public capacity that stayed in place.

The weekly charts, including channel and node counts: https://amboss.space/stats

Announcing Hosted Checkout for Amboss Payments! ⚡

Payment cards are more exclusive than ever. Now any business can get paid from anywhere on the globe.

Customers pay with Cash App or any Lightning wallet. You receive bitcoin or USDT.

Your brand. Our tech. Your name, logo and color, light or dark.

No chargebacks. Every payment is final.

Live today. Test it in sandbox: https://amboss.tech

The first question a finance team asks about Bitcoin payments is about price swings. It is a fair question, and the answer is that you do not have to hold bitcoin at all.

Bitcoin is the transport. With optional auto-conversion, payments that arrive over Lightning can settle to you as US-dollar stablecoins instead.

Invoices are for a fixed amount. The payer covers routing and conversion fees, so the amount you invoice is the amount you receive.

Customers pay with the app they already have. Your balance sheet can stay in dollars.

How it works: https://amboss.tech/payments

An AI agent asked a weather service for the Orlando forecast. The service answered "402 Payment Required" with a price. The agent paid less than a cent over Lightning and had its forecast about a second later.

No card, no account, no human approval. The proof of payment became the access key. That pattern is L402, and this run used Amboss with Lightning Enable, once in bitcoin and once from a dollar stablecoin balance.

Amboss is the payment rail for agent protocols like L402, x402 and MPP. Amazap, a marketplace where AI agents pay per API call, is one example of the model in use.

Request, price, payment, proof, data.

The case study: https://www.lightningenable.com/case-studies/machine-commerce-in-dollars/

In June 2022 the average public Lightning channel held 0.048 BTC. On 1 November 2026 it held 0.097 BTC, about twice as much.

There are fewer public channels than in 2022, but each one is larger. A larger channel can carry a larger payment along a single route, which matters once real business amounts start to move.

The figure is public capacity divided by active channels, from the Amboss Space daily series.

0.048 BTC then, 0.097 BTC now.

Live network charts: https://amboss.space/stats

Node operators bought 17.38 BTC of Lightning liquidity on Magma in October. In October 2025 the figure was 10.48 BTC. That is 66% more in a year.

The chart shows every month in between, so you can see the path, not just the two end points.

Magma is the Amboss marketplace for inbound liquidity: a seller opens a channel to your node for a fee agreed up front. Across all orders so far, the average price has been 4.42% a year.

Want to receive payments on your own node without asking peers one by one? Magma is built for that.

Magma: https://amboss.tech/magma

Picture a merchant taking $1 million a month in card payments with a 10% rolling reserve held for 180 days. Once the reserve fills, about $600,000 of its own revenue is held back at any time.

These numbers are illustrative, not from any one processor. The point is the arithmetic: while a rolling reserve is held, the money is earned, yet it cannot be spent.

Bitcoin and stablecoin payments through Amboss settle to your own wallet in seconds, with no rolling reserve. With optional auto-conversion, the balance can stay in US-dollar stablecoins.

If six months of reserves came back to your balance sheet, where would your team put them first?

How Amboss Payments works: https://amboss.tech/payments

Give a Lightning node a fixed budget. Which channels should it open so that the most payments can flow through it? Our research model, MPFlow, has made 4,640 of those channel-open decisions in production, placing 267.3 BTC across 30 managed nodes.

MPFlow treats the question as a machine learning problem. It learns which new channels raise max-flow, a measure of how much value can move between two points in the network.

In training, the biggest hubs were taken out, so the model had to learn good placement, not just "connect to the hubs". It now powers peer recommendations at Amboss.

Better placement means more payments find a route the first time.

The paper and a plain-English summary: https://amboss.tech/blog/mpflow

Lightning Network, week of 26 October to 1 November: 1,567 public channels were opened, 7% more than the week before. The average new channel held 0.45 BTC.

October as a whole: 6,892 channels opened with 3,102 BTC between them, an average of 0.45 BTC each. That is the largest monthly average of 2026, up from 0.28 BTC in March.

Closes were cleaner as well. 86.1% of October's channel closes were cooperative, the highest share of any month this year. A cooperative close avoids the waiting period and extra on-chain cost of a forced close.

0.45 BTC per new channel, and 86 in every 100 October closes agreed by both sides.

The full weekly table, including public capacity and node counts: https://amboss.space/stats

On 1 April 2026, Visa lowered the dispute ratio that marks a merchant as "excessive" from 2.2% to 1.5% in the US, EU, Canada and Asia Pacific. Above it, each counted fraud report or dispute carries an $8 fee.

The rule applies once a merchant has more than 1,500 fraud reports and disputes in a month. For high-volume, high-risk merchants such as iGaming operators, that line can sit close, and the fee comes on top of the reversed payment.

Lightning payments work differently. A completed payment is final, so there are no card chargebacks to count. When a customer needs a refund, you send a new payment under your own policy.

Amboss adds Bitcoin and stablecoin payments to the cashier you already run, next to cards.

How it works for iGaming operators: https://amboss.tech/use-cases/igaming

When a Lightning payment crosses a public channel, the node forwarding it can charge a fee. On 2 November 2026 the median fee rate across 65,101 public channel fee policies was 50 parts per million, or 0.005%. On a $1,000 payment, that is 5 cents for each channel that forwards it, plus a median base fee of 1 satoshi.

The median has stayed at 50 ppm in the Amboss Space snapshots for the past day, week and month.

For a payments team, this is the network layer of the cost: what routing nodes charge to pass a payment along. The sender pays it. A route can cross more than one channel, so the total depends on the path the payment takes.

It is not a merchant fee. Amboss Payments pricing is tailored to your volume and is not the network fee rate.

50 ppm is the middle of the public network today: half of all channel fee policies charge that or less.

Live Lightning fee rates and network charts: https://amboss.space/stats