# Evaluating Methods for the Identification of Off-Chain Transactions in the Lightning Network
## 5 Results
### First Data Collection Interval  
The first collection interval on the mainnet had a length of 1151 blocks. It was between Bitcoin block 517,855 and 519,005. Our modified LND implementation collected data from the LN and produced the set \(\alpha\) containing 715 channels which were closed during this interval. The same interval on the blockchain was parsed two times, once identifying channels using timelocked redeem scripts, and the second time getting all potential channels using multisig identification. This resulted in a \(\beta\) set containing 322 channels and a \(\gamma\) set with 1265 channels shown on the left in the Venn diagram Figure 10. We can see how both \(\beta\) and \(\alpha\) are a subset of \(\gamma\), but \(\beta\
ot\subseteq\alpha\). The intersection \(\beta\cap\alpha\) is the number of channels we identified using the timelocked redeem script which was also found through the LN node. On the mainnet, this intersection was 190 which is 36% of the total channels in \(\alpha\). This is reasonable, as the method only discovers a channel if it has been unilaterally closed as we explained in Section 4.1.2, and not if a channel is closed cooperatively which happens more frequently (64% of the time, to be precise). Taking the ideal world scenario \(\beta\subseteq\alpha\) discussed above, into account for this data, we have a large \(\beta\backslash\alpha\) relative complement of \(\alpha\) in \(\beta\) of 132, which is 40% of the channels in \(\beta\). With a false positive this high is unlikely because the uniqueness of the timelocked redeem scripts, so we assumed that these are actually LN channels which we have not been able to capture in our interaction with the LN. The reason we made this assumption was that it is more likely that not every channel is propagated successfully to our single LN node than there being this many instances of timelocked redeem scripts unrelated to the LN on the blockchain. Additionally, as we explained in Section 4.2 at least every node running the LND implementation will prune their LN graph of _zombie channels_ regularly, so these will eventually no longer be propagated through the network. This means even if our node does not prune its graph of the network, the channel will never be received in the first place. These are the likely causes of our timelocked channels not being found in the LN channel set. Taking this into account and assuming the union \(\alpha\cup\beta\) are all LN channels, the total number of LN channels closed in this interval would be 847. This would entail that 67% of 2 of2 multisig transactions in our interval are lightning channels.  
For the testnet, our LND node collected 838 snapshots starting on block 1,290,011 and ending on block 1,289,174. The results are similar to the mainnet, with the intersection \(\beta\cap\alpha\) being 27% of \(\alpha\), and the \(\beta\backslash\alpha\) relative complement of \(\alpha\) in \(\beta\) being 62% of channels in \(\beta\). Again, assuming the union \(\alpha\cup\beta\) are all LN channels, 55% of 2 of2 multisig transactions are lightning channels. This is however not an upper limit, as our \(\alpha\cup\beta\) union is the channels unilaterally closed on the blockchain and channels that have been propagated to our node in the LN. Our LN node might not be able to get all channels, so there should also be channels not closed unilaterally and therefore not discovered on the blockchain, which we similarly have not been able to collect through the LN, which would make the total channel count higher, and more of the 2 of2 multisig transactions being channels than indicated in our results for both the networks.