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Each Strand is related to certain game character and their missions/jobs/activities/abilities. When strand is terminated, that name gets removed from the phonebook.

Txtmsg Player Ambient Wait / Phone Player Repeat: those are important as they block the strand progress until they are answered. Phone Player Repeat Quick means that you can initiate the call instead of waiting for it. Quick calls are not affected by initial delay and can be made immediately.

Txtmsg Player Ambient / Ambient Phonecall: those don't unlock anything and just add some more story. Some of them are still unavoidable, which means they'll come instead of important calls later if skipped. It's worth mentioning that some ambient phonecalls ignore the fact that you're near random encounter and come anyway.

For example, Action/Reaction unlocks 2 texts: Billy text (slot 0, id 2) is Wait text and has to be received for Buyer's Market to appear; Jim text (slot 4, id 8) is not Wait but runners still receive it after Buyer's Market so it doesn't come later (it's never killed = practically unavoidable).

Buyer's Market activates 2 calls: Elisabeta call (id1, 60s initial delay, killed after Hit the Pipe) and Unknown caller (id4, 60s initial delay, killed after This Shit's Cursed), so both of those are avoidable.

After you call Ashley to unlock Diamonds in the Rough, Unknown caller is active again (id5, 60s initial delay, killed after Get Lost). This call ruins everything if it comes before Collector's Item, though it's very rare.

There is at least 1 inaccuracy: text after Heavy Toll is not Wait, next mission appears right away.

Wait texts also seem to have consistent cycles while non wait texts can have almost 15s difference.

Initial delay indicates that the text/call can't possibly be received for that period of time. However, it doesn't always correlate with actual time you'll have to wait (see Any% Guide for text/call cycles).

Synchronization Wall prevents strand from progressing any further until it receives Send Synchronization answer from another strand.

Flag Wall also waits for certain Mission Flow Flag to become True before progressing. For example, Flag Wall 26 waits for Gang Wars to be unlocked, so until then End of Chapter won't be available.

Check proximity to vector indicates that you have to be away from where the upcoming mission takes place to receive the call. Related to Coming Down and Collector's Item.

Chat Phonecall: those are calls that player can make to Angus, Ashley, Billy or Elisabeta after certain events. When a new Chat Phonecall is set, old one gets replaced by the new one. You will never receive chat calls and they're absolutely useless. However, a runner has to chat call Ashley at some point after Coming Down because it takes priority over important call which unlocks Ray.

Missions Level doesn't seem to be important as multiple events can set the level and it's not clear what it does.

Ambient Email is related to in-game computer, which is not used at all in any category.

Random Interaction Character puts Dave/Malc/Brian (if spared) side mission on the map, which are only required for 100%.

Pause Strand means that you won't be able to call to that character about anything, and their missions won't be available. It seems that if Collector's Item was started with any Friend on the map, Jim will not be paused properly and that will prevent his text from coming (which can be fixed by setting another friend activity and killing Jim).

Explanation of Side Missions Strand.

Terry call (unlocks Races) requires completion of Liberty City Choppers, but the game only checks for that once per 30s (that check starts running after Clean and Serene end). So it's a matter of luck/execution whether you'll be able to call Terry right after LCC. It's also unknown whether that 30s timer runs during loads.

1st Jim call: unlocks Gang Wars, which is required for End of Chapter to appear. This call is unlocked by beating Politics and Bad Cop Drop and having Races unlocked. If you forgot to call Terry, you'll have to wait for aforementioned 30s check before Jim call is possible.

2nd Jim call: unlocks Angus Job, which is required for Ray Strand to progress. It can be made immediately after Gang Wars are unlocked.

Chat calls related to Strand 8 are Angus'.