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I have two basic questions regarding the working of the Tangle, which is unclear to me.

  1. How are conflicting transactions detected in the Tangle?
  2. Suppose we have two conflicting transactions 'w' and 'y' as shown in the following figure(an excerpt from https://github.com/noneymous/iota-consensus-presentation/blob/master/README.md) enter image description here What happens if due to propagation delay, users might only have one of these conflicting transactions in their validation path and not see the conflict and as a result with time, both 'w' and 'y' attains confirmation confidence and is applied to the ledger state.

The section "Double Spend" in the site https://github.com/noneymous/iota-consensus-presentation/blob/master/README.md says, "However, sooner or later it must happen, that both conflicting transactions are in the path of validation of one transaction."

How can we be sure that is going to happen for sure. Can such a case arise where, both the transactions 'w' and 'y' get confirmed and applied to the ledger before getting detected?

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