Scalar Logical time

In a scalar logical clock system, what is the initial clock value for all processes?

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What is the purpose of the happens-before relation in distributed systems?
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What does the 'd' represent in the scalar logical clock increment rule C_i ← C_i + d?
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What happens to logical clock values when a message is sent between processes?
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If process P1 has clock value 5 and receives a message with timestamp 8, what will P1's clock value be after processing the message (assuming increment d=1)?

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In practice, how is total ordering typically achieved with scalar logical clocks?
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What is a fundamental limitation of scalar logical clocks compared to vector clocks?
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In the context of distributed systems, what does monotonicity mean for scalar logical clocks?
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How do scalar logical clocks ensure that the happens-before relation is preserved in a distributed system with message losses?
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