- This paper introduces solo-valency, a variation on the valency proof technique originated by Fis- cher, Lynch, and Paterson. The new technique focuses on critical events that influence the responses of solo runs by individual operations, rather than on critical events that influence a protocol's single deci- sion value. It allows us to derive √ n lower bounds on the time to perform an operation for lock-free implementations of concurrent objects such as linearizable queues, stacks, sets, hash tables, counters, approximate agreement, and more. Time is measured as the number of distinct base objects accessed and the number of stalls caused by contention in accessing memory, incurred by a process as it performs a single operation. We introduce the influence level metric that quantifies the extent to which the response of a so lo execution of one process can be changed by other processes. We then prove the existence of a rela- tionship between the space complexity, latency, contention and influence level of all lock-free object implementations. Our results are broad in that they hold for implementations that may use any collection of read-modify-write operations in addition to read and write, and in that they apply even if base objects have unbounded size.