I am working on proving a novel problem to be P-Complete, and this requires using a logspace reduction to reduce some known P-Complete problem to the novel problem. Particularly, I am reducing the Circuit Value Problem, the de facto P-Complete problem, to the novel problem.
The Experienced Difficulty
P-Complete reductions must use logarithmic space in the reduction in order to be meaningful. However, for the novel problem, it is very easy to show that the reduction takes logarithmic time, whereas it is difficult to show that it takes logarithmic space.
The Complicating Factor
There are many Q and A sites online which declare that an algorithm's space complexity is always less than its time complexity. For example: https://www.quora.com/Is-there-any-algorithm-whose-space-complexity-is-more-than-time-complexity. This is just one of many. I have scoured the literature on the subject, reading through Cook, Karp, Stockmeyer, and many more, yet I am unable to find this claim that space complexity is always less than time complexity captured in a rigorous manner. Yet this claim seems pervasive and almost treated as "common knowledge".
Why the Complication Matters
If it is true that space complexity is always less than or equal to time complexity, then instead of doing a logspace reduction, I can show that the reduction can be done in log time, which is much easier in my particular case.
What I Need
Can anyone point me to the paper which established this "common knowledge" idea that space complexity is always less than or equal to time complexity? Or a textbook or other authoritative source?