Has anyone shown a limit on recursive self-improvement?
Not with a number. Marcus Hutter, 'Can Intelligence Explode?' (arXiv:1202.6177, 2012), sets out to separate speed from intelligence explosion and consider possible bounds on intelligence: a philosophical treatment with no exponent, no reciprocal, no architecture dependence. David Chalmers gave the singularity its first full philosophical treatment. The question has owners; the programme's contribution is the replacement limit, its number, and its dependence on architecture.
The question has named owners on the record. Marcus Hutter's 'Can Intelligence Explode?' (arXiv:1202.6177, 2012; J Consciousness Studies 19(1-2):143-166) sets out to separate speed from intelligence explosion and consider possible bounds on intelligence. It is a philosophical treatment. Hutter derives no exponent, no reciprocal, no architecture dependence: an antecedent, never a rival. David Chalmers gave the singularity its first full philosophical treatment in 2010. Both belong to the lineage the programme inherits, and both are credited on the related-work page.
What the programme adds is narrower and more testable. The premise is West, Brown and Enquist (Science 276(5309):122-126, 1997): the transport network sets the terminal bound on growth in every case that has run. The question is Chalmers' and Hutter's. What is claimed here is the replacement limit, its number, and its dependence on architecture. When growth stops being fed through pipes, what limits it from the inside is the system's own capacity to correct itself: measurable on a running system, yielding a computable ceiling, depending on what the corrector is built from rather than how capable it is, which makes it engineerable.
An adversarial precedence review across ten frontier configurations, instructed to be hostile, reported no earlier work stating the quantitative criterion. That is a search result, not a proof of absence: an earlier statement in different vocabulary may yet surface. If one does, the related-work page is where it will be recorded, with the concession attached. The recorded measurement programme, ARC-Beta-k, was written and dated before data; the deciding registrations are drafted and awaiting human submission.