Exact asymptotic computation from a limiting program

Determine whether, as the output tolerance tends to zero, the family of finite programs that arbitrarily-precisely approximates a continuous target function admits a limiting program, thereby realizing exact asymptotic computation.

Background

For continuous-valued targets, the paper defines computation through arbitrary-precision approximation using finite dyadic input representations and tolerance-dependent finite programs. It then identifies a stronger unresolved question: whether those programs converge to a single program as the requested output tolerance approaches zero.

References

A stronger theoretical question, not addressed here, is whether as \varepsilon\to0, the family of programs \theta_\varepsilon admits a limit, implying that exact asymptotic computation could be realized by a program \theta.

— Emergent Models: Intelligence from Tiny Substrates  (2608.14019 - Bocchese et al., 14 Aug 2026) in Appendix, “Computation and Modeling on the Continuous,” subsection “Asymptotic form”