arXiv:2603.18955 · v4

Foundational Analysis Of The Solvability Complexity Index

首次提交 2026-03-19 22:24

版本更新 2026-11-12 22:05

雷达观测 2026-11-13 14:15

摘要

The Solvability Complexity Index (SCI) provides an extensional limit-height formalism for recovering a target map $Ξ$ from finite samples of an evaluation interface $Λ\subseteq\mathbb C^Ω$ by finite-height towers of pointwise limits. We first give a foundational analysis of what this extensional framework does and does not determine. In second place, we give a concrete non-trivial bridge result from a comparable SCI object to the well known limit rank of Weihrauch theory.

作者备注：Important: [arXiv:2603.18955v2]: additional discussions about evaluation-induced topologies, Kihara-style piecewise-continuity reducibilities, and feasible real RAM models and their connection to the SCI [arXiv:2603.18955v3]: Short+focused version on main results; this version: densified revised version with additional examples, algebraic properties of general algorithms