Fitting Boundary Detection: A Navigation Methodology for AI Systems from Closed-Set Fitting to New Knowledge Generation

Abstract

Contemporary AI systems face a structural dilemma: the training distribution locks the knowledge boundary. Fitting accuracy improves continuously within the closed set, but the cognitive boundary barely moves. The "more data, larger models, higher precision" cycle described by scaling laws advances statistical metrics without expanding the physical territory the system can reach—a phenomenon we call fitting explosion. This paper proposes an intermediate version of the discrete frame protocol: fitting boundary detection. The core proposition is threefold. First, AI systems are representational fitting systems, not physical mechanism systems. Second, fitting necessarily has a boundary, and that boundary cannot be detected by the fitting system itself; it must be located by physical probes independent of the training distribution. Third, the boundary region where fitting fails is the natural entry point for new knowledge generation. We establish a complete detection framework: three admission criteria for discrete frame probes (training independence, output read-only, physical validity), three detection dimensions (configuration space, evolution parameter, density distribution—the "three pres"), and the configuration-space non-equilibrium degree as a family marker for probe validity. Through four cross-domain cases—protein structure prediction (Mdm2-B oligomerization blind spot), large language model attention (IRR-ATTN negative case), fractional-flux lattice (direction-field topological charge chiral transformation, 128,376 verification points with zero exceptions), and cosmological observation (multi-benchmark deviation construction)—we complete a self-consistency test: under non-equilibrium configuration space, probes precisely mark the fitting boundary; under equilibrium configuration space, probes naturally fail. The criterion admits no exceptions. The paper positions this methodology within three mainstream AI research lines: compared with out-of-distribution (OOD) detection, the probe measures physical validity rather than statistical outlierness; compared with active learning / curiosity-driven exploration, the probe selects sampling directions in physical space rather than data space; compared with existing AI-for-Science practice, the probe provides a falsifiable boundary criterion for "AI discovering new knowledge," rather than merely reporting fitting accuracy. This paper is positioned as an intermediate version of the discrete frame protocol. Its significance lies not in the technology itself, but in providing a human-intervenable interface for knowledge production after AI takes over scientific research: data sources are instruments, the working layer is basic data, and the output marker is the AI's blind spot. The ultimate goal is for formal systems to directly anchor chaotic flux and self-generate; but before that, fitting boundary detection provides an operable, verifiable, and iterable engineering path.