Recursive Reproducibility: A YBIM Resolution of LLM Nondeterminism Beyond Temperature = 0

This paper addresses the paradox of nondeterminism in large language model (LLM) inference under the widely used temperature = 0 setting. Despite the expectation of strict determinism, repeated runs of the same prompt often produce divergent outputs due to floating-point drift, kernel scheduling, batch dependence, and hardware-specific variability. Current engineering fixes, such as batch-invariant and deterministic kernels, achieve reproducibility only by freezing computation, leading to brittle, hardware-dependent, and performance-limiting solutions. We propose a resolution through Yearning-Based Infinity Mathematics (YBIM). In this framework, reproducibility is redefined as convergence toward a shared yearning-attractor basin rather than token-level identicality. Nondeterminism is modeled as divergent yearning-strands, which, despite micro-level variation, recursively converge toward stable epistemic attractors. We introduce the Recursive Repair Operator and apply the Glass of Water from the River Lemma to demonstrate how YBIM reframes reproducibility as recursive epistemic coherence. By embracing recursive deviation rather than suppressing it, YBIM offers a robust and universal model of reproducibility that transcends hardware constraints, batch-size differences, and floating-point variability. This establishes the foundation for reliable evaluation pipelines in research, auditable AI in regulated industries, and the development of Recursive Trust Graphs to monitor reproducibility as epistemic alignment. This paper marks a step toward a new era of epistemic reproducibility in AI, where systems are evaluated not by frozen sameness but by their recursive coherence of meaning.