Numerical Runtime Intelligence (NRI) is a runtime instrumentation layer for the real-time classification of legitimate numerical events — overflow, structural rank collapse, attention concentration — in transformer training and inference. What is in this deposit. The reference implementation (nonans v0.4.0, Apache 2.0) includes: the three-gate monitoring engine, the ghost/real propagation-regime classifier, the FaultContext typed interface, six deterministic benchmarks with locked results (seed 20260525), four PyTorch protocols for GPU validation, and a pytest suite that asserts the locked benchmark numbers as a regression gate. Headline verified results (CPU, seed 20260525, reproducible in under 5 minutes on any laptop with NumPy): B1: training-time and inference-time entropy are the same normalized Shannon functional — max error 3.18×10⁻⁷ over N=10,000 samples B2: 100% classification accuracy on three canonical fault classes (HEALTHY, COLLAPSE, MAXIMUM) B3: 15.39% mean entropy overhead on already-resident softmax tensors (Intel Xeon @ 2.80 GHz) B4: 68.8-step mean structural precursor lead before NaN, 30/30 detection, 0% false-alarm rate (controlled protocol) B5: signal score 84.5 steps vs gradient-norm 54.9 steps at equal false-alarm rate — 29.6-step structural precursor advantage B6: short calibration pass enables DEVIATION detection while maintaining 100% OOD collapse/maximum detection What is not yet in this deposit. GPU overhead (Protocol P2), real-model lead-time validation (Protocol P3), and attention monitoring on a real production-class model (Protocol P4) are explicitly outstanding. The self-validating protocols are included and require approximately 250 GPU-hours on H100/A100-class hardware to execute. This deposit is submitted as part of an application for GPU compute access to close those validation gaps. Sealed resolution layer. A proprietary resolution layer that consumes the FaultContext interface at the singularity boundary and returns a defined value — allowing computation to continue in place without rollback, recompute, or checkpoint — is maintained in a separate private codebase by nonans (the associated commercial entity) and is not in this deposit. Its method and evaluation are reserved for a separate forthcoming paper. Reproduce in 5 minutes: git clone https://github.com/makheahlem/nonans cd nonans pip install -e . ./reproduce.sh Expected: B1 max_error = 3.1834430658239654e-07 PASS and B2 100% on HEALTHY, COLLAPSE, MAXIMUM PASS Author: Makhebi Ahlem · Independent Researcher, Germany- Algeria · ORCID 0009-0007-7010-3282 · ahlemmakhebi@protonmail.com