# Golden Ruler: A Numeric Format Catalog with Bit-Exact Conformance Vectors for FP8, BF16, MXFP4, and Microscaling Formats

arXiv: https://arxiv.org/abs/2606.09686 · HTML: https://mlsanity.com/paper/2606.09686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 5 of 5)

- [KernelBench: Can LLMs Write Efficient GPU Kernels?](https://mlsanity.com/paper/2502.10517/) (2025)
- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)
- [8-bit Numerical Formats for Deep Neural Networks](https://mlsanity.com/paper/2206.02915/) (2022)
- [Is Finer Better? The Limits of Microscaling Formats in Large Language Models](https://mlsanity.com/paper/2601.19026/) (2026)
- [Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning](https://mlsanity.com/paper/2606.04028/) (2026)

## Abstract (arXiv)

Numeric format proliferation in machine learning hardware -- FP8 (E4M3 and E5M2), BF16, MXFP4, microscaling block formats, and dozens of research variants -- has outpaced the availability of vendor-neutral, bit-exact reference material. Engineers porting models across accelerators encounter silent divergences that are difficult to diagnose without a shared ruler. This paper describes a catalog of 109 numeric formats spanning 12 clusters (83 at v2; the count is a catalog invariant, not a fixed number), a suite of six bit-exact conformance packs covering GF16, MXFP4 element, BF16, FP8 E4M3, FP8 E5M2, and E8M0 block scale, and an IEEE P3109 v3.2.0 cross-walk that maps each pack to its corresponding standards-track configured format. Each pack is a self-contained JSON document with a SHA-256 fingerprint, a shared row schema, and an anchor vector that encodes 3.0 -- the identity phi^2 + 1/phi^2 = 3 -- as a cross-pack sanity check. Packs are cross-validated against ml_dtypes 0.5.4 (Google/JAX); any divergence is documented explicitly and interpreted as a spec-permitted interpretation gap rather than hidden. The work is framed as registry filling: it does not propose new formats, make model-accuracy claims, or assert superiority over any vendor's implementation. All artifacts are publicly available at https://github.com/gHashTag/t27 under an open license.