paper3-methodology

Golden Ruler: A Numeric Format Catalog with Bit-Exact Conformance Vectors for FP8, BF16, MXFP4, and Microscaling Formats -- arXiv:2606.09686 (v3, announced 7 Sep 2026).

Author

Dmitrii Vasilev Trinity S^3 AI ORCID: 0009-0008-4294-6159 Email: admin@t27.ai GitHub: @gHashTag

Repository layout

File	Description
main.tex	LaTeX source of the manuscript (1094 lines, 16 pages).
paper3-methodology-2026-06-08-v3-trinity.pdf	Compiled PDF v3-trinity, 16 pp, 134 KB. SHA-256: f31f5dd243afc7b2ba4a423859a1e1dc67036c3a93affab30acc8d02f0a15eef.
ARXIV_METADATA.md	Submission metadata block (title, authors, categories, abstract).
LICENSE	Dual license: text under CC BY 4.0; code/metadata under MIT.

Abstract (excerpt)

This report documents the methodology used to construct a 84-format numeric catalog (FORMAT-SPEC-001.json) with bit-exact conformance vectors for six active formats: GF16, MXFP4 element, BF16, FP8 E4M3, FP8 E5M2, and E8M0 block scale. Vectors are cross-validated against ml_dtypes 0.5.4 (Google / JAX) and ship with honest abs_error columns -- non-representable inputs are not hidden as exact matches. A documented divergence on FP8 E4M3 overflow handling (saturate-to-max versus overflow-to-NaN, OCP MX v1.0 permits both) is published as a Discussion section rather than smoothed over.

Note (2026-09-05): the format count is a live SSOT invariant, not a fixed number -- 84 in this repository's manuscript revision, 83 at arXiv v2 (22 Jun 2026), 109 at arXiv v3 (Sep 2026). Source of truth: tools/gen_formats_catalog.py in gHashTag/t27 ("parsed N formats").

Anchor

phi^2 + 1/phi^2 = 3 (Lucas number L_2). Used as a universal numeric check point: 3.0 is exactly representable in nearly every binary and microscaling format in the catalog.

Companion artefacts

• arXiv:2606.05017 -- GoldenFloat preprint (cs.AR), anchor citation.
• gHashTag/t27 -- the SSOT catalog (specs/numeric/formats_catalog.t27); the format count is a live invariant, 109 formats as of Sep 2026.
• gHashTag/tt-lang-t27 -- Python package mirror (PyPI: tt-lang-t27), v0.4.0 release with 6 conformance packs.
• gHashTag/tt-trinity-corona -- format-conformance oracle design targeting TTGF26a / GF180MCU (GDS + precheck passed; not submitted, no die).
• gHashTag/claim-audit-lab -- public methodology audit cases.

Citation

The paper is on arXiv as arXiv:2606.09686 (v1 8 Jun 2026; v2 22 Jun 2026, live; v3 submitted 4 Sep 2026 under the title Golden Ruler ..., announced 7 Sep 2026). Cite:

Vasilev, D. (2026). Golden Ruler: A Numeric Format Catalog with Bit-Exact Conformance Vectors for FP8, BF16, MXFP4, and Microscaling Formats. arXiv:2606.09686.

To cite this repository's manuscript revision specifically, use the file SHA-256 above plus the repository URL.

Reproducibility

Build environment: tectonic 0.15.0+, LaTeX class article, fontspec-free pdfLaTeX-compatible pipeline. Build command:

tectonic -X compile main.tex

No external data dependencies; tables are inline literals.

Hard rules applied

• ASCII-only manuscript body (Greek letters spelled out: phi, mu).
• No hype vocabulary (no breakthrough, revolutionary, etc.).
• Honest abs_error on every conformance vector that is not representable -- no silent zeros.
• Claim-status discipline: [Verified], [Empirical fit], [Open conjecture] labels where relevant.

Status

Date	Event
2026-06-08	v3-trinity finalized, ORCID locked, repo published.
2026-06-08	arXiv v1 posted -- arXiv:2606.09686 (cs.AR primary; cs.AI, cs.MS, cs.PF, math.NA cross-lists).
2026-06-22	arXiv v2 (17 pp), the live version.
2026-09-04	arXiv v3 submitted under the title Golden Ruler: A Numeric Format Catalog with Bit-Exact Conformance Vectors for FP8, BF16, MXFP4, and Microscaling Formats (19 pp; 109 formats); announces 2026-09-07.