paper3-methodology

An 84-Format Numeric Catalog with Bit-Exact Conformance Vectors: A Vendor-Neutral Reference for FP8, BF16, MXFP4, and Microscaling Formats.

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.

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 -- 80-format SSOT catalog (specs/numeric/formats_catalog.t27).
• gHashTag/tt-lang-t27 -- Python package mirror (PyPI: tt-lang-t27), v0.4.0 release with 6 conformance packs.
• gHashTag/tt-trinity-corona -- silicon-grade format-conformance oracle (TTGF26a / GF180MCU).
• gHashTag/claim-audit-lab -- public methodology audit cases.

Citation

When the paper is on arXiv, a BibTeX entry will be added here. Until then, please cite by 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.
TBD	arXiv submission (cs.AR primary, cs.MS cross-list).