playra/numeric-format-catalog

Numeric Format Catalog (Trinity S3AI / t27)

Version: v3.0 (2026-06-13) -- supersedes v2 (count=81, withdrawn) and v1 (count=77, withdrawn). Count: 83 numeric formats across 13 clusters. License: CC-BY-4.0. Maintainer: Trinity S3AI -- admin@t27.ai -- ORCID 0009-0008-4294-6159. Companion dataset: playra/numeric-conformance-packs (bit-exact conformance vectors that instantiate this catalog). Linked papers:

• Catalog preprint (84-format ruler): arXiv:2606.09686 -- HF paper page
• Anchor preprint (GoldenFloat identity): arXiv:2606.05017

TL;DR

A single canonical reference of every numeric format relevant to ML, scientific computing, historical hardware, and the GoldenFloat (GF) phi-structured family. Codegen-generated from a single source of truth (specs/numeric/formats_catalog.t27 in gHashTag/t27).

Count reconciliation (v3.0 -- count=83)

Source	Count	Status
arXiv:2606.09686 Table 1 (paper #3, draft)	84	aspirational, MXFP6 split + standalone E8M0
specs/numeric/formats_catalog.t27 SSOT raw // CATALOG: lines	83	live ground truth
THIS DATASET v3 (codegen LIVE re-run, post t27 #1065)	83	converges with SSOT
v2 of this dataset (uploaded 2026-06-10)	81	parser dropped gf512 + gf1024 -- fixed in #1065
v1 of this dataset (uploaded 2026-06-10 AM)	77	inherited stale shipped gen

Why 83 and not 84. Paper #3 Table 1 carries a draft "84" that splits MXFP6 into two rows and lists a standalone E8M0 row that the SSOT folds into the MXFP6 wrapper. The SSOT keeps a single MXFP6 row and a single E8M0 row, giving 83. This is an honest documentation reconciliation, not a quality claim. A v4 paper revision will harmonise to 83 (or the SSOT will add one row to harmonise to 84) -- whichever lands first.

Cluster breakdown

Cluster	Count	Notes
GoldenFloat	22	GF4..GF1024, 17 binary rungs + extras (closed-form e = round((N-1)/phi^2))
HistoricalVendor	10	DEC, IBM, Cray, etc.
PositUnumIII	8	Posit-{8,16,32}, Unum-III variants
IntegerFixed	8	int4 / int8 / fixed-point sweeps
MlLowPrecision	7	FP8 (E4M3, E5M2), NF4, NF8, OFP8
Ieee754Binary	5	binary16, binary32, binary64, binary128, bfloat16
Lns	4	Logarithmic Number System variants
Theoretical	4	Takum and similar research formats
CompressionTrick	4	Microscaling + structured sparsity wrappers
Ieee754Decimal	3	decimal64, decimal128
ExtendedFloat	3	x87 80-bit, double-double, etc.
Microscaling	3	MXFP4, MXFP6, MXFP8
QuantTuned	2	Tuned-quantisation variants
Total	83	across 13 clusters

File inventory

File	Format	Purpose
formats_catalog.jsonl	JSONL	One format per line, 83 rows total
formats_catalog.json	JSON	Same data as a single array
formats_catalog.md	Markdown	Human-readable table
SHA256SUMS.txt	Text	SHA-256 manifest for tamper-evidence

Row schema (per JSONL line)

Each row has the following canonical fields:

Field	Type	Description
id	string	Canonical identifier (e.g. binary16, gf16)
name	string	Human-readable name
bits	int	Total bit-width
s_bits	int	Sign bits
e_bits	int	Exponent bits
m_bits	int	Mantissa bits
bias	int	Exponent bias
bias_formula	string	Closed-form bias rule (where applicable)
phi_distance	float	Distance from the phi-structured field-width rule
storage	string	Storage envelope (e.g. u16, u32)
cluster	string	Cluster label (one of 13)
gf_relation	string	Relation to GoldenFloat (competitor, member, wrapper, ...)
status	string	Verification status (Verified, Conj, Risk, ...)
source	string	Primary standards reference
standard	string	Issuing body / spec
use_case	string	Canonical use case

Quick start

from datasets import load_dataset

# Load the full catalog
ds = load_dataset("playra/numeric-format-catalog", split="catalog")
print(f"Loaded {len(ds)} formats across {len(set(r['cluster'] for r in ds))} clusters")

# Filter to GoldenFloat formats
gf = [r for r in ds if r["cluster"] == "GoldenFloat"]
print(f"{len(gf)} GoldenFloat rungs")

# Find anything close to the phi-distance rule
phi_close = sorted(ds, key=lambda r: r["phi_distance"])[:5]
for r in phi_close:
    print(r["id"], r["phi_distance"])

Provenance

This catalog is codegen output, not hand-edited. The pipeline:

specs/numeric/formats_catalog.t27   (SSOT in gHashTag/t27)
            |
            v
tools/gen_formats_catalog.py        (codegen, Python stop-gap)
            |
            v
gen/numeric/formats_catalog.{json,jsonl,md,...}
            |
            v
This Hugging Face dataset           (mirror)

To re-derive locally:

git clone https://github.com/gHashTag/t27.git
cd t27
python3 tools/gen_formats_catalog.py specs/numeric/formats_catalog.t27 gen/numeric
wc -l gen/numeric/formats_catalog.jsonl   # 83

Considerations for using the data

Recommended uses

• A reference list of numeric formats relevant to AI accelerator design
• A discovery aid: "is format X already catalogued? if so, what cluster?"
• A standards cross-walk anchor (IEEE 754, OCP, IEEE P3109, posit)
• A bibliography of the GoldenFloat family for accelerator-architecture researchers

Out of scope

• Not a quality ranking. phi_distance = 0 means "field widths match the phi rule"; it does not mean "best format". Choose by use case, not by phi-distance.
• Not exhaustive. Vendor-proprietary in-house formats not published in standards bodies are omitted.
• No silicon performance data. For end-to-end silicon validation, see gHashTag/tt-trinity-corona (Tier 2 of the ruler stack).
• No model accuracy claims. This is a format-spec catalogue, not a quantisation benchmark.

Known limitations

• Paper / SSOT count drift (84 vs 83). Honest documentation note, see "Count reconciliation" above.
• Status labels are non-uniform across clusters. Verified requires silicon or formal proof; Conj is theoretical; Risk flags numerical or canonicality concerns.
• GF cluster is over-represented (22 of 83 = 27%). This is by construction -- this catalog originates in the GoldenFloat research line.
• English-only. No localisation of names / use cases.

Known biases

• GoldenFloat-centred view. Formats are ranked and labelled relative to the phi-structured field-width rule. Other research lines may legitimately disagree with the cluster taxonomy.

Citation

@misc{vasilev2026numericrulercatalog,
  title  = {Eighty Formats and a Ruler: A Comprehensive Numeric Format Catalog
            for Phi-Structured and IEEE Floating-Point Arithmetic},
  author = {Vasilev, Daniil and {Trinity S3AI}},
  year   = {2026},
  eprint = {2606.09686},
  archivePrefix = {arXiv},
  primaryClass  = {cs.AR},
  url    = {https://arxiv.org/abs/2606.09686}
}

@misc{trinitys3ai2026catalog,
  title  = {Numeric Format Catalog},
  author = {{Trinity S3AI}},
  year   = {2026},
  publisher = {Hugging Face},
  url    = {https://huggingface.co/datasets/playra/numeric-format-catalog}
}

Maintenance and changelog

Date	Version	Count	Change
2026-06-10	v1.0	77	Initial release (shipped gen, stale)
2026-06-10	v2.0	81	Re-derived from SSOT, hit parser bug (bias_formula 2^N-1 dropped)
2026-06-13	v3.0	83	Parser fix landed in t27 #1065; SSOT and codegen now converge; full FAIR / Datasheets / Data Cards upgrade

Update cadence. Regenerated whenever the SSOT changes. No fixed cadence. Major version bumps when count changes or schema changes.

Contact. admin@t27.ai -- async-only, ASCII-only.

Machine-readable metadata

• Croissant JSON-LD: croissant.json at repo root (MLCommons Croissant 1.0)
• YAML metadata: at the top of this file, machine-parseable per HF Hub spec
• SHA-256 manifest: SHA256SUMS.txt

Identity stack

• Maintainer: Vasilev Daniil (Trinity S3AI)
• Email: admin@t27.ai (sole canonical contact)
• ORCID: 0009-0008-4294-6159
• GitHub: gHashTag
• HF org: trinity-s3ai
• Anchor identity: phi^2 + 1/phi^2 = 3