---
license: cc-by-4.0
language:
- en
tags:
- numeric-formats
- floating-point
- conformance
- audit-disclosed
size_categories:
- n<1K
---

# numeric-format-catalog v2 (audit-disclosed)

**Version:** v2.0 (2026-06-10) -- supersedes v1 (count=77, withdrawn).

**Count:** 81 formats across 13 clusters.

## Honest count-drift disclosure

This dataset is shipped with a known count-drift across four artefacts:

| Source | Count | Status |
|---|---|---|
| `arXiv:2606.09686` Table 1 (paper #3) | 84 | aspirational, MXFP6 split + standalone E8M0 |
| `specs/numeric/formats_catalog.t27` SSOT raw `// CATALOG:` lines | 83 | live ground truth |
| **THIS DATASET (codegen LIVE re-run)** | **81** | parser drops `gf512` + `gf1024` on bias-formula int() cast |
| `gen/numeric/formats_catalog.json` (committed in repo) | 77 | stale, pre-#1051 snapshot |
| v1 of this dataset (uploaded 2026-06-10 AM) | 77 | inherited stale gen |

**Why 81 and not 83 or 84:** the codegen `tools/gen_formats_catalog.py` cannot evaluate bias formulas of the form `2^N-1`, which are the canonical bias values for `gf512` and `gf1024`. Those two rows are silently dropped. We ship what the codegen actually produces, not a cherry-picked number. Patch tracked in [t27#1064](https://github.com/gHashTag/t27/issues/1064).

**Why ship 81 today instead of waiting for the patch:** because v1 shipped 77 yesterday. Replacing a stale 77 with an honest 81 + full audit is closer to the truth than leaving 77 up while the patch lands.

## What's in the dataset

- 81 row entries, each carrying: `id`, `name`, `bits`, `s` (sign bits), `e` (exponent bits), `m` (mantissa bits), `bias`, `phi_distance`, `storage`, `cluster`, `status`, `standard`, `use_case`, `source`
- 13 cluster groupings: IEEE754 binary, IEEE754 decimal, MLLowPrecision, GoldenFloat, Posit/Unum III, OCP MX, LNS, IntegerFixed, HistoricalVendor, Theoretical, Compression, Extended, QuantTuned
- Source SSOT: [`gHashTag/t27` `specs/numeric/formats_catalog.t27`](https://github.com/gHashTag/t27/blob/master/specs/numeric/formats_catalog.t27) HEAD `6ecad30`
- Regen output SHA-256: `546ba6fff1daec0b64483f599778ab63a9410405592c2e9dbc9d90dbb63bc48a`

## Known gaps vs paper #3 (arXiv:2606.09686)

| Cluster | Paper says | This dataset | Delta |
|---|---|---|---|
| GoldenFloat | 16 | 16 | 0 (both pre-#1051; current SSOT has 22, of which gen lifts 20) |
| OCP MX | 5 | 3 | -2 (no MXFP6 E2M3/E3M2 split; no standalone E8M0 block) |
| MLLowPrecision | 8 | 7 | -1 (NF4 placement) |
| Total | 84 | 81 | -3 |

## Reconciliation

- **t27#1064** -- tracking issue, five-step plan: parser patch -> regen -> CI invariant -> HF re-upload v3 -> arXiv erratum if needed
- Expected v3 ship count after parser patch: 83
- Expected v4 ship count after MXFP6/E8M0 reconciliation with paper: 84 (or paper erratum to whatever codegen produces)

## Citation

If you use this dataset, please cite the paper it accompanies:

```bibtex
@misc{vasilev2026numeric,
  title={An 84-Format Numeric Catalog with Bit-Exact Conformance Vectors},
  author={Vasilev, Dmitrii},
  year={2026},
  eprint={2606.09686},
  archivePrefix={arXiv},
  primaryClass={cs.MS}
}
```

Note: paper claims 84; this dataset ships 81 due to the parser bug. See "Honest count-drift disclosure" above.

## Provenance

- Uploader: `playra` (Dmitrii Vasilev, ORCID `0009-0008-4294-6159`)
- Affiliation: **Trinity S3AI**
- Repo: [`gHashTag/t27`](https://github.com/gHashTag/t27)
- License: CC BY 4.0
- Generated: 2026-06-10 +07 from HEAD `6ecad30`