Datasets:

playra
/

numeric-conformance-packs

license: mit
language:
  - en
pretty_name: Numeric Conformance Packs (Trinity S3AI / t27)
size_categories:
  - n<1K
task_categories:
  - other
task_ids:
  - other
multilinguality:
  - monolingual
annotations_creators:
  - expert-generated
language_creators:
  - machine-generated
source_datasets:
  - extended|playra/numeric-format-catalog
tags:
  - numeric-formats
  - conformance
  - bit-exact
  - goldenfloat
  - phi-identity
  - gf16
  - floating-point
  - numerical-conformance
  - formal-verification
  - audit-disclosed
  - trinity-s3ai
  - t27
  - audio-codecs-numerics
  - bench-vectors
paper:
  - arxiv: 2606.09686
  - arxiv: 2606.05017
configs:
  - config_name: gf4
    data_files:
      - split: vectors
        path: gf4.jsonl
  - config_name: gf8
    data_files:
      - split: vectors
        path: gf8.jsonl
  - config_name: gf12
    data_files:
      - split: vectors
        path: gf12.jsonl
  - config_name: gf16
    data_files:
      - split: vectors
        path: gf16.jsonl
  - config_name: gf20
    data_files:
      - split: vectors
        path: gf20.jsonl
  - config_name: gf24
    data_files:
      - split: vectors
        path: gf24.jsonl
  - config_name: gf32
    data_files:
      - split: vectors
        path: gf32.jsonl
  - config_name: goldenfloat_family
    data_files:
      - split: vectors
        path: goldenfloat_family.jsonl
  - config_name: phi_identity
    data_files:
      - split: vectors
        path: phi_identity.jsonl
  - config_name: phi_ratio
    data_files:
      - split: vectors
        path: phi_ratio.jsonl

Numeric Conformance Packs (Trinity S3AI / t27)

Version: v2.0 (2026-06-10). License: MIT. Maintainer: Trinity S3AI -- admin@t27.ai -- ORCID 0009-0008-4294-6159. Mirror of: gHashTag/t27 conformance/ and specs/numeric/ subtrees. Companion dataset: playra/numeric-format-catalog (the 80-format ruler this pack instantiates). Linked papers:

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

TL;DR

Bit-exact conformance vectors for the GoldenFloat (GF) family of phi-structured floating-point formats, plus two reference packs (phi_identity, phi_ratio) that exercise the canonical phi^2 + phi^-2 = 3 identity. The packs let any third-party kernel implementer check binary-level conformance with abs_error instead of "looks close in plots".

Quick start

from datasets import load_dataset

# Pull a single pack
gf16 = load_dataset("playra/numeric-conformance-packs", "gf16", split="vectors")
print(gf16.column_names)

# Verify round-trip on one vector
sample = gf16[0]
hex_bits   = sample["bits_hex"]
expected   = sample["f32_value"]
# Your decoder under test:
recovered  = your_gf16_decoder(int(hex_bits, 16))
abs_error  = abs(recovered - expected)
assert abs_error <= sample["tolerance"], f"GF16 conformance violated: {abs_error}"

The full call-and-response contract is documented per pack in manifest.json.

Pack inventory

Config	File	Lines	SHA-256 (8)	Purpose
`gf4`	`gf4.jsonl`	1	`dd264387`	GF4 reference vectors
`gf8`	`gf8.jsonl`	1	`44e27c75`	GF8 reference vectors
`gf12`	`gf12.jsonl`	1	`682e824d`	GF12 reference vectors
`gf16`	`gf16.jsonl`	1	`a7935733`	GF16 reference vectors (frozen silicon)
`gf20`	`gf20.jsonl`	34	`8bec16f1`	GF20 reference vectors
`gf24`	`gf24.jsonl`	34	`546019d0`	GF24 reference vectors
`gf32`	`gf32.jsonl`	37	`0dbb3a9c`	GF32 reference vectors
`goldenfloat_family`	`goldenfloat_family.jsonl`	25	`a6660f43`	Family-level invariants and cross-checks
`phi_identity`	`phi_identity.jsonl`	3	`88563e4e`	`phi^2 + phi^-2 = 3` reference points
`phi_ratio`	`phi_ratio.jsonl`	1	`90a183f4`	Canonical phi as f64 with hex tolerance

Full SHA-256 manifest: SHA256SUMS.txt. Machine-readable schema and per-pack manifest: manifest.json.

Provenance

This dataset is a mirror, not a primary source. The primary source of truth is the t27 repository:

Specs: gHashTag/t27 -> specs/numeric/ (.t27 SSOT files)
Conformance generators: gHashTag/t27 -> conformance/ + tools/gen_*.py
Frozen silicon anchor: GF16 is validated end-to-end against the TTGF26a / GF180MCU tape-out (35/35 vectors at 323 MHz, see arXiv:2606.09686 Section 6).

Every JSONL row carries:

format_name, format_bits, format_spec -- canonical identity
bit_layout / format_spec -- exact field widths
seal -- SHA-256 of the row payload for tamper-evidence
formal_proof (where applicable) -- Coq lemma name in coq/Kernel/*

How this fits the wider ruler

These packs sit at Tier 1 of a three-tier numeric-format corpus:

Tier 0 SSOT: specs/numeric/formats_catalog.t27 (machine-checked, 83 rows live)
Tier 1 Portable JSON packs (this dataset)
Tier 2 Silicon-validated ROM: tt-trinity-corona 80-format ROM + 19 RTL decoders + 5-layer dossier (TTGF26a / GF180MCU tape-out)

The companion dataset playra/numeric-format-catalog carries the full 80-format catalog with cluster, bit-width, and phi-distance metadata.

Considerations for using the data

Recommended uses

Verifying a third-party GF or phi-arithmetic kernel against a fixed reference
Cross-checking custom GoldenFloat decoders during silicon bring-up
Teaching: bit-exact rounding behaviour for non-IEEE phi-structured formats
Audit and reproducibility studies of phi-structured arithmetic

Out of scope

IEEE P3109 OFP8 -- cross-walk is documented in p3109_crosswalk.json (mapping only) but not a primary distribution here
NF4 / NF8 (NormalFloat) -- adjacent quantisation formats, not covered
MXFP4 / MXFP6 -- OCP mixed-precision wrappers, see arXiv:2606.09686 Section 4 for the cross-walk
Posit / Takum / LNS -- alternative number systems are catalogued in playra/numeric-format-catalog but no conformance pack here
Mixed-precision GEMM -- this is a per-format conformance dataset, not an end-to-end kernel benchmark

Known limitations

Pack size is uneven by design. Several packs ship 1 row (anchor); others ship 34-37 rows (sweep). The number of rows reflects how the format is tested in the kernel, not its importance.
abs_error only. PCC, FID, and other distributional metrics are explicitly out of scope; this is a pointwise conformance dataset.
GF dominance. Reflects the maintainer's research focus. For SOTA AI quantisation formats (NF4, MXFP4, posit), this dataset is not a substitute for OCP or open-compute reference implementations.
Single-language schema. All vectors and manifest are English-only. No localisation.
No social-bias dimension. Numeric format conformance is not a fairness-sensitive task; if you're using these vectors as part of a downstream model evaluation, fairness considerations live at the model level, not here.

Known biases

Equal weight per cluster. The pack distribution mirrors the maintainer's research priorities; it is not a representative sample of the AI accelerator format population.
Phi-structured emphasis. All formats with the goldenfloat tag are designed around the closed-form rule e = round((N-1)/phi^2). This is by construction, not a discovered property.

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{vasilev2026goldenfloatidentity,
  title  = {GoldenFloat: A Phi-Structured Floating-Point Family with Closed-Form
            Field Widths from the Identity Phi^2 + Phi^-2 = 3},
  author = {Vasilev, Daniil and {Trinity S3AI}},
  year   = {2026},
  eprint = {2606.05017},
  archivePrefix = {arXiv},
  primaryClass  = {cs.AR},
  url    = {https://arxiv.org/abs/2606.05017}
}

@misc{trinitys3ai2026numericpacks,
  title  = {Numeric Conformance Packs},
  author = {{Trinity S3AI}},
  year   = {2026},
  publisher = {Hugging Face},
  url    = {https://huggingface.co/datasets/playra/numeric-conformance-packs}
}

Maintenance and changelog

Date	Version	Change
2026-04-07	v1.0	Initial 10-pack release
2026-06-10	v2.0	Updated with audit-disclosed schema, SHA-256 manifest, anchor preprints
2026-06-13	v2.1	Added catalog preprint cross-link (arXiv:2606.09686), README upgrade per FAIR / Datasheets / Data Cards

Update cadence. No fixed cadence. New packs are added when (a) a new GF rung is verified, or (b) a new conformance contract is requested via gHashTag/t27 issues. Existing rows are immutable; if a format spec changes, the row is replaced and the SHA-256 manifest tracks the diff.

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

Machine-readable metadata

Croissant JSON-LD: croissant.json at repo root (MLCommons spec 1.0)
YAML metadata: at the top of this file, machine-parseable per HF Hub spec
SHA-256 manifest: SHA256SUMS.txt
P3109 cross-walk (read-only mapping): p3109_crosswalk.json

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