v3: count=83 truth (post PR #1065), 13 clusters, Croissant 1.0 JSON-LD, full datasheet sections

README.md

@@ -2,82 +2,238 @@
 license: cc-by-4.0
 language:
 - en
+pretty_name: Numeric Format Catalog (Trinity S3AI / t27)
+size_categories:
+- n<1K
+task_categories:
+- other
+multilinguality:
+- monolingual
+annotations_creators:
+- expert-generated
+language_creators:
+- machine-generated
 tags:
 - numeric-formats
 - floating-point
 - conformance
 - audit-disclosed
-size_categories:
-- n<1K
+- catalog
+- ruler
+- ieee-754
+- goldenfloat
+- posit
+- mxfp4
+- fp8
+- bf16
+- trinity-s3ai
+- t27
 paper:
 - arxiv: 2606.09686
+- arxiv: 2606.05017
+configs:
+- config_name: default
+  data_files:
+  - split: catalog
+    path: formats_catalog.jsonl
 ---
 
-# numeric-format-catalog v2 (audit-disclosed)
+# Numeric Format Catalog (Trinity S3AI / t27)
 
-**Version:** v2.0 (2026-06-10) -- supersedes v1 (count=77, withdrawn).
+**Version:** v3.0 (2026-06-13) -- supersedes v2 (count=81, withdrawn) and v1 (count=77, withdrawn).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](https://orcid.org/0009-0008-4294-6159).
+**Companion dataset:** [`playra/numeric-conformance-packs`](https://huggingface.co/datasets/playra/numeric-conformance-packs) (bit-exact conformance vectors that instantiate this catalog).
+**Linked papers:**
+- **Catalog preprint (84-format ruler):** [arXiv:2606.09686](https://arxiv.org/abs/2606.09686) -- [HF paper page](https://huggingface.co/papers/2606.09686)
+- **Anchor preprint (GoldenFloat identity):** [arXiv:2606.05017](https://arxiv.org/abs/2606.05017)
 
-**Count:** 81 formats across 13 clusters.
+## TL;DR
 
-## Honest count-drift disclosure
+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`](https://github.com/gHashTag/t27)).
 
-This dataset is shipped with a known count-drift across four artefacts:
+## Count reconciliation (v3.0 -- count=83)
 
-| Source | Count | Status |
+| 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 |
+| `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](https://github.com/gHashTag/t27/pull/1065) |
+| v1 of this dataset (uploaded 2026-06-10 AM)                       | 77    | inherited stale shipped 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 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.
 
-**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.
+## Cluster breakdown
 
-## What's in the dataset
+| 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     |
 
-- 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`
+## Row schema (per JSONL line)
 
-## Known gaps vs paper #3 (arXiv:2606.09686)
+Each row has the following canonical fields:
 
-| 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 |
+| 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
+
+```python
+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"])
+```
 
-## Reconciliation
+## Provenance
 
-- **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)
+This catalog is **codegen output**, not hand-edited. The pipeline:
 
-## Citation
+```
+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:
+
+```bash
+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
 
-If you use this dataset, please cite the paper it accompanies:
+- 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`](https://github.com/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
 
 ```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}
+@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}
 }
 ```
 
-Note: paper claims 84; this dataset ships 81 due to the parser bug. See "Honest count-drift disclosure" above.
+## Maintenance and changelog
 
-## Provenance
+| 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](https://github.com/gHashTag/t27/pull/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`](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`](SHA256SUMS.txt)
+
+## Identity stack
 
-- 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`
+- **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`

croissant.json

@@ -0,0 +1,187 @@
+{
+  "@context": {
+    "@language": "en",
+    "@vocab": "https://schema.org/",
+    "sc": "https://schema.org/",
+    "cr": "http://mlcommons.org/croissant/",
+    "rai": "http://mlcommons.org/croissant/RAI/",
+    "data": {
+      "@id": "cr:data",
+      "@type": "@json"
+    },
+    "dataType": {
+      "@id": "cr:dataType",
+      "@type": "@vocab"
+    },
+    "examples": {
+      "@id": "cr:examples",
+      "@type": "@json"
+    },
+    "extract": "cr:extract",
+    "field": "cr:field",
+    "fileObject": "cr:fileObject",
+    "fileSet": "cr:fileSet",
+    "format": "cr:format",
+    "includes": "cr:includes",
+    "isLiveDataset": "cr:isLiveDataset",
+    "jsonPath": "cr:jsonPath",
+    "key": "cr:key",
+    "md5": "cr:md5",
+    "parentField": "cr:parentField",
+    "path": "cr:path",
+    "recordSet": "cr:recordSet",
+    "references": "cr:references",
+    "regex": "cr:regex",
+    "repeated": "cr:repeated",
+    "replace": "cr:replace",
+    "separator": "cr:separator",
+    "source": "cr:source",
+    "subField": "cr:subField",
+    "transform": "cr:transform"
+  },
+  "@type": "sc:Dataset",
+  "conformsTo": "http://mlcommons.org/croissant/1.0",
+  "name": "numeric-format-catalog",
+  "description": "Single-source-of-truth catalog of 83 numeric formats across 13 clusters (IEEE-754 binary/decimal, ML low-precision FP8/FP4/FP6/bf16, GoldenFloat phi-structured ladder GF4..GF1024, Posit/Unum-III, OCP Microscaling MXFP4/MXFP6/MXFP8, Logarithmic LNS, integer/fixed, historical vendor, theoretical, compression-trick, quantisation-tuned). Codegen derived from the gHashTag/t27 .t27 specification language; cross-validated against ml_dtypes 0.5.4 (Google/JAX) on overlapping formats; reconciled with IEEE P3109 v3.2.0.",
+  "url": "https://huggingface.co/datasets/playra/numeric-format-catalog",
+  "version": "3.0.0",
+  "datePublished": "2026-06-13",
+  "creator": {
+    "@type": "Person",
+    "name": "Dmitrii Vasilev",
+    "identifier": "https://orcid.org/0009-0008-4294-6159",
+    "email": "admin@t27.ai",
+    "affiliation": {
+      "@type": "Organization",
+      "name": "Trinity S3AI (independent research collective)"
+    }
+  },
+  "publisher": {
+    "@type": "Organization",
+    "name": "Trinity S3AI",
+    "url": "https://github.com/gHashTag"
+  },
+  "license": "https://creativecommons.org/licenses/by/4.0/",
+  "citeAs": "@misc{vasilev2026catalog, author = {Vasilev, Dmitrii}, title = {An 84-Format Numeric Catalog with Bit-Exact Conformance Vectors}, year = {2026}, eprint = {2606.09686}, archivePrefix = {arXiv}, primaryClass = {cs.MS}, doi = {10.48550/arXiv.2606.09686}}",
+  "keywords": [
+    "numeric formats",
+    "floating point",
+    "FP8",
+    "MXFP4",
+    "bfloat16",
+    "GoldenFloat",
+    "posit",
+    "P3109",
+    "OCP Microscaling",
+    "machine learning systems"
+  ],
+  "isLiveDataset": false,
+  "distribution": [
+    {
+      "@type": "cr:FileObject",
+      "@id": "formats_catalog_jsonl",
+      "name": "formats_catalog.jsonl",
+      "description": "Newline-delimited JSON, one numeric format record per line (83 lines).",
+      "contentUrl": "formats_catalog.jsonl",
+      "encodingFormat": "application/jsonlines",
+      "sha256": "bd04ba0c7fdc7dbb8f38a04d2f2635bc64b3667fabb7b313e852bc8904af5553"
+    },
+    {
+      "@type": "cr:FileObject",
+      "@id": "formats_catalog_json",
+      "name": "formats_catalog.json",
+      "description": "Single-document JSON array of 83 numeric format records.",
+      "contentUrl": "formats_catalog.json",
+      "encodingFormat": "application/json",
+      "sha256": "451e4f320f03f91a92cfcc6a9a56bfe829d8ce669ead25b3fda117ad12ec9d93"
+    }
+  ],
+  "recordSet": [
+    {
+      "@type": "cr:RecordSet",
+      "@id": "formats",
+      "name": "formats",
+      "description": "One record per numeric format (83 records).",
+      "key": {"@id": "formats/name"},
+      "field": [
+        {
+          "@type": "cr:Field",
+          "@id": "formats/name",
+          "name": "name",
+          "description": "Canonical short name (e.g. gf16, fp8_e4m3, mxfp4, bf16, posit8).",
+          "dataType": "sc:Text",
+          "source": {
+            "fileObject": {"@id": "formats_catalog_jsonl"},
+            "extract": {"jsonPath": "$.name"}
+          }
+        },
+        {
+          "@type": "cr:Field",
+          "@id": "formats/cluster",
+          "name": "cluster",
+          "description": "One of 13 cluster labels: GoldenFloat, HistoricalVendor, PositUnumIII, IntegerFixed, MlLowPrecision, Ieee754Binary, Lns, Theoretical, CompressionTrick, Ieee754Decimal, ExtendedFloat, Microscaling, QuantTuned.",
+          "dataType": "sc:Text",
+          "source": {
+            "fileObject": {"@id": "formats_catalog_jsonl"},
+            "extract": {"jsonPath": "$.cluster"}
+          }
+        },
+        {
+          "@type": "cr:Field",
+          "@id": "formats/total_bits",
+          "name": "total_bits",
+          "description": "Total bit width of the format.",
+          "dataType": "sc:Integer",
+          "source": {
+            "fileObject": {"@id": "formats_catalog_jsonl"},
+            "extract": {"jsonPath": "$.total_bits"}
+          }
+        },
+        {
+          "@type": "cr:Field",
+          "@id": "formats/sign_bits",
+          "name": "sign_bits",
+          "description": "Number of sign bits.",
+          "dataType": "sc:Integer",
+          "source": {
+            "fileObject": {"@id": "formats_catalog_jsonl"},
+            "extract": {"jsonPath": "$.sign_bits"}
+          }
+        },
+        {
+          "@type": "cr:Field",
+          "@id": "formats/exp_bits",
+          "name": "exp_bits",
+          "description": "Number of exponent bits.",
+          "dataType": "sc:Integer",
+          "source": {
+            "fileObject": {"@id": "formats_catalog_jsonl"},
+            "extract": {"jsonPath": "$.exp_bits"}
+          }
+        },
+        {
+          "@type": "cr:Field",
+          "@id": "formats/mant_bits",
+          "name": "mant_bits",
+          "description": "Number of mantissa/fraction bits.",
+          "dataType": "sc:Integer",
+          "source": {
+            "fileObject": {"@id": "formats_catalog_jsonl"},
+            "extract": {"jsonPath": "$.mant_bits"}
+          }
+        },
+        {
+          "@type": "cr:Field",
+          "@id": "formats/status",
+          "name": "status",
+          "description": "Claim status label: Verified, Empirical_fit, Open_conjecture, Risk, Retracted.",
+          "dataType": "sc:Text",
+          "source": {
+            "fileObject": {"@id": "formats_catalog_jsonl"},
+            "extract": {"jsonPath": "$.status"}
+          }
+        }
+      ]
+    }
+  ]
+}

formats_catalog.json

@@ -1,5 +1,5 @@
 {
-  "count": 81,
+  "count": 83,
   "formats": [
     {
       "id": "binary16",
@@ -9,6 +9,7 @@
       "e_bits": 5,
       "m_bits": 10,
       "bias": 15,
+      "bias_formula": "15",
       "phi_distance": 0.118,
       "storage": "u16",
       "cluster": "Ieee754Binary",
@@ -26,6 +27,7 @@
       "e_bits": 8,
       "m_bits": 23,
       "bias": 127,
+      "bias_formula": "127",
       "phi_distance": 0.27,
       "storage": "u32",
       "cluster": "Ieee754Binary",
@@ -43,6 +45,7 @@
       "e_bits": 11,
       "m_bits": 52,
       "bias": 1023,
+      "bias_formula": "1023",
       "phi_distance": 0.406,
       "storage": "u64",
       "cluster": "Ieee754Binary",
@@ -60,6 +63,7 @@
       "e_bits": 15,
       "m_bits": 112,
       "bias": 16383,
+      "bias_formula": "16383",
       "phi_distance": 0.484,
       "storage": "u128",
       "cluster": "Ieee754Binary",
@@ -77,6 +81,7 @@
       "e_bits": 19,
       "m_bits": 236,
       "bias": 262143,
+      "bias_formula": "262143",
       "phi_distance": 0.538,
       "storage": "u256_software",
       "cluster": "Ieee754Binary",
@@ -94,6 +99,7 @@
       "e_bits": 11,
       "m_bits": 20,
       "bias": 101,
+      "bias_formula": "101",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "Ieee754Decimal",
@@ -111,6 +117,7 @@
       "e_bits": 13,
       "m_bits": 50,
       "bias": 398,
+      "bias_formula": "398",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "Ieee754Decimal",
@@ -128,6 +135,7 @@
       "e_bits": 17,
       "m_bits": 110,
       "bias": 6176,
+      "bias_formula": "6176",
       "phi_distance": -1.0,
       "storage": "u128",
       "cluster": "Ieee754Decimal",
@@ -145,6 +153,7 @@
       "e_bits": 15,
       "m_bits": 64,
       "bias": 16383,
+      "bias_formula": "16383",
       "phi_distance": -1.0,
       "storage": "u80_padded",
       "cluster": "ExtendedFloat",
@@ -162,6 +171,7 @@
       "e_bits": 22,
       "m_bits": 104,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "two_u64",
       "cluster": "ExtendedFloat",
@@ -179,6 +189,7 @@
       "e_bits": 44,
       "m_bits": 208,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "four_u64",
       "cluster": "ExtendedFloat",
@@ -196,6 +207,7 @@
       "e_bits": 8,
       "m_bits": 7,
       "bias": 127,
+      "bias_formula": "127",
       "phi_distance": 0.525,
       "storage": "u16",
       "cluster": "MlLowPrecision",
@@ -213,6 +225,7 @@
       "e_bits": 8,
       "m_bits": 10,
       "bias": 127,
+      "bias_formula": "127",
       "phi_distance": 0.27,
       "storage": "u32_padded",
       "cluster": "MlLowPrecision",
@@ -230,6 +243,7 @@
       "e_bits": 4,
       "m_bits": 3,
       "bias": 7,
+      "bias_formula": "7",
       "phi_distance": 0.715,
       "storage": "u8",
       "cluster": "MlLowPrecision",
@@ -247,6 +261,7 @@
       "e_bits": 5,
       "m_bits": 2,
       "bias": 15,
+      "bias_formula": "15",
       "phi_distance": 1.882,
       "storage": "u8",
       "cluster": "MlLowPrecision",
@@ -264,6 +279,7 @@
       "e_bits": 3,
       "m_bits": 2,
       "bias": 3,
+      "bias_formula": "3",
       "phi_distance": 0.882,
       "storage": "u8_packed",
       "cluster": "MlLowPrecision",
@@ -281,6 +297,7 @@
       "e_bits": 2,
       "m_bits": 3,
       "bias": 1,
+      "bias_formula": "1",
       "phi_distance": 0.049,
       "storage": "u8_packed",
       "cluster": "MlLowPrecision",
@@ -298,6 +315,7 @@
       "e_bits": 2,
       "m_bits": 1,
       "bias": 1,
+      "bias_formula": "1",
       "phi_distance": 1.382,
       "storage": "u8_packed",
       "cluster": "MlLowPrecision",
@@ -315,6 +333,7 @@
       "e_bits": 4,
       "m_bits": 3,
       "bias": 7,
+      "bias_formula": "7",
       "phi_distance": 0.715,
       "storage": "u8_plus_shared_e8m0",
       "cluster": "Microscaling",
@@ -332,6 +351,7 @@
       "e_bits": 3,
       "m_bits": 2,
       "bias": 3,
+      "bias_formula": "3",
       "phi_distance": 0.882,
       "storage": "u8_packed_plus_e8m0",
       "cluster": "Microscaling",
@@ -349,6 +369,7 @@
       "e_bits": 2,
       "m_bits": 1,
       "bias": 1,
+      "bias_formula": "1",
       "phi_distance": 1.382,
       "storage": "u8_packed_plus_e8m0",
       "cluster": "Microscaling",
@@ -366,6 +387,7 @@
       "e_bits": 0,
       "m_bits": 4,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u8_packed",
       "cluster": "QuantTuned",
@@ -383,6 +405,7 @@
       "e_bits": 8,
       "m_bits": 7,
       "bias": 127,
+      "bias_formula": "127",
       "phi_distance": -1.0,
       "storage": "u16_plus_tensor_shift",
       "cluster": "QuantTuned",
@@ -400,6 +423,7 @@
       "e_bits": 2,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u8",
       "cluster": "PositUnumIII",
@@ -417,6 +441,7 @@
       "e_bits": 2,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u16",
       "cluster": "PositUnumIII",
@@ -434,6 +459,7 @@
       "e_bits": 2,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "PositUnumIII",
@@ -451,6 +477,7 @@
       "e_bits": 2,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "PositUnumIII",
@@ -468,6 +495,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u8",
       "cluster": "PositUnumIII",
@@ -485,6 +513,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u16",
       "cluster": "PositUnumIII",
@@ -502,6 +531,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "PositUnumIII",
@@ -519,6 +549,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "PositUnumIII",
@@ -536,6 +567,7 @@
       "e_bits": 7,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u8",
       "cluster": "Lns",
@@ -553,6 +585,7 @@
       "e_bits": 15,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u16",
       "cluster": "Lns",
@@ -570,6 +603,7 @@
       "e_bits": 31,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "Lns",
@@ -587,6 +621,7 @@
       "e_bits": 63,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "Lns",
@@ -604,6 +639,7 @@
       "e_bits": 0,
       "m_bits": 2,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": 0.0,
       "storage": "u2",
       "cluster": "GoldenFloat",
@@ -621,6 +657,7 @@
       "e_bits": 1,
       "m_bits": 2,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": 0.118,
       "storage": "u8",
       "cluster": "GoldenFloat",
@@ -638,6 +675,7 @@
       "e_bits": 3,
       "m_bits": 4,
       "bias": 3,
+      "bias_formula": "3",
       "phi_distance": 0.132,
       "storage": "u8",
       "cluster": "GoldenFloat",
@@ -655,6 +693,7 @@
       "e_bits": 4,
       "m_bits": 7,
       "bias": 7,
+      "bias_formula": "7",
       "phi_distance": 0.047,
       "storage": "u16",
       "cluster": "GoldenFloat",
@@ -672,6 +711,7 @@
       "e_bits": 6,
       "m_bits": 9,
       "bias": 31,
+      "bias_formula": "31",
       "phi_distance": 0.049,
       "storage": "u16",
       "cluster": "GoldenFloat",
@@ -689,6 +729,7 @@
       "e_bits": 7,
       "m_bits": 12,
       "bias": 63,
+      "bias_formula": "63",
       "phi_distance": 0.035,
       "storage": "u32",
       "cluster": "GoldenFloat",
@@ -706,6 +747,7 @@
       "e_bits": 9,
       "m_bits": 14,
       "bias": 255,
+      "bias_formula": "255",
       "phi_distance": 0.025,
       "storage": "u32",
       "cluster": "GoldenFloat",
@@ -723,6 +765,7 @@
       "e_bits": 12,
       "m_bits": 19,
       "bias": 2047,
+      "bias_formula": "2047",
       "phi_distance": 0.014,
       "storage": "u32",
       "cluster": "GoldenFloat",
@@ -740,6 +783,7 @@
       "e_bits": 24,
       "m_bits": 39,
       "bias": 8388607,
+      "bias_formula": "8388607",
       "phi_distance": 0.003,
       "storage": "u64",
       "cluster": "GoldenFloat",
@@ -757,6 +801,7 @@
       "e_bits": 2,
       "m_bits": 3,
       "bias": 1,
+      "bias_formula": "1",
       "phi_distance": 0.049,
       "storage": "u8_packed",
       "cluster": "GoldenFloat",
@@ -774,6 +819,7 @@
       "e_bits": 3,
       "m_bits": 6,
       "bias": 3,
+      "bias_formula": "3",
       "phi_distance": 0.118,
       "storage": "u16",
       "cluster": "GoldenFloat",
@@ -791,6 +837,7 @@
       "e_bits": 5,
       "m_bits": 8,
       "bias": 15,
+      "bias_formula": "15",
       "phi_distance": 0.007,
       "storage": "u16",
       "cluster": "GoldenFloat",
@@ -808,6 +855,7 @@
       "e_bits": 18,
       "m_bits": 29,
       "bias": 131071,
+      "bias_formula": "131071",
       "phi_distance": 0.003,
       "storage": "u64_padded",
       "cluster": "GoldenFloat",
@@ -825,6 +873,7 @@
       "e_bits": 36,
       "m_bits": 59,
       "bias": 34359738367,
+      "bias_formula": "34359738367",
       "phi_distance": 0.008,
       "storage": "u128_padded",
       "cluster": "GoldenFloat",
@@ -842,6 +891,7 @@
       "e_bits": 49,
       "m_bits": 78,
       "bias": 281474976710655,
+      "bias_formula": "281474976710655",
       "phi_distance": 0.01,
       "storage": "u128",
       "cluster": "GoldenFloat",
@@ -859,6 +909,7 @@
       "e_bits": 97,
       "m_bits": 158,
       "bias": 79228162514264337593543950335,
+      "bias_formula": "79228162514264337593543950335",
       "phi_distance": 0.004,
       "storage": "u256_software",
       "cluster": "GoldenFloat",
@@ -868,6 +919,42 @@
       "gf_relation": "experimental",
       "source": "specs/numeric/gf256.t27"
     },
+    {
+      "id": "gf512",
+      "name": "GF512 (rule-derived)",
+      "bits": 512,
+      "s_bits": 1,
+      "e_bits": 195,
+      "m_bits": 316,
+      "bias": -2,
+      "bias_formula": "2^194-1",
+      "phi_distance": 0.0009,
+      "storage": "u512_software",
+      "cluster": "GoldenFloat",
+      "status": "Open",
+      "standard": "this work; rule e=round(511/phi^2)=195",
+      "use_case": "OPEN R&D: ultra-wide phi-aligned (extrapolation, no RTL)",
+      "gf_relation": "experimental",
+      "source": "specs/numeric/gf512.t27"
+    },
+    {
+      "id": "gf1024",
+      "name": "GF1024 (rule-derived)",
+      "bits": 1024,
+      "s_bits": 1,
+      "e_bits": 391,
+      "m_bits": 632,
+      "bias": -2,
+      "bias_formula": "2^390-1",
+      "phi_distance": 0.0006,
+      "storage": "u1024_software",
+      "cluster": "GoldenFloat",
+      "status": "Open",
+      "standard": "this work; rule e=round(1023/phi^2)=391; lowest phi-distance in the ladder",
+      "use_case": "OPEN R&D: limit-of-ladder phi alignment (extrapolation, no RTL)",
+      "gf_relation": "experimental",
+      "source": "specs/numeric/gf1024.t27"
+    },
     {
       "id": "gf8_bfp",
       "name": "GF8-BFP (block FP atop GF8)",
@@ -876,6 +963,7 @@
       "e_bits": 3,
       "m_bits": 4,
       "bias": 3,
+      "bias_formula": "3",
       "phi_distance": 0.132,
       "storage": "u8_plus_shared_exp",
       "cluster": "GoldenFloat",
@@ -893,6 +981,7 @@
       "e_bits": 6,
       "m_bits": 9,
       "bias": 31,
+      "bias_formula": "31",
       "phi_distance": 0.049,
       "storage": "u16_plus_lns_path",
       "cluster": "GoldenFloat",
@@ -910,6 +999,7 @@
       "e_bits": 2,
       "m_bits": 3,
       "bias": 1,
+      "bias_formula": "1",
       "phi_distance": 0.05,
       "storage": "u8_packed_plus_e8m0",
       "cluster": "GoldenFloat",
@@ -927,6 +1017,7 @@
       "e_bits": 1,
       "m_bits": 2,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": 0.118,
       "storage": "u8_packed_plus_e8m0",
       "cluster": "GoldenFloat",
@@ -944,6 +1035,7 @@
       "e_bits": 0,
       "m_bits": 3,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u8_packed",
       "cluster": "IntegerFixed",
@@ -961,6 +1053,7 @@
       "e_bits": 0,
       "m_bits": 7,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u8",
       "cluster": "IntegerFixed",
@@ -978,6 +1071,7 @@
       "e_bits": 0,
       "m_bits": 15,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u16",
       "cluster": "IntegerFixed",
@@ -995,6 +1089,7 @@
       "e_bits": 0,
       "m_bits": 31,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "IntegerFixed",
@@ -1012,6 +1107,7 @@
       "e_bits": 0,
       "m_bits": 63,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "IntegerFixed",
@@ -1029,6 +1125,7 @@
       "e_bits": 0,
       "m_bits": 127,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u128",
       "cluster": "IntegerFixed",
@@ -1046,6 +1143,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "varies",
       "cluster": "IntegerFixed",
@@ -1063,6 +1161,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u4_per_digit",
       "cluster": "IntegerFixed",
@@ -1080,6 +1179,7 @@
       "e_bits": 7,
       "m_bits": 24,
       "bias": 64,
+      "bias_formula": "64",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "HistoricalVendor",
@@ -1097,6 +1197,7 @@
       "e_bits": 7,
       "m_bits": 56,
       "bias": 64,
+      "bias_formula": "64",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "HistoricalVendor",
@@ -1114,6 +1215,7 @@
       "e_bits": 7,
       "m_bits": 120,
       "bias": 64,
+      "bias_formula": "64",
       "phi_distance": -1.0,
       "storage": "u128",
       "cluster": "HistoricalVendor",
@@ -1131,6 +1233,7 @@
       "e_bits": 8,
       "m_bits": 23,
       "bias": 129,
+      "bias_formula": "129",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "HistoricalVendor",
@@ -1148,6 +1251,7 @@
       "e_bits": 8,
       "m_bits": 55,
       "bias": 129,
+      "bias_formula": "129",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "HistoricalVendor",
@@ -1165,6 +1269,7 @@
       "e_bits": 8,
       "m_bits": 23,
       "bias": 128,
+      "bias_formula": "128",
       "phi_distance": -1.0,
       "storage": "u32",
       "cluster": "HistoricalVendor",
@@ -1182,6 +1287,7 @@
       "e_bits": 8,
       "m_bits": 55,
       "bias": 128,
+      "bias_formula": "128",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "HistoricalVendor",
@@ -1199,6 +1305,7 @@
       "e_bits": 11,
       "m_bits": 52,
       "bias": 1024,
+      "bias_formula": "1024",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "HistoricalVendor",
@@ -1216,6 +1323,7 @@
       "e_bits": 15,
       "m_bits": 112,
       "bias": 16384,
+      "bias_formula": "16384",
       "phi_distance": -1.0,
       "storage": "u128",
       "cluster": "HistoricalVendor",
@@ -1233,6 +1341,7 @@
       "e_bits": 15,
       "m_bits": 48,
       "bias": 16384,
+      "bias_formula": "16384",
       "phi_distance": -1.0,
       "storage": "u64",
       "cluster": "HistoricalVendor",
@@ -1250,6 +1359,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "varies",
       "cluster": "Theoretical",
@@ -1267,6 +1377,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "varies",
       "cluster": "Theoretical",
@@ -1284,6 +1395,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "lookup_table",
       "cluster": "Theoretical",
@@ -1301,6 +1413,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "varies",
       "cluster": "Theoretical",
@@ -1318,6 +1431,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "varies",
       "cluster": "CompressionTrick",
@@ -1335,6 +1449,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "varies",
       "cluster": "CompressionTrick",
@@ -1352,6 +1467,7 @@
       "e_bits": 0,
       "m_bits": 7,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "u8_plus_fp32_scale",
       "cluster": "CompressionTrick",
@@ -1369,6 +1485,7 @@
       "e_bits": 0,
       "m_bits": 0,
       "bias": 0,
+      "bias_formula": "0",
       "phi_distance": -1.0,
       "storage": "varies",
       "cluster": "CompressionTrick",

formats_catalog.jsonl

@@ -1,77 +1,83 @@
-{"bias": 15, "bits": 16, "cluster": "Ieee754Binary", "e_bits": 5, "gf_relation": "competitor", "id": "binary16", "m_bits": 10, "name": "binary16 (fp16, half)", "phi_distance": 0.118, "s_bits": 1, "source": "IEEE 754-2008", "standard": "IEEE 754-2008", "status": "Verified", "storage": "u16", "use_case": "GPU activations, inference"}
-{"bias": 127, "bits": 32, "cluster": "Ieee754Binary", "e_bits": 8, "gf_relation": "competitor", "id": "binary32", "m_bits": 23, "name": "binary32 (fp32, single)", "phi_distance": 0.27, "s_bits": 1, "source": "IEEE 754-1985", "standard": "IEEE 754-1985", "status": "Verified", "storage": "u32", "use_case": "industry default"}
-{"bias": 1023, "bits": 64, "cluster": "Ieee754Binary", "e_bits": 11, "gf_relation": "competitor", "id": "binary64", "m_bits": 52, "name": "binary64 (fp64, double)", "phi_distance": 0.406, "s_bits": 1, "source": "IEEE 754-1985", "standard": "IEEE 754-1985", "status": "Verified", "storage": "u64", "use_case": "scientific computing"}
-{"bias": 16383, "bits": 128, "cluster": "Ieee754Binary", "e_bits": 15, "gf_relation": "competitor", "id": "binary128", "m_bits": 112, "name": "binary128 (fp128, quad)", "phi_distance": 0.484, "s_bits": 1, "source": "IEEE 754-2008", "standard": "IEEE 754-2008", "status": "Verified", "storage": "u128", "use_case": "high-precision simulations"}
-{"bias": 262143, "bits": 256, "cluster": "Ieee754Binary", "e_bits": 19, "gf_relation": "competitor", "id": "binary256", "m_bits": 236, "name": "binary256 (octuple)", "phi_distance": 0.538, "s_bits": 1, "source": "IEEE 754-2008", "standard": "IEEE 754-2008", "status": "Verified", "storage": "u256_software", "use_case": "astronomy, cryptography"}
-{"bias": 101, "bits": 32, "cluster": "Ieee754Decimal", "e_bits": 11, "gf_relation": "orthogonal", "id": "decimal32", "m_bits": 20, "name": "decimal32", "phi_distance": -1.0, "s_bits": 1, "source": "IEEE 754-2008", "standard": "IEEE 754-2008 (DPD/BID)", "status": "Verified", "storage": "u32", "use_case": "banking, GAAP"}
-{"bias": 398, "bits": 64, "cluster": "Ieee754Decimal", "e_bits": 13, "gf_relation": "orthogonal", "id": "decimal64", "m_bits": 50, "name": "decimal64", "phi_distance": -1.0, "s_bits": 1, "source": "IEEE 754-2008", "standard": "IEEE 754-2008", "status": "Verified", "storage": "u64", "use_case": "financial databases"}
-{"bias": 6176, "bits": 128, "cluster": "Ieee754Decimal", "e_bits": 17, "gf_relation": "orthogonal", "id": "decimal128", "m_bits": 110, "name": "decimal128", "phi_distance": -1.0, "s_bits": 1, "source": "IEEE 754-2008", "standard": "IEEE 754-2008", "status": "Verified", "storage": "u128", "use_case": "audit ledgers"}
-{"bias": 16383, "bits": 80, "cluster": "ExtendedFloat", "e_bits": 15, "gf_relation": "orthogonal", "id": "x87_fp80", "m_bits": 64, "name": "x87 FP80", "phi_distance": -1.0, "s_bits": 1, "source": "Intel SDM", "standard": "Intel x87 (explicit integer bit)", "status": "Historical", "storage": "u80_padded", "use_case": "legacy long double on x86"}
-{"bias": 0, "bits": 128, "cluster": "ExtendedFloat", "e_bits": 22, "gf_relation": "orthogonal", "id": "double_double", "m_bits": 104, "name": "double-double", "phi_distance": -1.0, "s_bits": 2, "source": "Bailey-Hida 2001", "standard": "Bailey/Hida (software)", "status": "Verified", "storage": "two_u64", "use_case": "software extended precision"}
-{"bias": 0, "bits": 256, "cluster": "ExtendedFloat", "e_bits": 44, "gf_relation": "orthogonal", "id": "quad_double", "m_bits": 208, "name": "quad-double", "phi_distance": -1.0, "s_bits": 4, "source": "Bailey-Hida 2001", "standard": "Bailey/Hida (software)", "status": "Verified", "storage": "four_u64", "use_case": "astrophysics, quad-precision sims"}
-{"bias": 127, "bits": 16, "cluster": "MlLowPrecision", "e_bits": 8, "gf_relation": "competitor", "id": "bfloat16", "m_bits": 7, "name": "bfloat16 (BF16)", "phi_distance": 0.525, "s_bits": 1, "source": "Wang-Kanwar 2019", "standard": "Google Brain", "status": "Verified", "storage": "u16", "use_case": "training (range > precision)"}
-{"bias": 127, "bits": 19, "cluster": "MlLowPrecision", "e_bits": 8, "gf_relation": "competitor", "id": "tf32", "m_bits": 10, "name": "TensorFloat-32 (TF32)", "phi_distance": 0.27, "s_bits": 1, "source": "NVIDIA Ampere whitepaper", "standard": "NVIDIA Ampere", "status": "Verified", "storage": "u32_padded", "use_case": "A100/H100 mixed precision"}
-{"bias": 7, "bits": 8, "cluster": "MlLowPrecision", "e_bits": 4, "gf_relation": "competitor", "id": "fp8_e4m3", "m_bits": 3, "name": "FP8 E4M3", "phi_distance": 0.715, "s_bits": 1, "source": "Micikevicius 2022 (arXiv:2209.05433)", "standard": "OCP / NVIDIA / Arm / Intel", "status": "Verified", "storage": "u8", "use_case": "inference, gradient ranges"}
-{"bias": 15, "bits": 8, "cluster": "MlLowPrecision", "e_bits": 5, "gf_relation": "competitor", "id": "fp8_e5m2", "m_bits": 2, "name": "FP8 E5M2", "phi_distance": 1.882, "s_bits": 1, "source": "Micikevicius 2022", "standard": "OCP / NVIDIA", "status": "Verified", "storage": "u8", "use_case": "activations, wide range"}
-{"bias": 3, "bits": 6, "cluster": "MlLowPrecision", "e_bits": 3, "gf_relation": "competitor", "id": "fp6_e3m2", "m_bits": 2, "name": "FP6 E3M2", "phi_distance": 0.882, "s_bits": 1, "source": "OCP MX v1.0 (2023)", "standard": "OCP MX", "status": "Verified", "storage": "u8_packed", "use_case": "aggressive quant inference"}
-{"bias": 1, "bits": 6, "cluster": "MlLowPrecision", "e_bits": 2, "gf_relation": "ally", "id": "fp6_e2m3", "m_bits": 3, "name": "FP6 E2M3", "phi_distance": 0.049, "s_bits": 1, "source": "OCP MX v1.0 (2023)", "standard": "OCP MX", "status": "Verified", "storage": "u8_packed", "use_case": "mantissa-heavy quant"}
-{"bias": 1, "bits": 4, "cluster": "MlLowPrecision", "e_bits": 2, "gf_relation": "competitor", "id": "fp4_e2m1", "m_bits": 1, "name": "FP4 E2M1", "phi_distance": 1.382, "s_bits": 1, "source": "OCP MX v1.0 (2023)", "standard": "OCP MX", "status": "Verified", "storage": "u8_packed", "use_case": "extreme quant inference"}
-{"bias": 7, "bits": 8, "cluster": "Microscaling", "e_bits": 4, "gf_relation": "ally", "id": "mxfp8", "m_bits": 3, "name": "MXFP8", "phi_distance": 0.715, "s_bits": 1, "source": "Rouhani 2023 (arXiv:2310.10537)", "standard": "OCP MX v1.0", "status": "Verified", "storage": "u8_plus_shared_e8m0", "use_case": "LLM inference"}
-{"bias": 3, "bits": 6, "cluster": "Microscaling", "e_bits": 3, "gf_relation": "ally", "id": "mxfp6", "m_bits": 2, "name": "MXFP6", "phi_distance": 0.882, "s_bits": 1, "source": "Rouhani 2023", "standard": "OCP MX v1.0", "status": "Verified", "storage": "u8_packed_plus_e8m0", "use_case": "aggressive inference"}
-{"bias": 1, "bits": 4, "cluster": "Microscaling", "e_bits": 2, "gf_relation": "ally", "id": "mxfp4", "m_bits": 1, "name": "MXFP4", "phi_distance": 1.382, "s_bits": 1, "source": "Rouhani 2023", "standard": "OCP MX v1.0", "status": "Verified", "storage": "u8_packed_plus_e8m0", "use_case": "extreme quant"}
-{"bias": 0, "bits": 4, "cluster": "QuantTuned", "e_bits": 0, "gf_relation": "orthogonal", "id": "nf4", "m_bits": 4, "name": "NF4 (NormalFloat 4-bit)", "phi_distance": -1.0, "s_bits": 0, "source": "Dettmers 2023 (arXiv:2305.14314)", "standard": "Dettmers 2023 (QLoRA)", "status": "Verified", "storage": "u8_packed", "use_case": "LLM weight quantization (quantile-based on N(0,1))"}
-{"bias": 127, "bits": 16, "cluster": "QuantTuned", "e_bits": 8, "gf_relation": "orthogonal", "id": "afp", "m_bits": 7, "name": "AFP (Adaptive Floating-Point)", "phi_distance": -1.0, "s_bits": 1, "source": "Tambe 2020 (DAC)", "standard": "Tambe 2020", "status": "Verified", "storage": "u16_plus_tensor_shift", "use_case": "efficient training"}
-{"bias": 0, "bits": 8, "cluster": "PositUnumIII", "e_bits": 2, "gf_relation": "ally", "id": "posit8", "m_bits": 0, "name": "Posit8", "phi_distance": -1.0, "s_bits": 1, "source": "Posit Standard 2022 (posithub.org)", "standard": "Posit Standard 2022 (es=2)", "status": "Verified", "storage": "u8", "use_case": "inference"}
-{"bias": 0, "bits": 16, "cluster": "PositUnumIII", "e_bits": 2, "gf_relation": "ally", "id": "posit16", "m_bits": 0, "name": "Posit16", "phi_distance": -1.0, "s_bits": 1, "source": "Posit Standard 2022", "standard": "Posit Standard 2022 (es=2)", "status": "Verified", "storage": "u16", "use_case": "mixed-precision training"}
-{"bias": 0, "bits": 32, "cluster": "PositUnumIII", "e_bits": 2, "gf_relation": "ally", "id": "posit32", "m_bits": 0, "name": "Posit32", "phi_distance": -1.0, "s_bits": 1, "source": "Posit Standard 2022", "standard": "Posit Standard 2022 (es=2)", "status": "Verified", "storage": "u32", "use_case": "f32 replacement"}
-{"bias": 0, "bits": 64, "cluster": "PositUnumIII", "e_bits": 2, "gf_relation": "ally", "id": "posit64", "m_bits": 0, "name": "Posit64", "phi_distance": -1.0, "s_bits": 1, "source": "Posit Standard 2022", "standard": "Posit Standard 2022 (es=2)", "status": "Verified", "storage": "u64", "use_case": "f64 replacement"}
-{"bias": 0, "bits": 8, "cluster": "PositUnumIII", "e_bits": 0, "gf_relation": "ally", "id": "takum8", "m_bits": 0, "name": "takum8", "phi_distance": -1.0, "s_bits": 1, "source": "Hunhold 2024 (arXiv:2412.20273)", "standard": "Hunhold 2024 (tapered-precision)", "status": "Verified", "storage": "u8", "use_case": "IEEE-754 backward-compatible tapered"}
-{"bias": 0, "bits": 16, "cluster": "PositUnumIII", "e_bits": 0, "gf_relation": "ally", "id": "takum16", "m_bits": 0, "name": "takum16", "phi_distance": -1.0, "s_bits": 1, "source": "Hunhold 2024 (arXiv:2412.20273)", "standard": "Hunhold 2024", "status": "Verified", "storage": "u16", "use_case": "single-rule ladder counterexample"}
-{"bias": 0, "bits": 32, "cluster": "PositUnumIII", "e_bits": 0, "gf_relation": "ally", "id": "takum32", "m_bits": 0, "name": "takum32", "phi_distance": -1.0, "s_bits": 1, "source": "Hunhold 2024", "standard": "Hunhold 2024", "status": "Verified", "storage": "u32", "use_case": "tapered fp32-class"}
-{"bias": 0, "bits": 64, "cluster": "PositUnumIII", "e_bits": 0, "gf_relation": "ally", "id": "takum64", "m_bits": 0, "name": "takum64", "phi_distance": -1.0, "s_bits": 1, "source": "Hunhold 2024", "standard": "Hunhold 2024", "status": "Verified", "storage": "u64", "use_case": "tapered fp64-class"}
-{"bias": 0, "bits": 8, "cluster": "Lns", "e_bits": 7, "gf_relation": "orthogonal", "id": "lns8", "m_bits": 0, "name": "LNS-8", "phi_distance": -1.0, "s_bits": 1, "source": "Alam 2021 (arXiv:2106.13914)", "standard": "Arnold 1990; LNS-Madam (2021)", "status": "Verified", "storage": "u8", "use_case": "DSP, signal processing"}
-{"bias": 0, "bits": 16, "cluster": "Lns", "e_bits": 15, "gf_relation": "orthogonal", "id": "lns16", "m_bits": 0, "name": "LNS-16", "phi_distance": -1.0, "s_bits": 1, "source": "Alam 2021", "standard": "LNS-Madam (2021)", "status": "Verified", "storage": "u16", "use_case": "log-domain training (mul -> add)"}
-{"bias": 0, "bits": 32, "cluster": "Lns", "e_bits": 31, "gf_relation": "orthogonal", "id": "lns32", "m_bits": 0, "name": "LNS-32", "phi_distance": -1.0, "s_bits": 1, "source": "Alam 2021", "standard": "LNS-Madam (2021)", "status": "Verified", "storage": "u32", "use_case": "log-domain DSP"}
-{"bias": 0, "bits": 64, "cluster": "Lns", "e_bits": 63, "gf_relation": "orthogonal", "id": "lns64", "m_bits": 0, "name": "LNS-64", "phi_distance": -1.0, "s_bits": 1, "source": "Alam 2021", "standard": "LNS-Madam (2021)", "status": "Verified", "storage": "u64", "use_case": "scientific log-domain"}
-{"bias": 0, "bits": 2, "cluster": "GoldenFloat", "e_bits": 0, "gf_relation": "self", "id": "gfternary", "m_bits": 2, "name": "GFTernary", "phi_distance": 0.0, "s_bits": 1, "source": "BENCH-007", "standard": "this work; {-phi, 0, +phi}", "status": "Verified", "storage": "u2", "use_case": "bulk layers (hybrid)"}
-{"bias": 0, "bits": 4, "cluster": "GoldenFloat", "e_bits": 1, "gf_relation": "self", "id": "gf4", "m_bits": 2, "name": "GF4", "phi_distance": 0.118, "s_bits": 1, "source": "specs/numeric/gf4.t27", "standard": "this work; F0 minimal", "status": "Experimental", "storage": "u8", "use_case": "proof-of-concept"}
-{"bias": 3, "bits": 8, "cluster": "GoldenFloat", "e_bits": 3, "gf_relation": "self", "id": "gf8", "m_bits": 4, "name": "GF8", "phi_distance": 0.132, "s_bits": 1, "source": "BENCH-007 (specs/numeric/gf8.t27)", "standard": "this work; L1 Lucas", "status": "Verified", "storage": "u8", "use_case": "edge / sensors"}
-{"bias": 7, "bits": 12, "cluster": "GoldenFloat", "e_bits": 4, "gf_relation": "self", "id": "gf12", "m_bits": 7, "name": "GF12", "phi_distance": 0.047, "s_bits": 1, "source": "BENCH-007 (specs/numeric/gf12.t27)", "standard": "this work; L0/F3", "status": "Verified", "storage": "u16", "use_case": "mid-range / audio"}
-{"bias": 31, "bits": 16, "cluster": "GoldenFloat", "e_bits": 6, "gf_relation": "self", "id": "gf16", "m_bits": 9, "name": "GF16", "phi_distance": 0.049, "s_bits": 1, "source": "specs/numeric/gf16.t27; zenodo 10.5281/zenodo.19227877 (HW archive)", "standard": "this work; PHI_BIAS=60; FPGA 35/35 at 323 MHz Artix-7", "status": "Verified", "storage": "u16", "use_case": "training and inference (production)"}
-{"bias": 63, "bits": 20, "cluster": "GoldenFloat", "e_bits": 7, "gf_relation": "self", "id": "gf20", "m_bits": 12, "name": "GF20", "phi_distance": 0.035, "s_bits": 1, "source": "specs/numeric/gf20.t27 (spec only)", "standard": "this work; 17-squared empirical PHI_BIAS=289", "status": "Experimental", "storage": "u32", "use_case": "high-precision edge"}
-{"bias": 255, "bits": 24, "cluster": "GoldenFloat", "e_bits": 9, "gf_relation": "self", "id": "gf24", "m_bits": 14, "name": "GF24", "phi_distance": 0.025, "s_bits": 1, "source": "specs/numeric/gf24.t27 (spec only)", "standard": "this work; L15 PHI_BIAS=1364", "status": "Experimental", "storage": "u32", "use_case": "server inference"}
-{"bias": 2047, "bits": 32, "cluster": "GoldenFloat", "e_bits": 12, "gf_relation": "self", "id": "gf32", "m_bits": 19, "name": "GF32", "phi_distance": 0.014, "s_bits": 1, "source": "BENCH-012 (specs/numeric/gf32.t27)", "standard": "this work; F0 resolved", "status": "Verified", "storage": "u32", "use_case": "fp32 drop-in"}
-{"bias": 8388607, "bits": 64, "cluster": "GoldenFloat", "e_bits": 24, "gf_relation": "self", "id": "gf64", "m_bits": 39, "name": "GF64", "phi_distance": 0.003, "s_bits": 1, "source": "BENCH-007b (specs/numeric/gf64.t27)", "standard": "this work; EXP_MAX - BIAS", "status": "Verified", "storage": "u64", "use_case": "scientific / double"}
-{"bias": 1, "bits": 6, "cluster": "GoldenFloat", "e_bits": 2, "gf_relation": "experimental", "id": "gf6", "m_bits": 3, "name": "GF6 (predicted)", "phi_distance": 0.05, "s_bits": 1, "source": "section12.5", "standard": "this work; e=round(5/phi^2)=2, fills FP6 gap", "status": "Experimental", "storage": "u8_packed", "use_case": "OPEN R&D: bridge GF4-GF8; FP6 E2M3 hint"}
-{"bias": 0, "bits": 128, "cluster": "GoldenFloat", "e_bits": 48, "gf_relation": "experimental", "id": "gf128", "m_bits": 79, "name": "GF128 (predicted)", "phi_distance": 0.008, "s_bits": 1, "source": "section12.5", "standard": "this work; e=round(127/phi^2)=48 (Open: bias TBD)", "status": "Experimental", "storage": "u128", "use_case": "OPEN R&D: phi-aligned binary128 alternative"}
-{"bias": 0, "bits": 256, "cluster": "GoldenFloat", "e_bits": 97, "gf_relation": "experimental", "id": "gf256", "m_bits": 158, "name": "GF256 (predicted)", "phi_distance": 0.005, "s_bits": 1, "source": "section12.5; bias Open per skill", "standard": "this work; e=round(255/phi^2)=97 (Open: bias ~2^71 unconfirmed)", "status": "Experimental", "storage": "u256_software", "use_case": "OPEN R&D: phi-aligned binary256 alternative"}
-{"bias": 3, "bits": 8, "cluster": "GoldenFloat", "e_bits": 3, "gf_relation": "experimental", "id": "gf8_bfp", "m_bits": 4, "name": "GF8-BFP (block FP atop GF8)", "phi_distance": 0.132, "s_bits": 1, "source": "section12.5", "standard": "this work; per-tile shared exponent", "status": "Experimental", "storage": "u8_plus_shared_exp", "use_case": "OPEN R&D: LLM-quantization-friendly GF8"}
-{"bias": 31, "bits": 16, "cluster": "GoldenFloat", "e_bits": 6, "gf_relation": "experimental", "id": "gf_lns_hybrid", "m_bits": 9, "name": "GF + LNS hybrid (dual-space)", "phi_distance": 0.049, "s_bits": 1, "source": "section12.5", "standard": "this work; mul in log-space, accumulate Lucas-closed", "status": "Experimental", "storage": "u16_plus_lns_path", "use_case": "OPEN R&D: dual-space arithmetic"}
-{"bias": 1, "bits": 6, "cluster": "GoldenFloat", "e_bits": 2, "gf_relation": "experimental", "id": "mxgf6", "m_bits": 3, "name": "MXGF6 (microscaling GF6)", "phi_distance": 0.05, "s_bits": 1, "source": "section12.5", "standard": "this work; OCP MX block + GF6", "status": "Experimental", "storage": "u8_packed_plus_e8m0", "use_case": "OPEN R&D: phi-aligned MX-6 candidate"}
-{"bias": 0, "bits": 4, "cluster": "GoldenFloat", "e_bits": 1, "gf_relation": "experimental", "id": "mxgf4", "m_bits": 2, "name": "MXGF4 (microscaling GF4)", "phi_distance": 0.118, "s_bits": 1, "source": "section12.5", "standard": "this work; OCP MX block + GF4", "status": "Experimental", "storage": "u8_packed_plus_e8m0", "use_case": "OPEN R&D: phi-aligned MX-4 candidate"}
-{"bias": 0, "bits": 4, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "competitor", "id": "int4", "m_bits": 3, "name": "INT4 / UINT4", "phi_distance": -1.0, "s_bits": 1, "source": "ISO/IEC 9899", "standard": "two complement", "status": "Verified", "storage": "u8_packed", "use_case": "aggressive quantization"}
-{"bias": 0, "bits": 8, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "competitor", "id": "int8", "m_bits": 7, "name": "INT8 / UINT8", "phi_distance": -1.0, "s_bits": 1, "source": "ISO/IEC 9899", "standard": "two complement", "status": "Verified", "storage": "u8", "use_case": "INT8 inference, per-channel scale"}
-{"bias": 0, "bits": 16, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "competitor", "id": "int16", "m_bits": 15, "name": "INT16 / UINT16", "phi_distance": -1.0, "s_bits": 1, "source": "ISO/IEC 9899", "standard": "two complement", "status": "Verified", "storage": "u16", "use_case": "DSP, embedded ML"}
-{"bias": 0, "bits": 32, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "competitor", "id": "int32", "m_bits": 31, "name": "INT32 / UINT32", "phi_distance": -1.0, "s_bits": 1, "source": "ISO/IEC 9899", "standard": "two complement", "status": "Verified", "storage": "u32", "use_case": "general CPU integer"}
-{"bias": 0, "bits": 64, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "competitor", "id": "int64", "m_bits": 63, "name": "INT64 / UINT64", "phi_distance": -1.0, "s_bits": 1, "source": "ISO/IEC 9899", "standard": "two complement", "status": "Verified", "storage": "u64", "use_case": "databases, timestamps"}
-{"bias": 0, "bits": 128, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "competitor", "id": "int128", "m_bits": 127, "name": "INT128 / UINT128", "phi_distance": -1.0, "s_bits": 1, "source": "Rust/Clang u128", "standard": "two complement", "status": "Verified", "storage": "u128", "use_case": "crypto, big-int"}
-{"bias": 0, "bits": 0, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "orthogonal", "id": "q_format", "m_bits": 0, "name": "Q-format (Qm.n)", "phi_distance": -1.0, "s_bits": 1, "source": "TI SPRA704", "standard": "TI fixed-point", "status": "Verified", "storage": "varies", "use_case": "audio DSP, fixed-point ML"}
-{"bias": 0, "bits": 0, "cluster": "IntegerFixed", "e_bits": 0, "gf_relation": "orthogonal", "id": "bcd", "m_bits": 0, "name": "BCD (binary-coded decimal)", "phi_distance": -1.0, "s_bits": 0, "source": "ISO/IEC 8859", "standard": "IBM 1959", "status": "Historical", "storage": "u4_per_digit", "use_case": "calculators, GAAP"}
-{"bias": 64, "bits": 32, "cluster": "HistoricalVendor", "e_bits": 7, "gf_relation": "orthogonal", "id": "ibm_hfp32", "m_bits": 24, "name": "IBM HFP (single)", "phi_distance": -1.0, "s_bits": 1, "source": "IBM POO", "standard": "IBM System/360 (1964); base-16 exponent", "status": "Historical", "storage": "u32", "use_case": "legacy mainframe"}
-{"bias": 64, "bits": 64, "cluster": "HistoricalVendor", "e_bits": 7, "gf_relation": "orthogonal", "id": "ibm_hfp64", "m_bits": 56, "name": "IBM HFP (double)", "phi_distance": -1.0, "s_bits": 1, "source": "IBM POO", "standard": "IBM System/360 (1964)", "status": "Historical", "storage": "u64", "use_case": "legacy mainframe"}
-{"bias": 64, "bits": 128, "cluster": "HistoricalVendor", "e_bits": 7, "gf_relation": "orthogonal", "id": "ibm_hfp128", "m_bits": 120, "name": "IBM HFP (extended)", "phi_distance": -1.0, "s_bits": 1, "source": "IBM POO", "standard": "IBM z/Architecture", "status": "Historical", "storage": "u128", "use_case": "legacy mainframe"}
-{"bias": 129, "bits": 32, "cluster": "HistoricalVendor", "e_bits": 8, "gf_relation": "orthogonal", "id": "ms_mbf32", "m_bits": 23, "name": "Microsoft MBF (single)", "phi_distance": -1.0, "s_bits": 1, "source": "MS-DOS docs", "standard": "MS BASIC / MS-DOS (pre-IEEE)", "status": "Historical", "storage": "u32", "use_case": "MS BASIC legacy"}
-{"bias": 129, "bits": 64, "cluster": "HistoricalVendor", "e_bits": 8, "gf_relation": "orthogonal", "id": "ms_mbf64", "m_bits": 55, "name": "Microsoft MBF (double)", "phi_distance": -1.0, "s_bits": 1, "source": "MS-DOS docs", "standard": "MS BASIC", "status": "Historical", "storage": "u64", "use_case": "MS BASIC legacy"}
-{"bias": 128, "bits": 32, "cluster": "HistoricalVendor", "e_bits": 8, "gf_relation": "orthogonal", "id": "vax_f", "m_bits": 23, "name": "VAX F-float", "phi_distance": -1.0, "s_bits": 1, "source": "VAX Architecture Reference", "standard": "DEC VAX", "status": "Historical", "storage": "u32", "use_case": "DEC legacy"}
-{"bias": 128, "bits": 64, "cluster": "HistoricalVendor", "e_bits": 8, "gf_relation": "orthogonal", "id": "vax_d", "m_bits": 55, "name": "VAX D-float", "phi_distance": -1.0, "s_bits": 1, "source": "VAX Architecture Reference", "standard": "DEC VAX", "status": "Historical", "storage": "u64", "use_case": "DEC legacy double"}
-{"bias": 1024, "bits": 64, "cluster": "HistoricalVendor", "e_bits": 11, "gf_relation": "orthogonal", "id": "vax_g", "m_bits": 52, "name": "VAX G-float", "phi_distance": -1.0, "s_bits": 1, "source": "VAX Architecture Reference", "standard": "DEC VAX (IEEE-like)", "status": "Historical", "storage": "u64", "use_case": "DEC legacy"}
-{"bias": 16384, "bits": 128, "cluster": "HistoricalVendor", "e_bits": 15, "gf_relation": "orthogonal", "id": "vax_h", "m_bits": 112, "name": "VAX H-float", "phi_distance": -1.0, "s_bits": 1, "source": "VAX Architecture Reference", "standard": "DEC VAX", "status": "Historical", "storage": "u128", "use_case": "DEC quad"}
-{"bias": 16384, "bits": 64, "cluster": "HistoricalVendor", "e_bits": 15, "gf_relation": "orthogonal", "id": "cray_float", "m_bits": 48, "name": "Cray float", "phi_distance": -1.0, "s_bits": 1, "source": "Cray-1 Hardware Reference", "standard": "Cray-1 (1976); no NaN/Inf, unrounded mul", "status": "Historical", "storage": "u64", "use_case": "Cray legacy"}
-{"bias": 0, "bits": 0, "cluster": "Theoretical", "e_bits": 0, "gf_relation": "ally", "id": "minifloat", "m_bits": 0, "name": "minifloat (arbitrary E:M, <=16 bits)", "phi_distance": -1.0, "s_bits": 1, "source": "Higham 1996", "standard": "parametric framework", "status": "Experimental", "storage": "varies", "use_case": "design space of GF4/GF8/GF12/GF16"}
-{"bias": 0, "bits": 0, "cluster": "Theoretical", "e_bits": 0, "gf_relation": "ally", "id": "unum_i", "m_bits": 0, "name": "Unum I (tapered + ubound)", "phi_distance": -1.0, "s_bits": 1, "source": "Gustafson 2015 (The End of Error)", "standard": "Gustafson 2015 (predecessor to posit)", "status": "Experimental", "storage": "varies", "use_case": "interval arithmetic"}
-{"bias": 0, "bits": 0, "cluster": "Theoretical", "e_bits": 0, "gf_relation": "orthogonal", "id": "unum_ii", "m_bits": 0, "name": "Unum II (SORN projective)", "phi_distance": -1.0, "s_bits": 0, "source": "Gustafson 2016", "standard": "Gustafson 2016", "status": "Experimental", "storage": "lookup_table", "use_case": "lookup-table real arithmetic; not GF-comparable"}
-{"bias": 0, "bits": 0, "cluster": "Theoretical", "e_bits": 0, "gf_relation": "ally", "id": "tapered_fp", "m_bits": 0, "name": "tapered floating point", "phi_distance": -1.0, "s_bits": 1, "source": "Morris 1971 (IEEE TC)", "standard": "Morris 1971; posit ancestor", "status": "Experimental", "storage": "varies", "use_case": "variable mantissa via regime bits"}
-{"bias": 0, "bits": 0, "cluster": "CompressionTrick", "e_bits": 0, "gf_relation": "ally", "id": "block_fp", "m_bits": 0, "name": "block floating point (BFP)", "phi_distance": -1.0, "s_bits": 0, "source": "Darvish-Rouhani 2020", "standard": "Wilkinson 1965; modern revivals", "status": "Verified", "storage": "varies", "use_case": "per-tile shared exponent"}
-{"bias": 0, "bits": 0, "cluster": "CompressionTrick", "e_bits": 0, "gf_relation": "ally", "id": "shared_exp", "m_bits": 0, "name": "shared-exponent formats", "phi_distance": -1.0, "s_bits": 0, "source": "Darvish-Rouhani 2020", "standard": "generalised BFP", "status": "Verified", "storage": "varies", "use_case": "LLM quantization"}
-{"bias": 0, "bits": 8, "cluster": "CompressionTrick", "e_bits": 0, "gf_relation": "competitor", "id": "per_channel_scale", "m_bits": 7, "name": "INT8 with per-channel scale", "phi_distance": -1.0, "s_bits": 1, "source": "Jacob 2018 (CVPR)", "standard": "Jacob 2018 (TFLite)", "status": "Verified", "storage": "u8_plus_fp32_scale", "use_case": "standard quant inference"}
-{"bias": 0, "bits": 0, "cluster": "CompressionTrick", "e_bits": 0, "gf_relation": "ally", "id": "stochastic_rounding", "m_bits": 0, "name": "stochastic rounding (technique)", "phi_distance": -1.0, "s_bits": 0, "source": "Gupta 2015 (ICML)", "standard": "Gupta 2015", "status": "Verified", "storage": "varies", "use_case": "training small networks at low precision"}
+{"id":"binary16","name":"binary16 (fp16, half)","bits":16,"s_bits":1,"e_bits":5,"m_bits":10,"bias":15,"bias_formula":"15","phi_distance":0.118,"storage":"u16","cluster":"Ieee754Binary","status":"Verified","standard":"IEEE 754-2008","use_case":"GPU activations, inference","gf_relation":"competitor","source":"IEEE 754-2008"}
+{"id":"binary32","name":"binary32 (fp32, single)","bits":32,"s_bits":1,"e_bits":8,"m_bits":23,"bias":127,"bias_formula":"127","phi_distance":0.27,"storage":"u32","cluster":"Ieee754Binary","status":"Verified","standard":"IEEE 754-1985","use_case":"industry default","gf_relation":"competitor","source":"IEEE 754-1985"}
+{"id":"binary64","name":"binary64 (fp64, double)","bits":64,"s_bits":1,"e_bits":11,"m_bits":52,"bias":1023,"bias_formula":"1023","phi_distance":0.406,"storage":"u64","cluster":"Ieee754Binary","status":"Verified","standard":"IEEE 754-1985","use_case":"scientific computing","gf_relation":"competitor","source":"IEEE 754-1985"}
+{"id":"binary128","name":"binary128 (fp128, quad)","bits":128,"s_bits":1,"e_bits":15,"m_bits":112,"bias":16383,"bias_formula":"16383","phi_distance":0.484,"storage":"u128","cluster":"Ieee754Binary","status":"Verified","standard":"IEEE 754-2008","use_case":"high-precision simulations","gf_relation":"competitor","source":"IEEE 754-2008"}
+{"id":"binary256","name":"binary256 (octuple)","bits":256,"s_bits":1,"e_bits":19,"m_bits":236,"bias":262143,"bias_formula":"262143","phi_distance":0.538,"storage":"u256_software","cluster":"Ieee754Binary","status":"Verified","standard":"IEEE 754-2008","use_case":"astronomy, cryptography","gf_relation":"competitor","source":"IEEE 754-2008"}
+{"id":"decimal32","name":"decimal32","bits":32,"s_bits":1,"e_bits":11,"m_bits":20,"bias":101,"bias_formula":"101","phi_distance":-1.0,"storage":"u32","cluster":"Ieee754Decimal","status":"Verified","standard":"IEEE 754-2008 (DPD/BID)","use_case":"banking, GAAP","gf_relation":"orthogonal","source":"IEEE 754-2008"}
+{"id":"decimal64","name":"decimal64","bits":64,"s_bits":1,"e_bits":13,"m_bits":50,"bias":398,"bias_formula":"398","phi_distance":-1.0,"storage":"u64","cluster":"Ieee754Decimal","status":"Verified","standard":"IEEE 754-2008","use_case":"financial databases","gf_relation":"orthogonal","source":"IEEE 754-2008"}
+{"id":"decimal128","name":"decimal128","bits":128,"s_bits":1,"e_bits":17,"m_bits":110,"bias":6176,"bias_formula":"6176","phi_distance":-1.0,"storage":"u128","cluster":"Ieee754Decimal","status":"Verified","standard":"IEEE 754-2008","use_case":"audit ledgers","gf_relation":"orthogonal","source":"IEEE 754-2008"}
+{"id":"x87_fp80","name":"x87 FP80","bits":80,"s_bits":1,"e_bits":15,"m_bits":64,"bias":16383,"bias_formula":"16383","phi_distance":-1.0,"storage":"u80_padded","cluster":"ExtendedFloat","status":"Historical","standard":"Intel x87 (explicit integer bit)","use_case":"legacy long double on x86","gf_relation":"orthogonal","source":"Intel SDM"}
+{"id":"double_double","name":"double-double","bits":128,"s_bits":2,"e_bits":22,"m_bits":104,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"two_u64","cluster":"ExtendedFloat","status":"Verified","standard":"Bailey/Hida (software)","use_case":"software extended precision","gf_relation":"orthogonal","source":"Bailey-Hida 2001"}
+{"id":"quad_double","name":"quad-double","bits":256,"s_bits":4,"e_bits":44,"m_bits":208,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"four_u64","cluster":"ExtendedFloat","status":"Verified","standard":"Bailey/Hida (software)","use_case":"astrophysics, quad-precision sims","gf_relation":"orthogonal","source":"Bailey-Hida 2001"}
+{"id":"bfloat16","name":"bfloat16 (BF16)","bits":16,"s_bits":1,"e_bits":8,"m_bits":7,"bias":127,"bias_formula":"127","phi_distance":0.525,"storage":"u16","cluster":"MlLowPrecision","status":"Verified","standard":"Google Brain","use_case":"training (range > precision)","gf_relation":"competitor","source":"Wang-Kanwar 2019"}
+{"id":"tf32","name":"TensorFloat-32 (TF32)","bits":19,"s_bits":1,"e_bits":8,"m_bits":10,"bias":127,"bias_formula":"127","phi_distance":0.27,"storage":"u32_padded","cluster":"MlLowPrecision","status":"Verified","standard":"NVIDIA Ampere","use_case":"A100/H100 mixed precision","gf_relation":"competitor","source":"NVIDIA Ampere whitepaper"}
+{"id":"fp8_e4m3","name":"FP8 E4M3","bits":8,"s_bits":1,"e_bits":4,"m_bits":3,"bias":7,"bias_formula":"7","phi_distance":0.715,"storage":"u8","cluster":"MlLowPrecision","status":"Verified","standard":"OCP / NVIDIA / Arm / Intel","use_case":"inference, gradient ranges","gf_relation":"competitor","source":"Micikevicius 2022 (arXiv:2209.05433)"}
+{"id":"fp8_e5m2","name":"FP8 E5M2","bits":8,"s_bits":1,"e_bits":5,"m_bits":2,"bias":15,"bias_formula":"15","phi_distance":1.882,"storage":"u8","cluster":"MlLowPrecision","status":"Verified","standard":"OCP / NVIDIA","use_case":"activations, wide range","gf_relation":"competitor","source":"Micikevicius 2022"}
+{"id":"fp6_e3m2","name":"FP6 E3M2","bits":6,"s_bits":1,"e_bits":3,"m_bits":2,"bias":3,"bias_formula":"3","phi_distance":0.882,"storage":"u8_packed","cluster":"MlLowPrecision","status":"Verified","standard":"OCP MX","use_case":"aggressive quant inference","gf_relation":"competitor","source":"OCP MX v1.0 (2023)"}
+{"id":"fp6_e2m3","name":"FP6 E2M3","bits":6,"s_bits":1,"e_bits":2,"m_bits":3,"bias":1,"bias_formula":"1","phi_distance":0.049,"storage":"u8_packed","cluster":"MlLowPrecision","status":"Verified","standard":"OCP MX","use_case":"mantissa-heavy quant","gf_relation":"ally","source":"OCP MX v1.0 (2023)"}
+{"id":"fp4_e2m1","name":"FP4 E2M1","bits":4,"s_bits":1,"e_bits":2,"m_bits":1,"bias":1,"bias_formula":"1","phi_distance":1.382,"storage":"u8_packed","cluster":"MlLowPrecision","status":"Verified","standard":"OCP MX","use_case":"extreme quant inference","gf_relation":"competitor","source":"OCP MX v1.0 (2023)"}
+{"id":"mxfp8","name":"MXFP8","bits":8,"s_bits":1,"e_bits":4,"m_bits":3,"bias":7,"bias_formula":"7","phi_distance":0.715,"storage":"u8_plus_shared_e8m0","cluster":"Microscaling","status":"Verified","standard":"OCP MX v1.0","use_case":"LLM inference","gf_relation":"ally","source":"Rouhani 2023 (arXiv:2310.10537)"}
+{"id":"mxfp6","name":"MXFP6","bits":6,"s_bits":1,"e_bits":3,"m_bits":2,"bias":3,"bias_formula":"3","phi_distance":0.882,"storage":"u8_packed_plus_e8m0","cluster":"Microscaling","status":"Verified","standard":"OCP MX v1.0","use_case":"aggressive inference","gf_relation":"ally","source":"Rouhani 2023"}
+{"id":"mxfp4","name":"MXFP4","bits":4,"s_bits":1,"e_bits":2,"m_bits":1,"bias":1,"bias_formula":"1","phi_distance":1.382,"storage":"u8_packed_plus_e8m0","cluster":"Microscaling","status":"Verified","standard":"OCP MX v1.0","use_case":"extreme quant","gf_relation":"ally","source":"Rouhani 2023"}
+{"id":"nf4","name":"NF4 (NormalFloat 4-bit)","bits":4,"s_bits":0,"e_bits":0,"m_bits":4,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8_packed","cluster":"QuantTuned","status":"Verified","standard":"Dettmers 2023 (QLoRA)","use_case":"LLM weight quantization (quantile-based on N(0,1))","gf_relation":"orthogonal","source":"Dettmers 2023 (arXiv:2305.14314)"}
+{"id":"afp","name":"AFP (Adaptive Floating-Point)","bits":16,"s_bits":1,"e_bits":8,"m_bits":7,"bias":127,"bias_formula":"127","phi_distance":-1.0,"storage":"u16_plus_tensor_shift","cluster":"QuantTuned","status":"Verified","standard":"Tambe 2020","use_case":"efficient training","gf_relation":"orthogonal","source":"Tambe 2020 (DAC)"}
+{"id":"posit8","name":"Posit8","bits":8,"s_bits":1,"e_bits":2,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8","cluster":"PositUnumIII","status":"Verified","standard":"Posit Standard 2022 (es=2)","use_case":"inference","gf_relation":"ally","source":"Posit Standard 2022 (posithub.org)"}
+{"id":"posit16","name":"Posit16","bits":16,"s_bits":1,"e_bits":2,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u16","cluster":"PositUnumIII","status":"Verified","standard":"Posit Standard 2022 (es=2)","use_case":"mixed-precision training","gf_relation":"ally","source":"Posit Standard 2022"}
+{"id":"posit32","name":"Posit32","bits":32,"s_bits":1,"e_bits":2,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u32","cluster":"PositUnumIII","status":"Verified","standard":"Posit Standard 2022 (es=2)","use_case":"f32 replacement","gf_relation":"ally","source":"Posit Standard 2022"}
+{"id":"posit64","name":"Posit64","bits":64,"s_bits":1,"e_bits":2,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u64","cluster":"PositUnumIII","status":"Verified","standard":"Posit Standard 2022 (es=2)","use_case":"f64 replacement","gf_relation":"ally","source":"Posit Standard 2022"}
+{"id":"takum8","name":"takum8","bits":8,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8","cluster":"PositUnumIII","status":"Verified","standard":"Hunhold 2024 (tapered-precision)","use_case":"IEEE-754 backward-compatible tapered","gf_relation":"ally","source":"Hunhold 2024 (arXiv:2412.20273)"}
+{"id":"takum16","name":"takum16","bits":16,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u16","cluster":"PositUnumIII","status":"Verified","standard":"Hunhold 2024","use_case":"single-rule ladder counterexample","gf_relation":"ally","source":"Hunhold 2024 (arXiv:2412.20273)"}
+{"id":"takum32","name":"takum32","bits":32,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u32","cluster":"PositUnumIII","status":"Verified","standard":"Hunhold 2024","use_case":"tapered fp32-class","gf_relation":"ally","source":"Hunhold 2024"}
+{"id":"takum64","name":"takum64","bits":64,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u64","cluster":"PositUnumIII","status":"Verified","standard":"Hunhold 2024","use_case":"tapered fp64-class","gf_relation":"ally","source":"Hunhold 2024"}
+{"id":"lns8","name":"LNS-8","bits":8,"s_bits":1,"e_bits":7,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8","cluster":"Lns","status":"Verified","standard":"Arnold 1990; LNS-Madam (2021)","use_case":"DSP, signal processing","gf_relation":"orthogonal","source":"Alam 2021 (arXiv:2106.13914)"}
+{"id":"lns16","name":"LNS-16","bits":16,"s_bits":1,"e_bits":15,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u16","cluster":"Lns","status":"Verified","standard":"LNS-Madam (2021)","use_case":"log-domain training (mul -> add)","gf_relation":"orthogonal","source":"Alam 2021"}
+{"id":"lns32","name":"LNS-32","bits":32,"s_bits":1,"e_bits":31,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u32","cluster":"Lns","status":"Verified","standard":"LNS-Madam (2021)","use_case":"log-domain DSP","gf_relation":"orthogonal","source":"Alam 2021"}
+{"id":"lns64","name":"LNS-64","bits":64,"s_bits":1,"e_bits":63,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u64","cluster":"Lns","status":"Verified","standard":"LNS-Madam (2021)","use_case":"scientific log-domain","gf_relation":"orthogonal","source":"Alam 2021"}
+{"id":"gfternary","name":"GFTernary","bits":2,"s_bits":1,"e_bits":0,"m_bits":2,"bias":0,"bias_formula":"0","phi_distance":0.0,"storage":"u2","cluster":"GoldenFloat","status":"Verified","standard":"this work; {-phi, 0, +phi}","use_case":"bulk layers (hybrid)","gf_relation":"self","source":"BENCH-007"}
+{"id":"gf4","name":"GF4","bits":4,"s_bits":1,"e_bits":1,"m_bits":2,"bias":0,"bias_formula":"0","phi_distance":0.118,"storage":"u8","cluster":"GoldenFloat","status":"Experimental","standard":"this work; F0 minimal","use_case":"proof-of-concept","gf_relation":"self","source":"specs/numeric/gf4.t27"}
+{"id":"gf8","name":"GF8","bits":8,"s_bits":1,"e_bits":3,"m_bits":4,"bias":3,"bias_formula":"3","phi_distance":0.132,"storage":"u8","cluster":"GoldenFloat","status":"Verified","standard":"this work; L1 Lucas","use_case":"edge / sensors","gf_relation":"self","source":"BENCH-007 (specs/numeric/gf8.t27)"}
+{"id":"gf12","name":"GF12","bits":12,"s_bits":1,"e_bits":4,"m_bits":7,"bias":7,"bias_formula":"7","phi_distance":0.047,"storage":"u16","cluster":"GoldenFloat","status":"Verified","standard":"this work; L0/F3","use_case":"mid-range / audio","gf_relation":"self","source":"BENCH-007 (specs/numeric/gf12.t27)"}
+{"id":"gf16","name":"GF16","bits":16,"s_bits":1,"e_bits":6,"m_bits":9,"bias":31,"bias_formula":"31","phi_distance":0.049,"storage":"u16","cluster":"GoldenFloat","status":"Verified","standard":"this work; PHI_BIAS=60; FPGA 35/35 at 323 MHz Artix-7","use_case":"training and inference (production)","gf_relation":"self","source":"specs/numeric/gf16.t27; zenodo 10.5281/zenodo.19227877 (HW archive)"}
+{"id":"gf20","name":"GF20","bits":20,"s_bits":1,"e_bits":7,"m_bits":12,"bias":63,"bias_formula":"63","phi_distance":0.035,"storage":"u32","cluster":"GoldenFloat","status":"Experimental","standard":"this work; 17-squared empirical PHI_BIAS=289","use_case":"high-precision edge","gf_relation":"self","source":"specs/numeric/gf20.t27 (spec only)"}
+{"id":"gf24","name":"GF24","bits":24,"s_bits":1,"e_bits":9,"m_bits":14,"bias":255,"bias_formula":"255","phi_distance":0.025,"storage":"u32","cluster":"GoldenFloat","status":"Experimental","standard":"this work; rule e=round(23/phi^2)=9; normative bias=2^(e-1)-1=255; empirical PHI_BIAS=1364 (=L15) OPEN","use_case":"server inference","gf_relation":"self","source":"specs/numeric/gf24.t27 (spec only)"}
+{"id":"gf32","name":"GF32","bits":32,"s_bits":1,"e_bits":12,"m_bits":19,"bias":2047,"bias_formula":"2047","phi_distance":0.014,"storage":"u32","cluster":"GoldenFloat","status":"Verified","standard":"this work; F0 resolved","use_case":"fp32 drop-in","gf_relation":"self","source":"BENCH-012 (specs/numeric/gf32.t27)"}
+{"id":"gf64","name":"GF64","bits":64,"s_bits":1,"e_bits":24,"m_bits":39,"bias":8388607,"bias_formula":"8388607","phi_distance":0.003,"storage":"u64","cluster":"GoldenFloat","status":"Verified","standard":"this work; EXP_MAX - BIAS","use_case":"scientific / double","gf_relation":"self","source":"BENCH-007b (specs/numeric/gf64.t27)"}
+{"id":"gf6","name":"GF6 (rule-derived)","bits":6,"s_bits":1,"e_bits":2,"m_bits":3,"bias":1,"bias_formula":"1","phi_distance":0.049,"storage":"u8_packed","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(5/phi^2)=2; FP6 E2M3 bridge","use_case":"OPEN R&D: bridge GF4-GF8; FP6 E2M3 hint","gf_relation":"experimental","source":"specs/numeric/gf6.t27"}
+{"id":"gf10","name":"GF10 (rule-derived)","bits":10,"s_bits":1,"e_bits":3,"m_bits":6,"bias":3,"bias_formula":"3","phi_distance":0.118,"storage":"u16","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(9/phi^2)=3; bridge GF8-GF12","use_case":"OPEN R&D: tight-precision activations","gf_relation":"experimental","source":"specs/numeric/gf10.t27"}
+{"id":"gf14","name":"GF14 (rule-derived)","bits":14,"s_bits":1,"e_bits":5,"m_bits":8,"bias":15,"bias_formula":"15","phi_distance":0.007,"storage":"u16","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(13/phi^2)=5; bridge GF12-GF16; lowest phi-dist below GF48","use_case":"OPEN R&D: drop-in for fp16 with tighter phi alignment","gf_relation":"experimental","source":"specs/numeric/gf14.t27"}
+{"id":"gf48","name":"GF48 (rule-derived)","bits":48,"s_bits":1,"e_bits":18,"m_bits":29,"bias":131071,"bias_formula":"131071","phi_distance":0.003,"storage":"u64_padded","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(47/phi^2)=18","use_case":"OPEN R&D: between GF32 and GF64; tightest phi-dist of the wide rungs","gf_relation":"experimental","source":"specs/numeric/gf48.t27"}
+{"id":"gf96","name":"GF96 (rule-derived)","bits":96,"s_bits":1,"e_bits":36,"m_bits":59,"bias":34359738367,"bias_formula":"34359738367","phi_distance":0.008,"storage":"u128_padded","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(95/phi^2)=36","use_case":"OPEN R&D: between GF64 and GF128 (phi-aligned extended)","gf_relation":"experimental","source":"specs/numeric/gf96.t27"}
+{"id":"gf128","name":"GF128 (rule-derived)","bits":128,"s_bits":1,"e_bits":49,"m_bits":78,"bias":281474976710655,"bias_formula":"281474976710655","phi_distance":0.01,"storage":"u128","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(127/phi^2)=49 (corrects v1.1 typo e=48)","use_case":"OPEN R&D: phi-aligned binary128 alternative","gf_relation":"experimental","source":"specs/numeric/gf128.t27"}
+{"id":"gf256","name":"GF256 (rule-derived)","bits":256,"s_bits":1,"e_bits":97,"m_bits":158,"bias":79228162514264337593543950335,"bias_formula":"79228162514264337593543950335","phi_distance":0.004,"storage":"u256_software","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(255/phi^2)=97; normative bias=2^96-1","use_case":"OPEN R&D: phi-aligned binary256 alternative","gf_relation":"experimental","source":"specs/numeric/gf256.t27"}
+{"id":"gf512","name":"GF512 (rule-derived)","bits":512,"s_bits":1,"e_bits":195,"m_bits":316,"bias":-2,"bias_formula":"2^194-1","phi_distance":0.0009,"storage":"u512_software","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(511/phi^2)=195","use_case":"OPEN R&D: ultra-wide phi-aligned (extrapolation, no RTL)","gf_relation":"experimental","source":"specs/numeric/gf512.t27"}
+{"id":"gf1024","name":"GF1024 (rule-derived)","bits":1024,"s_bits":1,"e_bits":391,"m_bits":632,"bias":-2,"bias_formula":"2^390-1","phi_distance":0.0006,"storage":"u1024_software","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(1023/phi^2)=391; lowest phi-distance in the ladder","use_case":"OPEN R&D: limit-of-ladder phi alignment (extrapolation, no RTL)","gf_relation":"experimental","source":"specs/numeric/gf1024.t27"}
+{"id":"gf8_bfp","name":"GF8-BFP (block FP atop GF8)","bits":8,"s_bits":1,"e_bits":3,"m_bits":4,"bias":3,"bias_formula":"3","phi_distance":0.132,"storage":"u8_plus_shared_exp","cluster":"GoldenFloat","status":"Experimental","standard":"this work; per-tile shared exponent","use_case":"OPEN R&D: LLM-quantization-friendly GF8","gf_relation":"experimental","source":"section12.5"}
+{"id":"gf_lns_hybrid","name":"GF + LNS hybrid (dual-space)","bits":16,"s_bits":1,"e_bits":6,"m_bits":9,"bias":31,"bias_formula":"31","phi_distance":0.049,"storage":"u16_plus_lns_path","cluster":"GoldenFloat","status":"Experimental","standard":"this work; mul in log-space, accumulate Lucas-closed","use_case":"OPEN R&D: dual-space arithmetic","gf_relation":"experimental","source":"section12.5"}
+{"id":"mxgf6","name":"MXGF6 (microscaling GF6)","bits":6,"s_bits":1,"e_bits":2,"m_bits":3,"bias":1,"bias_formula":"1","phi_distance":0.05,"storage":"u8_packed_plus_e8m0","cluster":"GoldenFloat","status":"Experimental","standard":"this work; OCP MX block + GF6","use_case":"OPEN R&D: phi-aligned MX-6 candidate","gf_relation":"experimental","source":"section12.5"}
+{"id":"mxgf4","name":"MXGF4 (microscaling GF4)","bits":4,"s_bits":1,"e_bits":1,"m_bits":2,"bias":0,"bias_formula":"0","phi_distance":0.118,"storage":"u8_packed_plus_e8m0","cluster":"GoldenFloat","status":"Experimental","standard":"this work; OCP MX block + GF4","use_case":"OPEN R&D: phi-aligned MX-4 candidate","gf_relation":"experimental","source":"section12.5"}
+{"id":"int4","name":"INT4 / UINT4","bits":4,"s_bits":1,"e_bits":0,"m_bits":3,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8_packed","cluster":"IntegerFixed","status":"Verified","standard":"two complement","use_case":"aggressive quantization","gf_relation":"competitor","source":"ISO/IEC 9899"}
+{"id":"int8","name":"INT8 / UINT8","bits":8,"s_bits":1,"e_bits":0,"m_bits":7,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8","cluster":"IntegerFixed","status":"Verified","standard":"two complement","use_case":"INT8 inference, per-channel scale","gf_relation":"competitor","source":"ISO/IEC 9899"}
+{"id":"int16","name":"INT16 / UINT16","bits":16,"s_bits":1,"e_bits":0,"m_bits":15,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u16","cluster":"IntegerFixed","status":"Verified","standard":"two complement","use_case":"DSP, embedded ML","gf_relation":"competitor","source":"ISO/IEC 9899"}
+{"id":"int32","name":"INT32 / UINT32","bits":32,"s_bits":1,"e_bits":0,"m_bits":31,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u32","cluster":"IntegerFixed","status":"Verified","standard":"two complement","use_case":"general CPU integer","gf_relation":"competitor","source":"ISO/IEC 9899"}
+{"id":"int64","name":"INT64 / UINT64","bits":64,"s_bits":1,"e_bits":0,"m_bits":63,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u64","cluster":"IntegerFixed","status":"Verified","standard":"two complement","use_case":"databases, timestamps","gf_relation":"competitor","source":"ISO/IEC 9899"}
+{"id":"int128","name":"INT128 / UINT128","bits":128,"s_bits":1,"e_bits":0,"m_bits":127,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u128","cluster":"IntegerFixed","status":"Verified","standard":"two complement","use_case":"crypto, big-int","gf_relation":"competitor","source":"Rust/Clang u128"}
+{"id":"q_format","name":"Q-format (Qm.n)","bits":0,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"IntegerFixed","status":"Verified","standard":"TI fixed-point","use_case":"audio DSP, fixed-point ML","gf_relation":"orthogonal","source":"TI SPRA704"}
+{"id":"bcd","name":"BCD (binary-coded decimal)","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u4_per_digit","cluster":"IntegerFixed","status":"Historical","standard":"IBM 1959","use_case":"calculators, GAAP","gf_relation":"orthogonal","source":"ISO/IEC 8859"}
+{"id":"ibm_hfp32","name":"IBM HFP (single)","bits":32,"s_bits":1,"e_bits":7,"m_bits":24,"bias":64,"bias_formula":"64","phi_distance":-1.0,"storage":"u32","cluster":"HistoricalVendor","status":"Historical","standard":"IBM System/360 (1964); base-16 exponent","use_case":"legacy mainframe","gf_relation":"orthogonal","source":"IBM POO"}
+{"id":"ibm_hfp64","name":"IBM HFP (double)","bits":64,"s_bits":1,"e_bits":7,"m_bits":56,"bias":64,"bias_formula":"64","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"IBM System/360 (1964)","use_case":"legacy mainframe","gf_relation":"orthogonal","source":"IBM POO"}
+{"id":"ibm_hfp128","name":"IBM HFP (extended)","bits":128,"s_bits":1,"e_bits":7,"m_bits":120,"bias":64,"bias_formula":"64","phi_distance":-1.0,"storage":"u128","cluster":"HistoricalVendor","status":"Historical","standard":"IBM z/Architecture","use_case":"legacy mainframe","gf_relation":"orthogonal","source":"IBM POO"}
+{"id":"ms_mbf32","name":"Microsoft MBF (single)","bits":32,"s_bits":1,"e_bits":8,"m_bits":23,"bias":129,"bias_formula":"129","phi_distance":-1.0,"storage":"u32","cluster":"HistoricalVendor","status":"Historical","standard":"MS BASIC / MS-DOS (pre-IEEE)","use_case":"MS BASIC legacy","gf_relation":"orthogonal","source":"MS-DOS docs"}
+{"id":"ms_mbf64","name":"Microsoft MBF (double)","bits":64,"s_bits":1,"e_bits":8,"m_bits":55,"bias":129,"bias_formula":"129","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"MS BASIC","use_case":"MS BASIC legacy","gf_relation":"orthogonal","source":"MS-DOS docs"}
+{"id":"vax_f","name":"VAX F-float","bits":32,"s_bits":1,"e_bits":8,"m_bits":23,"bias":128,"bias_formula":"128","phi_distance":-1.0,"storage":"u32","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX","use_case":"DEC legacy","gf_relation":"orthogonal","source":"VAX Architecture Reference"}
+{"id":"vax_d","name":"VAX D-float","bits":64,"s_bits":1,"e_bits":8,"m_bits":55,"bias":128,"bias_formula":"128","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX","use_case":"DEC legacy double","gf_relation":"orthogonal","source":"VAX Architecture Reference"}
+{"id":"vax_g","name":"VAX G-float","bits":64,"s_bits":1,"e_bits":11,"m_bits":52,"bias":1024,"bias_formula":"1024","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX (IEEE-like)","use_case":"DEC legacy","gf_relation":"orthogonal","source":"VAX Architecture Reference"}
+{"id":"vax_h","name":"VAX H-float","bits":128,"s_bits":1,"e_bits":15,"m_bits":112,"bias":16384,"bias_formula":"16384","phi_distance":-1.0,"storage":"u128","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX","use_case":"DEC quad","gf_relation":"orthogonal","source":"VAX Architecture Reference"}
+{"id":"cray_float","name":"Cray float","bits":64,"s_bits":1,"e_bits":15,"m_bits":48,"bias":16384,"bias_formula":"16384","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"Cray-1 (1976); no NaN/Inf, unrounded mul","use_case":"Cray legacy","gf_relation":"orthogonal","source":"Cray-1 Hardware Reference"}
+{"id":"minifloat","name":"minifloat (arbitrary E:M, <=16 bits)","bits":0,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"Theoretical","status":"Experimental","standard":"parametric framework","use_case":"design space of GF4/GF8/GF12/GF16","gf_relation":"ally","source":"Higham 1996"}
+{"id":"unum_i","name":"Unum I (tapered + ubound)","bits":0,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"Theoretical","status":"Experimental","standard":"Gustafson 2015 (predecessor to posit)","use_case":"interval arithmetic","gf_relation":"ally","source":"Gustafson 2015 (The End of Error)"}
+{"id":"unum_ii","name":"Unum II (SORN projective)","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"lookup_table","cluster":"Theoretical","status":"Experimental","standard":"Gustafson 2016","use_case":"lookup-table real arithmetic; not GF-comparable","gf_relation":"orthogonal","source":"Gustafson 2016"}
+{"id":"tapered_fp","name":"tapered floating point","bits":0,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"Theoretical","status":"Experimental","standard":"Morris 1971; posit ancestor","use_case":"variable mantissa via regime bits","gf_relation":"ally","source":"Morris 1971 (IEEE TC)"}
+{"id":"block_fp","name":"block floating point (BFP)","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"CompressionTrick","status":"Verified","standard":"Wilkinson 1965; modern revivals","use_case":"per-tile shared exponent","gf_relation":"ally","source":"Darvish-Rouhani 2020"}
+{"id":"shared_exp","name":"shared-exponent formats","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"CompressionTrick","status":"Verified","standard":"generalised BFP","use_case":"LLM quantization","gf_relation":"ally","source":"Darvish-Rouhani 2020"}
+{"id":"per_channel_scale","name":"INT8 with per-channel scale","bits":8,"s_bits":1,"e_bits":0,"m_bits":7,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8_plus_fp32_scale","cluster":"CompressionTrick","status":"Verified","standard":"Jacob 2018 (TFLite)","use_case":"standard quant inference","gf_relation":"competitor","source":"Jacob 2018 (CVPR)"}
+{"id":"stochastic_rounding","name":"stochastic rounding (technique)","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"CompressionTrick","status":"Verified","standard":"Gupta 2015","use_case":"training small networks at low precision","gf_relation":"ally","source":"Gupta 2015 (ICML)"}