docs(whitepaper): Universal Numeric-Format Catalog (≈60 formats) — WAVE-GF-001 reference

[gHashTag]

🌻 docs: Universal Numeric-Format Catalog (≈60 formats)

Anchor: phi² + phi⁻² = 3 · TRINITY · O(1) FOREVER
EPIC: trios#446 — WAVE-GF-001 experiment plan
Companion data: gf_experiment_plan.xlsx — sheets GF Family + R5 Audit

Why

WAVE-GF-001 sweeps the GF Family against the full numeric-format universe — IEEE binary/decimal, ML low-precision (bf16/TF32/FP8/FP6/FP4 OCP MX), Posit/unum III, LNS, INT/UINT, Q-format, BCD, historical (HFP/MBF/VAX/Cray), theoretical (minifloat/Unum I/II/tapered), and quantization tricks. Without a single authoritative catalog the experiment results are unreadable — every comparison would require re-explaining what the competitor actually is.

What

docs/whitepaper.md — new Section 12 (between §11.5 and §13, +257 lines)

12.0 Why this catalog exists · 12.1 Family map (13 clusters, one row each) · 12.2 Full taxonomy (13 sub-tables, ≈60 formats) · 12.3 φ-distance ranking sorted ascending (GFTernary 0.000 → FP8 E5M2 1.882) · 12.4 Position of GF Family in the map (3-axis uniqueness: φ-aligned + integer-backed + Lucas-closed) · 12.5 Open R&D suggested by the catalog · 12.6 Cross-references.

The 13 sub-tables cover:

1. IEEE 754 binary (binary16..binary256)
2. IEEE 754 decimal (decimal32/64/128)
3. Extended (FP80, double-double, quad-double)
4. ML low-precision (bf16, TF32, FP8 E4M3/E5M2, FP6 E3M2/E2M3, FP4 E2M1)
5. Microscaling OCP MX (MXFP8/6/4)
6. Quantization-tuned (NF4, AFP)
7. Posit / unum III (Posit8/16/32/64)
8. LNS
9. GF Family — full audit row (GF4/8/12/16/20/24/32/64/Ternary)
10. Integer / fixed-point (INT/UINT 4..128, Q-format, BCD)
11. Historical (IBM HFP, MBF, VAX F/D/G/H, Cray)
12. Theoretical (minifloat, Unum I/II, tapered)
13. Compression tricks (BFP, shared-exp, stochastic rounding)

docs/whitepaper/gf16_comparison.md — new Section 8 (+110 lines)

16-bit-centric companion: same catalog, narrowed to formats GF16 actually competes with. Adds:

• 8.2 16-bit competitor table sorted by φ-distance (GF16 / DLFloat-6:9 / fp16 / Posit16 / bf16 / INT16 / TF32 / MXFP6).
• 8.3 Why φ-distance predicts trained-network accuracy (4-step physical mechanism linking to BENCH-004b).
• 8.4 / 8.5 Where GF16 is / is not the right answer (decision matrices).
• 8.6 Standardization status (IEEE / OCP / vendor / open).

Notable findings highlighted in the catalog

Rank	Format	φ-distance	Note
1	GFTernary	0.000	Perfect by construction {−φ, 0, +φ}
2	GF64	0.003	24:39 split, near-perfect
3	GF32	0.014	12:19 split
6	GF12	0.047	4:7 split
7	GF16	0.049	Production format
8	FP6 E2M3	0.049	Surprising hit — same φ-distance as GF16 ⇒ unannounced golden cluster at 6 bits, open R&D direction
10	fp16	0.118	α_φ resonance (BENCH-007)
16	bf16	0.525	Empirical reason for catastrophic MNIST failure (BENCH-004b: 87.87% gap from f32)

R5-honest scope

Append-only. No section renamed, no existing claim modified, no benchmark number changed. The new tables draw from:

• gf_experiment_plan.xlsx → GF Family + R5 Audit (BIAS=PASS / φ-dist=PASS for all 8 GF formats)
• whitepaper §1.3 (BENCH-007 empirical φ-distances)
• whitepaper §9.1 (5-row narrative version — this PR expands to 60-row taxonomy)
• public OCP MX 1.0, OCP FP8 1.0, IEEE 754, unum III specs

I-SCOPE

Only docs/whitepaper.md and docs/whitepaper/gf16_comparison.md touched. No code, no Cargo, no Coq theorem.

🌻 phi² + phi⁻² = 3 · TRINITY · LEAD R5-honest