Ring 041: GoldenFloat arXiv paper draft — phi-distance metric formal definition

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Ring 041: GoldenFloat arXiv Paper Draft

Phase: HARDEN | Layer: RESEARCH | Parent: #126

Problem

GF16's phi-distance advantage over bfloat16 and takum is currently only asserted in specs. Without a peer-reviewed arXiv paper, the academic community cannot validate or cite this claim. DARPA CLARA peer reviewers will require published evidence.

Goal

Create research/gf16_arxiv_draft.md containing the formal paper draft: abstract, phi-distance definition, benchmark methodology, related work (posit, takum, bfloat16), and expected results structure.

Formal content

Title: GoldenFloat: Phi-Structured Floating-Point Arithmetic for Neural Networks

Abstract: We introduce GoldenFloat (GF), a family of floating-point formats
where exp/mant ~ 1/phi minimizes phi-distance for neural network weight
distributions. We formally define phi-distance, prove its minimization
under GoldenFloat encoding, and benchmark GF16 against bfloat16, float16,
and takum-16 on MNIST and CIFAR-10.

Key formula:
  d_phi(e, m) = |e/m - 1/phi|
  GF16 achieves d_phi = 0.049 vs float16 d_phi = 0.118

Specs to create

• research/gf16_arxiv_draft.md
• research/benchmark_protocol.md

Acceptance criteria

• Draft contains: abstract, introduction, formal phi-distance definition
• Related work section covers posit, takum, bfloat16
• Benchmark methodology defined (MNIST, CIFAR-10, NMSE metric)
• LaTeX-ready equation formatting
• Target venue: ARITH 2027 or NeurIPS Efficient ML Workshop 2026

Seal requirements

• seal --save research/gf16_arxiv_draft.md

Dependencies

• Ring 034 (Ring 034: GoldenFloat benchmark spec — GF16 vs bfloat16 vs float16 NMSE #129) - GF16 benchmark spec
• Ring 038 (Ring 038: conformance vector schema v2 — add phi_distance and verdict fields #133) - conformance schema v2

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Branch: task/041-arxiv-draft | Commit: docs(ring-041): GoldenFloat arXiv paper draft [SEED-41]