Working repository for the ARITH 2027 (IEEE Symposium on Computer Arithmetic, 34th edition) submission of the GoldenFloat paper.
Target venue: ARITH 2027 — outside North America, summer 2027 Format: 8 pages two-column IEEE CS Conference, double-blind review Expected paper deadline: ~29 Jan - 5 Feb 2027 (pattern-extrapolated) Status: scaffold and pre-registered protocol, v0.1
arith2027-goldenfloat/
├── PLAN.md # Full submission plan (timeline, decisions, risks)
├── README.md # This file
├── paper/
│ ├── OUTLINE.md # Section-by-section 8-page layout with word counts
│ ├── ANONYMISATION_CHECKLIST.md # Double-blind redaction list (run before every iteration)
│ └── arith2027_paper.tex # LaTeX scaffold in IEEEtran conference class
├── protocol/
│ └── MATCHED_SUBSTRATE_EXPERIMENT.md # Pre-registered head-to-head experiment protocol
└── supplementary/
└── (RTL, conformance vectors, replication scripts to be added)
The paper describes GoldenFloat (GF), a family of floating-point formats whose exponent:mantissa split is generated, for each total width N, by a single closed rule:
e = round((N-1)/phi^2), m = N-1-e
where phi = (1+sqrt(5))/2.
The contribution is three-fold:
- A rule that reproduces nine realised widths (GF4 through GF256) exactly [Verified] and extends consistently to eight further rule-derived rungs: GF6, GF10, GF14, GF48, GF96, GF128 [Conj, no returned silicon] and GF512, GF1024 [Conj, bias > u128, symbolic only].
- A classical integer identity
phi^(2n) + phi^(-2n) = L_(2n)(Lucas numbers), verified symbolically for n = 1..256 and numerically at 500 decimal places. Attribution to Lucas (1878) and Binet — not original to this work. - One hardware artefact — a GF16 codec on Artix-7 FPGA passing a 35-of-35 testbench at 323 MHz — plus a pre-registered matched-substrate head-to-head experiment against posit-16, takum-16, and binary16 on the same board.
Per the goldenfloat-ladder operating rules:
- No uniqueness of base. Phi is not claimed to be the unique algebraic base for a multi-width float family.
- No per-rung superiority. No GF rung is claimed to outperform posit, takum, MX, or LNS on any specific task at matched substrate.
- No silicon validation. No die has been returned from fabrication.
- No software-BPB falsification. Software-stack BPB measurements are insufficient to settle the breadth-as-moat hypothesis on their own — the matched-substrate experiment is required.
The breadth-as-moat hypothesis is [Open-conjecture] with an explicit F1/F2/F3 falsification path; see protocol/MATCHED_SUBSTRATE_EXPERIMENT.md.
Takum (Hunhold, arXiv:2412.20273; Hunhold and Gustafson, arXiv:2504.21197, arXiv:2504.21130) is the closest live alternative with peer-reviewed multi-width hardware. Takum is cited as an ally, not a defeated competitor. The matched-substrate experiment in protocol/MATCHED_SUBSTRATE_EXPERIMENT.md uses an open-source takum-16 RTL as one of the four reference implementations.
This work is independent of:
- Foundations of Physics manuscript (phi-structured physical constants, different track, different authorship).
- IGLA RACE training architecture (machine-learning training pipeline, different track).
- Any DARPA / CLARA programme submission (separate document, not a basis for any claim made here).
- All visa-track and immigration-track correspondence.
The paper stands on computer-arithmetic content alone: rule, identity, measurement.
cd paper/
pdflatex arith2027_paper.tex
bibtex arith2027_paper # if a .bib file is added later
pdflatex arith2027_paper.tex
pdflatex arith2027_paper.texThe scaffold is currently a skeleton with % PLACEHOLDER comments marking each subsection. Content is filled in iteratively from gf_preprint-2.pdf (the 32-page research-note version on arXiv cs.AR) following the page budget in paper/OUTLINE.md.
Before every submission iteration, run the checks in paper/ANONYMISATION_CHECKLIST.md. The reviewer-facing PDF must contain no author name, no email, no ORCID, no affiliation, no first-person repository identifiers, and no identifying URLs.
A single missed identifier is a desk-reject risk under ARITH double-blind policy.
Every section of the paper must satisfy the goldenfloat-ladder operating rules:
- Claim-status labels [Verified] / [Open] / [Open-conjecture] / [Retracted] visible in body text.
- No banned words: no "breakthrough", "revolutionary", "first-ever", "world-first", "industry-leading", "Nobel".
- ASCII-only headers and body where feasible.
- All raw data, RTL sources, conversion oracles, and synthesis reports published with the supplementary materials at camera-ready.
goldenfloat-ladderskill — normative rules for claim status, breadth-as-moat, FL-002 ledger discipline.quantization-research-canonskill — literature canon and SOTA positioning.task-status-boardskill — priority queue including this thread (3-bis).
These are user-side operating rules; they do not appear in the public paper.
Source files in this repository are released under MIT (planned, to be confirmed before any external visibility of identifying information). The reviewer-facing PDF is submitted to ARITH 2027 under IEEE copyright terms upon acceptance.
| Milestone | Target | Status |
|---|---|---|
| Submission plan v0.1 | 01 Jun 2026 | Done |
| Paper outline v0.1 | 01 Jun 2026 | Done |
| Anonymisation checklist v0.1 | 01 Jun 2026 | Done |
| Matched-substrate protocol v0.1 | 01 Jun 2026 | Done |
| LaTeX scaffold v0.1 | 01 Jun 2026 | Done |
| Stand up reference RTL builds | 30 Jul 2026 | Pending |
| Testbench harness | 15 Aug 2026 | Pending |
| First synthesis runs | 30 Sep 2026 | Pending |
| Data audit | 15 Oct 2026 | Pending |
| Internal full-paper draft | 30 Nov 2026 | Pending |
| Final reviewer-facing PDF | 15 Jan 2027 | Pending |
| ARITH 2027 submission | ~29 Jan - 5 Feb 2027 | Pending |