{"ID":3049960,"CreatedAt":"2026-06-04T02:13:16.786527022Z","UpdatedAt":"2026-06-06T15:28:14.12845936Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05017","arxiv_id":"2606.05017","title":"GoldenFloat: A Phi-Derived Static-Split Floating-Point Family from GF4 to GF256 with a Lucas-Exact Integer Identity","abstract":"We present a hardware-oriented description of GoldenFloat (GF), a static-split floating-point family generated by a single closed rule, and three concrete artefacts: (i) an open multi-width RTL generator covering GF4-GF256 with a continuous-integration differential sweep against a correctly-rounded reference; (ii) an integer-backed Lucas-exact accumulator path verified at 500-digit precision for n = 1, ..., 256; and (iii) a GF16 FPGA codec passing a 35-of-35 testbench at 323 MHz on Artix-7 (Xilinx XC7A35T). For each total width N \u003e= 4, the exponent width is e = round((N-1)/phi^2) with fraction f = N-1-e and phi = (1+sqrt(5))/2. The rule reproduces the realised exponent widths of nine formats (9/9) and extends consistently to GF128, GF512, GF1024. The rule is positioned alongside posit, takum, OCP-MX, and the IEEE P3109 multi-width float draft. We make no per-rung accuracy or superiority claim against any of them. The breadth/toolchain-coherence framing is recorded as an open conjecture with a pre-registered falsification path. A falsification ledger (FL-002) records open questions and the experiments that would settle them. An RTL-correctness erratum dated 2026-05-31 is reported; the fabricated TTSKY26b dies carry the defective multiplier portfolio, and the corrected generator is the regeneration baseline.","short_abstract":"We present a hardware-oriented description of GoldenFloat (GF), a static-split floating-point family generated by a single closed rule, and three concrete artefacts: (i) an open multi-width RTL generator covering GF4-GF256 with a continuous-integration differential sweep against a correctly-rounded reference; (ii) an i...","url_abs":"https://arxiv.org/abs/2606.05017","url_pdf":"https://arxiv.org/pdf/2606.05017v1","authors":"[\"Dmitrii Vasiliev\"]","published":"2026-06-03T15:41:16Z","proceeding":"cs.AR","tasks":"[\"cs.AR\",\"cs.MS\"]","methods":"[]","has_code":false}