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      "source": "specs/numeric/gf24.t27 (spec only)"
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      "standard": "this work; F0 resolved",
      "use_case": "fp32 drop-in",
      "gf_relation": "self",
      "source": "BENCH-012 (specs/numeric/gf32.t27)"
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      "standard": "this work; EXP_MAX - BIAS",
      "use_case": "scientific / double",
      "gf_relation": "self",
      "source": "BENCH-007b (specs/numeric/gf64.t27)"
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      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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": "gf8_bfp",
      "name": "GF8-BFP (block FP atop GF8)",
      "bits": 8,
      "s_bits": 1,
      "e_bits": 3,
      "m_bits": 4,
      "bias": 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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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,
      "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)"
    }
  ]
}