{
  "schema": "szl.lambda/v1.vectors",
  "spec": "spec/szl.lambda.v1.json",
  "float_encoding": "Every float is \"f64:<16 lowercase hex digits of the IEEE-754 binary64 bits, big-endian>\"; the *_decimal fields are Python repr() for humans. A JSON value that is not an f64 string (true, null, another string, an integer) is passed to the implementation unchanged.",
  "expect": "value_f64 or error describes lambda_v1(axes, weights); verdict and code describe gate_v1(axes, weights, tau).",
  "value_tol": "Absolute tolerance on Λ for implementations other than reference/szl_lambda_v1.py, which must match value_f64 bit for bit. Error codes and verdicts are always exact.",
  "vectors": [
    {
      "id": "nominal",
      "source": "szl-math-core.md §3 differential table (nominal)",
      "axes": ["f64:3fee666666666666", "f64:3fed70a3d70a3d71", "f64:3fec28f5c28f5c29", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.95", "0.92", "0.88", "0.9"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fed3035e27f23fe", "value_decimal": "0.9121350692522581", "verdict": "GO", "code": null}
    },
    {
      "id": "hidden_weak",
      "source": "szl-math-core.md §3 differential table (hidden_weak); admit contract hidden_weak_lock gm 0.7653",
      "note": "the arithmetic mean 0.8125 would pass tau 0.8; the geometric mean does not",
      "axes": ["f64:3fee666666666666", "f64:3fee666666666666", "f64:3fee666666666666", "f64:3fd999999999999a"],
      "axes_decimal": ["0.95", "0.95", "0.95", "0.4"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe87cfdb14e60f2", "value_decimal": "0.7652576888094968", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "hidden_weak_permuted",
      "source": "szl.lambda/v1 domain: a permutation of hidden_weak gives identical bits (fsum)",
      "axes": ["f64:3fd999999999999a", "f64:3fee666666666666", "f64:3fee666666666666", "f64:3fee666666666666"],
      "axes_decimal": ["0.4", "0.95", "0.95", "0.95"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe87cfdb14e60f2", "value_decimal": "0.7652576888094968", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "x_gt_1",
      "source": "szl-math-core.md §3 differential table (x>1 [1.5, .9])",
      "note": "torch and the legacy Python source clamp to 0.948683; szl-formulas and szl-khipu return 1.1619",
      "axes": ["f64:3ff8000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["1.5", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_AXIS_OUT_OF_RANGE"}
    },
    {
      "id": "nan_axis",
      "source": "szl-math-core.md §3 differential table (NaN axis)",
      "axes": ["f64:7ff8000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["nan", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "pos_inf_axis",
      "source": "szl-math-core.md §3 differential table (+Inf axis)",
      "note": "the legacy Python source treats +Inf as 1 (0.948683)",
      "axes": ["f64:7ff0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["inf", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "neg_inf_axis",
      "source": "szl-math-core.md §3 differential table (-Inf axis)",
      "axes": ["f64:fff0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["-inf", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "negative_axis",
      "source": "szl-math-core.md §3 differential table (negative axis)",
      "axes": ["f64:bfb999999999999a", "f64:3feccccccccccccd"],
      "axes_decimal": ["-0.1", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_AXIS_OUT_OF_RANGE"}
    },
    {
      "id": "zero_axis",
      "source": "szl-math-core.md §3 differential table (zero axis)",
      "note": "a veto, not an error: log Λ = -inf gives NO_GO",
      "axes": ["f64:0000000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.0", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:0000000000000000", "value_decimal": "0.0", "verdict": "NO_GO", "code": "ZERO_VETO"}
    },
    {
      "id": "negative_zero_axis",
      "source": "szl.lambda/v1 domain: -0.0 is a zero axis",
      "axes": ["f64:8000000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["-0.0", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:0000000000000000", "value_decimal": "0.0", "verdict": "NO_GO", "code": "ZERO_VETO"}
    },
    {
      "id": "zero_axis_min_subnormal_tau",
      "source": "szl.lambda/v1 domain: the zero-axis veto holds for every valid tau",
      "axes": ["f64:0000000000000000", "f64:3ff0000000000000"],
      "axes_decimal": ["0.0", "1.0"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:0000000000000001",
      "tau_decimal": "5e-324",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:0000000000000000", "value_decimal": "0.0", "verdict": "NO_GO", "code": "ZERO_VETO"}
    },
    {
      "id": "w_unnormalised_2_2",
      "source": "szl-math-core.md §3 differential table (unnormalised w=[2,2] on [.81,.64])",
      "note": "never renormalised (torch returns 0.72)",
      "axes": ["f64:3fe9eb851eb851ec", "f64:3fe47ae147ae147b"],
      "axes_decimal": ["0.81", "0.64"],
      "weights": ["f64:4000000000000000", "f64:4000000000000000"],
      "weights_decimal": ["2.0", "2.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_WEIGHT_SUM", "verdict": "BLOCK", "code": "LAMBDA_WEIGHT_SUM"}
    },
    {
      "id": "w_zero_weight",
      "source": "szl-math-core.md §3 differential table (zero weight w=[1,0] on [.5,.9])",
      "axes": ["f64:3fe0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.5", "0.9"],
      "weights": ["f64:3ff0000000000000", "f64:0000000000000000"],
      "weights_decimal": ["1.0", "0.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_WEIGHT_NONPOSITIVE", "verdict": "BLOCK", "code": "LAMBDA_WEIGHT_NONPOSITIVE"}
    },
    {
      "id": "empty",
      "source": "szl-math-core.md §3 differential table (empty)",
      "note": "never 0.0",
      "axes": [],
      "axes_decimal": [],
      "weights": [],
      "weights_decimal": [],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_EMPTY", "verdict": "BLOCK", "code": "LAMBDA_EMPTY"}
    },
    {
      "id": "empty_axes_nonempty_weights",
      "source": "szl.lambda/v1 domain: empty axes",
      "axes": [],
      "axes_decimal": [],
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_EMPTY", "verdict": "BLOCK", "code": "LAMBDA_EMPTY"}
    },
    {
      "id": "e5_round_4dp_not_a_pass",
      "source": "FUSION_BRIEF.md E5 (4-dp rounding before the compare)",
      "note": "round(Λ, 4) = 0.65 would pass tau 0.65; the unrounded Λ is below it",
      "axes": ["f64:3fe4cc660a201472"],
      "axes_decimal": ["0.649951"],
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe4cccccccccccd",
      "tau_decimal": "0.65",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe4cc660a201472", "value_decimal": "0.649951", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "e5_dropped_axis_present",
      "source": "FUSION_BRIEF.md E5 (triage weights, integrity = 0.1 present)",
      "note": "weights from szl-typesafe-triage src/szl_triage/data/triage_policy.v3.json",
      "axes": ["f64:3feb26e978d4fdf4", "f64:3feb26e978d4fdf4", "f64:3fb999999999999a", "f64:3feb26e978d4fdf4"],
      "axes_decimal": ["0.8485", "0.8485", "0.1", "0.8485"],
      "weights": ["f64:3fd0000000000000", "f64:3fd999999999999a", "f64:3fc999999999999a", "f64:3fc3333333333333"],
      "weights_decimal": ["0.25", "0.4", "0.2", "0.15"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe1b4397d7da1fc", "value_decimal": "0.5532500697127598", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "e5_dropped_axis_renormalised",
      "source": "FUSION_BRIEF.md E5 (integrity axis dropped)",
      "note": "renormalising over the present axes would give 0.8485",
      "axes": ["f64:3feb26e978d4fdf4", "f64:3feb26e978d4fdf4", "f64:3feb26e978d4fdf4"],
      "axes_decimal": ["0.8485", "0.8485", "0.8485"],
      "weights": ["f64:3fd0000000000000", "f64:3fd999999999999a", "f64:3fc999999999999a", "f64:3fc3333333333333"],
      "weights_decimal": ["0.25", "0.4", "0.2", "0.15"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_LENGTH_MISMATCH", "verdict": "BLOCK", "code": "LAMBDA_LENGTH_MISMATCH"}
    },
    {
      "id": "e5_negative_weight",
      "source": "FUSION_BRIEF.md E5 (w = (1.5, -0.5) breaks monotonicity)",
      "note": "the weights sum to 1; szl-formulas accepts them and returns 0.3727",
      "axes": ["f64:3fe0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.5", "0.9"],
      "weights": ["f64:3ff8000000000000", "f64:bfe0000000000000"],
      "weights_decimal": ["1.5", "-0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_WEIGHT_NONPOSITIVE", "verdict": "BLOCK", "code": "LAMBDA_WEIGHT_NONPOSITIVE"}
    },
    {
      "id": "length_mismatch_extra_weight",
      "source": "szl.lambda/v1 domain: more weights than axes",
      "axes": ["f64:3feccccccccccccd"],
      "axes_decimal": ["0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_LENGTH_MISMATCH", "verdict": "BLOCK", "code": "LAMBDA_LENGTH_MISMATCH"}
    },
    {
      "id": "tie_exact",
      "source": "INVENTION.md §2.3 tie band (TIE_EPS = 1e-9, log space)",
      "axes": ["f64:3fe999999999999a"],
      "axes_decimal": ["0.8"],
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe999999999999a", "value_decimal": "0.8", "verdict": "ABSTAIN", "code": "NUMERIC_TIE"}
    },
    {
      "id": "tie_inside_above",
      "source": "INVENTION.md §2.3 tie band (TIE_EPS = 1e-9, log space): log Λ - log tau ≈ +5e-10",
      "axes": ["f64:3fe9999999d0935a"],
      "axes_decimal": ["0.8000000004000001"],
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe9999999d0935a", "value_decimal": "0.8000000004000001", "verdict": "ABSTAIN", "code": "NUMERIC_TIE"}
    },
    {
      "id": "tie_inside_below",
      "source": "INVENTION.md §2.3 tie band (TIE_EPS = 1e-9, log space): log Λ - log tau ≈ -5e-10",
      "axes": ["f64:3fe9999999629fda"],
      "axes_decimal": ["0.7999999996"],
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe9999999629fda", "value_decimal": "0.7999999996", "verdict": "ABSTAIN", "code": "NUMERIC_TIE"}
    },
    {
      "id": "tie_outside_above",
      "source": "INVENTION.md §2.3 tie band (TIE_EPS = 1e-9, log space): log Λ - log tau ≈ +2e-9",
      "axes": ["f64:3fe999999a758098"],
      "axes_decimal": ["0.8000000016"],
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe999999a758098", "value_decimal": "0.8000000016", "verdict": "GO", "code": null}
    },
    {
      "id": "tie_outside_below",
      "source": "INVENTION.md §2.3 tie band (TIE_EPS = 1e-9, log space): log Λ - log tau ≈ -2e-9",
      "axes": ["f64:3fe9999998bdb29b"],
      "axes_decimal": ["0.7999999984"],
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe9999998bdb29b", "value_decimal": "0.7999999984", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "tie_multi_axis_at_own_value",
      "source": "INVENTION.md §2.3 tie band (TIE_EPS = 1e-9, log space): hidden_weak against tau = its own Λ",
      "axes": ["f64:3fee666666666666", "f64:3fee666666666666", "f64:3fee666666666666", "f64:3fd999999999999a"],
      "axes_decimal": ["0.95", "0.95", "0.95", "0.4"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:3fe87cfdb14e60f2",
      "tau_decimal": "0.7652576888094968",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe87cfdb14e60f2", "value_decimal": "0.7652576888094968", "verdict": "ABSTAIN", "code": "NUMERIC_TIE"}
    },
    {
      "id": "all_ones_thirds",
      "source": "szl.lambda/v1 domain: weights 1/3 each (fsum within 1e-12 of 1)",
      "axes": ["f64:3ff0000000000000", "f64:3ff0000000000000", "f64:3ff0000000000000"],
      "axes_decimal": ["1.0", "1.0", "1.0"],
      "weights": ["f64:3fd5555555555555", "f64:3fd5555555555555", "f64:3fd5555555555555"],
      "weights_decimal": ["0.3333333333333333", "0.3333333333333333", "0.3333333333333333"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3ff0000000000000", "value_decimal": "1.0", "verdict": "GO", "code": null}
    },
    {
      "id": "int_axes_accepted",
      "source": "szl.lambda/v1 type contract: integers are real numbers",
      "axes": [1, 1],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3ff0000000000000", "value_decimal": "1.0", "verdict": "GO", "code": null}
    },
    {
      "id": "subnormal_axis",
      "source": "szl.lambda/v1 domain: the smallest positive axis is not a zero axis",
      "axes": ["f64:0000000000000001", "f64:3ff0000000000000"],
      "axes_decimal": ["5e-324", "1.0"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:1e60000000000064", "value_decimal": "2.222758749485127e-162", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "weight_sum_within_tol",
      "source": "szl.lambda/v1 domain: |fsum(w) - 1| = 4e-13 <= 1e-12",
      "axes": ["f64:3feccccccccccccd", "f64:3fe0000000000000"],
      "axes_decimal": ["0.9", "0.5"],
      "weights": ["f64:3fe0000000000e13", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5000000000004", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fe5775c544ff164", "value_decimal": "0.6708203932499086", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "weight_sum_outside_tol",
      "source": "szl.lambda/v1 domain: |fsum(w) - 1| = 3e-12 > 1e-12",
      "axes": ["f64:3feccccccccccccd", "f64:3fe0000000000000"],
      "axes_decimal": ["0.9", "0.5"],
      "weights": ["f64:3fe000000000698e", "f64:3fe0000000000000"],
      "weights_decimal": ["0.500000000003", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_WEIGHT_SUM", "verdict": "BLOCK", "code": "LAMBDA_WEIGHT_SUM"}
    },
    {
      "id": "weight_nan",
      "source": "szl.lambda/v1 domain: NaN weight",
      "axes": ["f64:3fe0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.5", "0.9"],
      "weights": ["f64:7ff8000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["nan", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_WEIGHT", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_WEIGHT"}
    },
    {
      "id": "weight_pos_inf",
      "source": "szl.lambda/v1 domain: +Inf weight",
      "axes": ["f64:3fe0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.5", "0.9"],
      "weights": ["f64:7ff0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["inf", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_WEIGHT", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_WEIGHT"}
    },
    {
      "id": "weight_neg_inf",
      "source": "szl.lambda/v1 domain: -Inf weight",
      "axes": ["f64:3fe0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.5", "0.9"],
      "weights": ["f64:fff0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["-inf", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_WEIGHT", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_WEIGHT"}
    },
    {
      "id": "precedence_nonfinite_before_range_a",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant)",
      "axes": ["f64:3ff8000000000000", "f64:7ff8000000000000"],
      "axes_decimal": ["1.5", "nan"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "precedence_nonfinite_before_range_b",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant)",
      "axes": ["f64:7ff8000000000000", "f64:3ff8000000000000"],
      "axes_decimal": ["nan", "1.5"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "precedence_axis_before_weight",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant)",
      "axes": ["f64:3ff8000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["1.5", "0.9"],
      "weights": ["f64:4000000000000000", "f64:4000000000000000"],
      "weights_decimal": ["2.0", "2.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_AXIS_OUT_OF_RANGE"}
    },
    {
      "id": "precedence_zero_does_not_mask_nan_a",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:0000000000000000", "f64:7ff8000000000000"],
      "axes_decimal": ["0.0", "nan"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "precedence_zero_does_not_mask_nan_b",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:7ff8000000000000", "f64:0000000000000000"],
      "axes_decimal": ["nan", "0.0"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "precedence_zero_does_not_mask_pos_inf_a",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:0000000000000000", "f64:7ff0000000000000"],
      "axes_decimal": ["0.0", "inf"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "precedence_zero_does_not_mask_pos_inf_b",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:7ff0000000000000", "f64:0000000000000000"],
      "axes_decimal": ["inf", "0.0"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_NONFINITE_AXIS", "verdict": "BLOCK", "code": "LAMBDA_NONFINITE_AXIS"}
    },
    {
      "id": "precedence_zero_does_not_mask_x_gt_1_a",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:0000000000000000", "f64:3ff8000000000000"],
      "axes_decimal": ["0.0", "1.5"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_AXIS_OUT_OF_RANGE"}
    },
    {
      "id": "precedence_zero_does_not_mask_x_gt_1_b",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:3ff8000000000000", "f64:0000000000000000"],
      "axes_decimal": ["1.5", "0.0"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_AXIS_OUT_OF_RANGE"}
    },
    {
      "id": "precedence_zero_does_not_mask_negative_a",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:0000000000000000", "f64:bfb999999999999a"],
      "axes_decimal": ["0.0", "-0.1"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_AXIS_OUT_OF_RANGE"}
    },
    {
      "id": "precedence_zero_does_not_mask_negative_b",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:bfb999999999999a", "f64:0000000000000000"],
      "axes_decimal": ["-0.1", "0.0"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_AXIS_OUT_OF_RANGE"}
    },
    {
      "id": "precedence_zero_does_not_mask_bool_a",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": ["f64:0000000000000000", true],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_TYPE_INVALID", "verdict": "BLOCK", "code": "LAMBDA_TYPE_INVALID"}
    },
    {
      "id": "precedence_zero_does_not_mask_bool_b",
      "source": "szl.lambda/v1 error precedence (phases, permutation-invariant): every axis is validated before the zero veto (szl-receipt#38, FF-03b)",
      "axes": [true, "f64:0000000000000000"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe0000000000000",
      "tau_decimal": "0.5",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_TYPE_INVALID", "verdict": "BLOCK", "code": "LAMBDA_TYPE_INVALID"}
    },
    {
      "id": "type_bool_axis",
      "source": "szl.lambda/v1 type contract: bool is not a number",
      "axes": [true, "f64:3feccccccccccccd"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_TYPE_INVALID", "verdict": "BLOCK", "code": "LAMBDA_TYPE_INVALID"}
    },
    {
      "id": "type_null_axis",
      "source": "szl.lambda/v1 type contract: null axis",
      "axes": [null, "f64:3feccccccccccccd"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_TYPE_INVALID", "verdict": "BLOCK", "code": "LAMBDA_TYPE_INVALID"}
    },
    {
      "id": "type_string_axis",
      "source": "szl.lambda/v1 type contract: a string is not a number",
      "axes": ["0.9", "f64:3feccccccccccccd"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_TYPE_INVALID", "verdict": "BLOCK", "code": "LAMBDA_TYPE_INVALID"}
    },
    {
      "id": "type_axes_not_array",
      "source": "szl.lambda/v1 type contract: axes must be an array",
      "axes": null,
      "weights": ["f64:3ff0000000000000"],
      "weights_decimal": ["1.0"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_TYPE_INVALID", "verdict": "BLOCK", "code": "LAMBDA_TYPE_INVALID"}
    },
    {
      "id": "type_bool_weight",
      "source": "szl.lambda/v1 type contract: bool weight",
      "note": "the element type is checked before the weight value",
      "axes": ["f64:3fe0000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.5", "0.9"],
      "weights": [true, "f64:0000000000000000"],
      "tau": "f64:3fe999999999999a",
      "tau_decimal": "0.8",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_TYPE_INVALID", "verdict": "BLOCK", "code": "LAMBDA_TYPE_INVALID"}
    },
    {
      "id": "tau_one",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first",
      "axes": ["f64:3fee666666666666", "f64:3fed70a3d70a3d71", "f64:3fec28f5c28f5c29", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.95", "0.92", "0.88", "0.9"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:3ff0000000000000",
      "tau_decimal": "1.0",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fed3035e27f23fe", "value_decimal": "0.9121350692522581", "verdict": "NO_GO", "code": "BELOW_TAU"}
    },
    {
      "id": "tau_nan",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first",
      "axes": ["f64:3fee666666666666", "f64:3fed70a3d70a3d71", "f64:3fec28f5c28f5c29", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.95", "0.92", "0.88", "0.9"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:7ff8000000000000",
      "tau_decimal": "nan",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fed3035e27f23fe", "value_decimal": "0.9121350692522581", "verdict": "BLOCK", "code": "LAMBDA_TAU_INVALID"}
    },
    {
      "id": "tau_zero_would_admit_veto",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first: tau 0 would pass a vetoed Λ = 0",
      "axes": ["f64:0000000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.0", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:0000000000000000",
      "tau_decimal": "0.0",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:0000000000000000", "value_decimal": "0.0", "verdict": "BLOCK", "code": "LAMBDA_TAU_INVALID"}
    },
    {
      "id": "tau_above_one",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first",
      "axes": ["f64:3fee666666666666", "f64:3fed70a3d70a3d71", "f64:3fec28f5c28f5c29", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.95", "0.92", "0.88", "0.9"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:3ff8000000000000",
      "tau_decimal": "1.5",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fed3035e27f23fe", "value_decimal": "0.9121350692522581", "verdict": "BLOCK", "code": "LAMBDA_TAU_INVALID"}
    },
    {
      "id": "tau_negative",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first",
      "axes": ["f64:3fee666666666666", "f64:3fed70a3d70a3d71", "f64:3fec28f5c28f5c29", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.95", "0.92", "0.88", "0.9"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": "f64:bfb999999999999a",
      "tau_decimal": "-0.1",
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fed3035e27f23fe", "value_decimal": "0.9121350692522581", "verdict": "BLOCK", "code": "LAMBDA_TAU_INVALID"}
    },
    {
      "id": "tau_bool",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first: bool is not a number",
      "axes": ["f64:3fee666666666666", "f64:3fed70a3d70a3d71", "f64:3fec28f5c28f5c29", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.95", "0.92", "0.88", "0.9"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": true,
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fed3035e27f23fe", "value_decimal": "0.9121350692522581", "verdict": "BLOCK", "code": "LAMBDA_TAU_INVALID"}
    },
    {
      "id": "tau_null",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first: tau is required",
      "axes": ["f64:3fee666666666666", "f64:3fed70a3d70a3d71", "f64:3fec28f5c28f5c29", "f64:3feccccccccccccd"],
      "axes_decimal": ["0.95", "0.92", "0.88", "0.9"],
      "weights": ["f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000", "f64:3fd0000000000000"],
      "weights_decimal": ["0.25", "0.25", "0.25", "0.25"],
      "tau": null,
      "value_tol": 1e-12,
      "expect": {"value_f64": "f64:3fed3035e27f23fe", "value_decimal": "0.9121350692522581", "verdict": "BLOCK", "code": "LAMBDA_TAU_INVALID"}
    },
    {
      "id": "tau_precedes_axis_error",
      "source": "szl.lambda/v1 tau domain (0, 1], required, checked first: tau is checked before Λ",
      "axes": ["f64:3ff8000000000000", "f64:3feccccccccccccd"],
      "axes_decimal": ["1.5", "0.9"],
      "weights": ["f64:3fe0000000000000", "f64:3fe0000000000000"],
      "weights_decimal": ["0.5", "0.5"],
      "tau": "f64:7ff8000000000000",
      "tau_decimal": "nan",
      "value_tol": 1e-12,
      "expect": {"error": "LAMBDA_AXIS_OUT_OF_RANGE", "verdict": "BLOCK", "code": "LAMBDA_TAU_INVALID"}
    }
  ]
}