{
  "schema": "wolfram_verification_v2",
  "generated_at": "2026-06-30T22:50:11.469446",
  "n_queries": 20,
  "queries": {
    "q16_scale_factor": {
      "query": "65536",
      "result": "65536"
    },
    "q16_mul_identity": {
      "query": "simplify (a * b / 65536) when a = 65536",
      "result": "simplify | a \u00d7 b/65536 where a = 65536"
    },
    "q16_saturation_bounds": {
      "query": "range of int32 signed integer",
      "result": "[no plaintext result]"
    },
    "rossby_dispersion": {
      "query": "omega = -beta * k / (k^2 + l^2) Rossby wave dispersion",
      "result": "[no plaintext result]"
    },
    "kelvin_wave_nondispersive": {
      "query": "omega = k * sqrt(g * H) Kelvin wave",
      "result": "[no plaintext result]"
    },
    "rossby_deformation_radius": {
      "query": "L_D = sqrt(g * H) / f Rossby deformation radius",
      "result": "[no plaintext result]"
    },
    "golden_ratio_conjugate": {
      "query": "solve x^2 - x - 1 = 0",
      "result": "solve x^2 - x - 1 = 0"
    },
    "corkscrew_angle": {
      "query": "2 * pi / ((1 + sqrt(5)) / 2)^2",
      "result": "2 \u00d7 \u03c0/(1/2 (1 + sqrt(5)))^2"
    },
    "fisher_metric_simplex": {
      "query": "arccos(sum sqrt(p_i * q_i))",
      "result": "cos^(-1)( sum sqrt(p_i q_i))"
    },
    "fisher_distance": {
      "query": "2 * arccos(sqrt(p * q)) Fisher distance",
      "result": "2 cos^(-1)(sqrt(p q)) distance | from | near HradecKralove, Kralovehradecky\nto | Fisher, Mobile, United States"
    },
    "cauchy_schwarz_fisher": {
      "query": "sum sqrt(p_i * q_i) <= 1 for probability distributions",
      "result": "sum sqrt(p_i q_i) P(X<=1) where \nX distributed normal distribution | mean | \u03bc = 0\nstandard deviation | \u03c3 = 1"
    },
    "pair_averaging_idempotent": {
      "query": "simplify ((a+b)/2 + (c+d)/2) / 2",
      "result": "simplify | 1/2 ((a + b)/2 + (c + d)/2)"
    },
    "pair_averaging_contractive": {
      "query": "prove |(a+b)/2 - (c+d)/2| < |a-c| + |b-d|",
      "result": "simplify | abs((a + b)/2 - (c + d)/2)<abs(a - c) + abs(b - d)"
    },
    "chaos_game_contraction": {
      "query": "prove (1-eps)^k < 2^(-k) for 0 < eps < 1",
      "result": "simplify | (1 - \u03f5)^k<2^(-k) \u00d7 0<\u03f5<1"
    },
    "nuvmap_eigenmass": {
      "query": "limit lambda * v * S * L / (R + epsilon) as R -> 0",
      "result": "lim_(R->0) (\u03bb v S L)/(R + \u03f5) = (L S v \u03bb)/\u03f5"
    },
    "bekenstein_bound": {
      "query": "A / (4 * L_p^2) Bekenstein bound",
      "result": "[no plaintext result]"
    },
    "eigenvalue_power_iteration": {
      "query": "Rayleigh quotient convergence power iteration",
      "result": "[no plaintext result]"
    },
    "sidon_condition": {
      "query": "powers of 2 pairwise distinct sums",
      "result": "[no plaintext result]"
    },
    "sidon_slack_128": {
      "query": "128 - 2^7 =",
      "result": "128 - 2^7"
    },
    "binary_sidon_max_sum": {
      "query": "max sum of distinct powers of 2 from 1,2,4,...,128",
      "result": "[no plaintext result]"
    }
  },
  "claim_boundary": "wolfram-alpha-algebraic-verification-only",
  "receipt_hash": "a75dda235676ea71"
}