Random Number & Distribution Sampler mechanism

Model scope

The named methods are standard and conceptually appropriate, and the honest-label warning is adequate. However, deterministic behavior cannot be verified from the declared inputs because the custom RNG, seed behavior, inverse-CDF boundary rules, and histogram binning are unspecified. The four vectors therefore use deterministic_uniforms as a conformance-harness input; the implementation specification should either expose an equivalent seeded RNG interface or document that test override explicitly.

• The Box-Muller transform is correctly named, but the specification does not define whether both generated normal values are returned, nor how uniform inputs equal to 0 or 1 are handled. A value of 0 causes log(0), and the implementation must enforce 0 < u1 <= 1 (normally 0 < u1 < 1).
• Inverse-CDF sampling is a standard method, but the specification does not provide the actual inverse-CDF algorithms or boundary convention for uniform values exactly at cumulative-probability boundaries.
• The phrase 'inverse-CDF sampling for others' is underspecified for binomial and Poisson distributions: the implementation must define the PMFs, cumulative summation procedure, and numerical stopping rule.
• The custom RNG is not specified by algorithm, seed interface, or state transition. Without this, sample lists cannot be independently reproduced from only distribution type, parameters, and sample count.
• Histogram generation is underspecified: bin count or edges, interval inclusion rules, handling of values on bin boundaries, and normalization versus raw counts are missing.
• No explicit uniform-distribution formula is given; the standard formula should be x = a + (b - a)u for u in [0,1), with a stated endpoint convention.

Units and conventions

• Distribution parameters are dimensionless unless the caller supplies an external unit; generated values inherit the parameter units.
• Uniform bounds a and b use the same units.
• Normal mu and sigma use the same units, and sigma is a standard deviation, not a variance.
• Binomial n is a dimensionless nonnegative integer and p is a dimensionless probability.
• Poisson lambda is a dimensionless mean count for the sampling interval; changing the interval changes lambda.
• Histogram bin edges use the same units as the sampled values, and the test vector uses raw counts rather than density normalization.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "distribution": "uniform",
    "a": 2,
    "b": 6,
    "sample_count": 2,
    "deterministic_uniforms": [
      0,
      0.75
    ],
    "histogram_edges": [
      2,
      4,
      6
    ],
    "histogram_rule": "[2,4), [4,6]"
  },
  "expected_outputs": {
    "samples": [
      2,
      5
    ],
    "histogram_counts": [
      1,
      1
    ]
  },
  "working": "Use x = a + (b - a)u. For u = 0: x = 2 + (6 - 2)*0 = 2 + 0 = 2. For u = 0.75: x = 2 + (6 - 2)*0.75 = 2 + 4*0.75 = 5. Histogram: sample 2 is in [2,4), so the first count is 1. Sample 5 is in [4,6], so the second count is 1. Therefore samples = [2,5] and histogram_counts = [1,1]. The u = 0 case checks the lower-bound convention."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

An adversarial Box-Muller input u1 = 0 produces an undefined logarithm; the instrument must reject it. Reversed uniform bounds also expose an unresolved convention difference that can change the result from 12.5 to 17.5.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json