Bloom Filter Sizing Calculator mechanism

Model scope

Core sizing formulas are correct under the stated ideal assumptions, but the instrument is not fully specified. Exact ambiguity: the claimed actual false-positive-rate output has no formula, and neither m nor k has a defined integer-rounding policy. Verdict remains NEEDS_REVIEW until those behaviors and input constraints are documented.

• The formulas are standard for the continuous, ideal Bloom-filter optimum: m=-(n·ln(p))/(ln(2)^2) and k=(m/n)·ln(2).
• m is generally non-integer but the output claims a bit-array size; the specification does not define whether m is rounded, floored, or ceiled.
• k is generally non-integer but the output claims a hash-function count; the specification does not define whether k is rounded, ceiled, or constrained to at least 1.
• The specification claims an actual false-positive-rate output but provides no formula for it. The standard model formula is FPR=(1-exp(-k·n/m))^k, subject to integer m and k and independent uniform hashing assumptions.

Units and conventions

• n is a positive item count, dimensionless and normally an integer.
• p is a dimensionless probability supplied as a fraction strictly between 0 and 1, not as a percentage; for example, 1% must be entered as 0.01.
• m is measured in bits.
• k is a dimensionless count of hash functions.
• ln denotes the natural logarithm.
• The test vectors below use the continuous formulas without integer rounding; their ideal-model false-positive rate therefore equals the target p.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "n": 1000,
    "p": 0.01
  },
  "expected_outputs": {
    "m": 9585.058377,
    "k": 6.64385619,
    "actual_false_positive_rate": 0.01
  },
  "working": "ln(0.01)=-4.605170186; ln(2)^2=0.480453014. m=-(1000×-4.605170186)/0.480453014=4605.170186/0.480453014=9585.058377 bits. k=(9585.058377/1000)×0.693147181=6.64385619. Ideal FPR=(1-exp(-(6.64385619×1000)/9585.058377))^6.64385619=(1-exp(-0.693147181))^6.64385619=(1-0.5)^6.64385619=0.5^6.64385619=0.01."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification permits boundary and zero-item inputs for which k or the actual false-positive rate is undefined, and it does not state whether p is a fraction or a percentage. A plain arithmetic implementation that lacks validation or an explicit unit convention can return misleading zeroes, NaN, or degenerate results.

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-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json