Bloom Filter Sizing Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Computing & Information

Tranche

tranche-5

Evidence ID

t5-134

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json