Database Index Selectivity / Cardinality Estimator mechanism

Model scope

The exact ambiguity requiring review is whether selectivity means the catalog's uniqueness ratio (distinct_values/total_rows) or standard equality-predicate selectivity (approximately 1/distinct_values under uniform distribution). Rename the current output to uniqueness_ratio or redefine selectivity. Specify the index-usefulness rule, input validation, NULL counting, and zero-input behavior before release.

• The formula selectivity=distinct_values/total_rows is a uniqueness ratio, not the standard equality-predicate selectivity in most database terminology. Under a uniform-distribution assumption, equality selectivity is 1/distinct_values, while estimated rows per equality lookup is total_rows/distinct_values.
• The specification does not define the rule for the required index-usefulness verdict, so that output cannot be computed from the supplied formulas.
• The uniform-distribution assumption is required for estimated rows per value to be meaningful and should be stated as a constraint, including how NULLs and nonuniform values are handled.

Units and conventions

• total_rows and distinct_values are nonnegative integer counts with the same scope and population.
• For valid nonempty data, total_rows must be greater than 0 and distinct_values must be greater than 0.
• For a conventional column, distinct_values must not exceed total_rows; NULL handling must be specified because counting NULL as a distinct value affects both results.
• selectivity as currently named is dimensionless; estimated rows per lookup has units of rows per distinct value.
• The estimated-rows formula assumes uniformly distributed values and an equality lookup.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "total_rows": 1000000,
    "distinct_values": 1000000
  },
  "expected_outputs": {
    "selectivity_ratio": 1,
    "estimated_rows_per_lookup": 1,
    "index_usefulness_verdict": "UNDEFINED_BY_SPEC"
  },
  "working": "selectivity_ratio = distinct_values / total_rows = 1000000 / 1000000 = 1. estimated_rows_per_lookup = total_rows / distinct_values = 1000000 / 1000000 = 1 row per lookup. The index-usefulness verdict has no specified formula or threshold."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The formulas have undefined results when total_rows or distinct_values is zero, and the specification does not state input validation for zero or for distinct_values greater than total_rows. The specification also does not define a threshold or rule for the requested index-usefulness verdict, so that output cannot be reliably produced.

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